## 13.1 – The Curvature

We now know for a fact that the Delta of an option is a variable, as it constantly changes its value relative to the change in the underlying. Let me repost the graph of the delta’s movement here –

If you look at the blue line representing the delta of a call option, it is quite clear that it traverses between 0 and 1 or maybe from 1 to 0 as the situation would demand. Similar observations can be made on the red line representing the put option’s delta (except the value changes between 0 to -1). This graph reemphasizes what we already know i.e the delta is a variable and it changes all the time. Given this, the question that one needs to answer is –

- I know the delta changes, but why should I care about it?
- If the change in delta really matters, how do I estimate the likely change in delta?

We will talk about the 2^{nd} question first as I’m reasonably certain the answer to the first question will reveal itself as we progress through this chapter.

As introduced in the previous chapter, ‘The Gamma’ (2^{nd} order derivative of premium) also referred to as **the curvature of the option** gives the rate at which the option’s delta changes as the underlying changes. The gamma is usually expressed in deltas gained or lost per one point change in the underlying – with the delta increasing by the amount of the gamma when the underlying rises and falling by the amount of the gamma when the underlying falls.

For example consider this –

- Nifty Spot = 8326
- Strike = 8400
- Option type = CE
- Moneyness of Option = Slightly OTM
- Premium = Rs.26/-
- Delta = 0.3
- Gamma = 0.0025
- Change in Spot = 70 points
- New Spot price = 8326 + 70 = 8396
- New Premium =??
- New Delta =??
- New moneyness =??

Let’s figure this out –

- Change in Premium = Delta * change in spot i.e 0.3 * 70 = 21
- New premium = 21 + 26 = 47
- Rate of change of delta = 0.0025 units for every 1 point change in underlying
- Change in delta = Gamma * Change in underlying i.e 0.0025*70 = 0.175
**New Delta = Old Delta + Change in Delta i.e 0.3 + 0.175 = 0.475**- New Moneyness = ATM

When Nifty moves from 8326 to 8396, the 8400 CE premium changed from Rs.26 to Rs.47, and along with this the Delta changed from 0.3 to 0.475.

Notice with the change of 70 points, the option transitions from slightly OTM to ATM option. Which means the option’s delta has to change from 0.3 to somewhere close to 0.5. This is exactly what’s happening here.

Further let us assume Nifty moves up another 70 points from 8396; let us see what happens with the 8400 CE option –

- Old spot = 8396
- New spot value = 8396 + 70 = 8466
- Old Premium = 47
- Old Delta = 0.475
- Change in Premium = 0.475 * 70 = 33.25
- New Premium = 47 + 33.25 = 80.25
- New moneyness = ITM (hence delta should be higher than 0.5)
- Change in delta =0.0025 * 70 = 0.175
- New Delta = 0.475 + 0.175 =
**0.65**

Let’s take this forward a little further, now assume Nifty falls by 50 points, let us see what happens with the 8400 CE option –

- Old spot = 8466
- New spot value = 8466 – 50 = 8416
- Old Premium = 80.25
- Old Delta = 0.65
- Change in Premium = 0.65 *(50) = – 32.5
- New Premium = 80.25 – 32. 5 =
**47.75** - New moneyness = slightly ITM (hence delta should be higher than 0.5)
- Change in delta = 0.0025 * (50) =
**– 0.125** - New Delta = 0.65 – 0.125 =
**0.525**

Notice how well the delta transitions and adheres to the delta value rules we discussed in the earlier chapters. Also, you may wonder why the Gamma value is kept constant in the above examples. Well, in reality the Gamma also changes with the change in the underlying. This change in Gamma due to changes in underlying is captured by 3^{rd} derivative of underlying called “Speed” or “Gamma of Gamma” or “**D**gamma**D**spot”. For all practical purposes, it is not necessary to get into the discussion of Speed, unless you are mathematically inclined or you work for an Investment Bank where the trading book risk can run into several $ Millions.

Unlike the delta, the Gamma is always a positive number for both Call and Put Option. Therefore when a trader is long options (both Calls and Puts) the trader is considered ‘Long Gamma’ and when he is short options (both calls and puts) he is considered ‘Short Gamma’.

For example consider this – The Gamma of an ATM Put option is 0.004, if the underlying moves 10 points, what do you think the new delta is?

Before you proceed I would suggest you spend few minutes to think about the solution for the above.

Here is the solution – Since we are talking about an ATM Put option, the Delta must be around – 0.5. Remember Put options have a –ve Delta. Gamma as you notice is a positive number i.e +0.004. The underlying moves by 10 points without specifying the direction, so let us figure out what happens in both cases.

**Case 1 – Underlying moves up by 10 points**

- Delta = – 0.5
- Gamma = 0.004
- Change in underlying = 10 points
- Change in Delta = Gamma * Change in underlying = 0.004 * 10 = 0.04
- New Delta = We know the Put option loses delta when underlying increases, hence – 0.5 + 0.04 =
**– 0.46**

**Case 2 – Underlying goes down by 10 points**

- Delta = – 0.5
- Gamma = 0.004
- Change in underlying = – 10 points
- Change in Delta = Gamma * Change in underlying = 0.004 * – 10 = – 0.04
- New Delta = We know the Put option gains delta when underlying goes down, hence – 0.5 + (-0.04) =
**– 0.54**

Now, here is trick question for you – In the earlier chapters, we had discussed that the Delta of the Futures contract in always 1, so what do you think the gamma of the Futures contract is? Please leave your answers in the comment box below :).

## 13.2 – Estimating Risk using Gamma

I know there are many traders who define their risk limits while trading. Here is what I mean by a risk limit – for example the trader may have a capital of Rs.300,000/- in his trading account. Margin required for each Nifty Futures is approximately Rs.16,500/-. Do note you can use Zerodha’s **SPAN calculator** to figure out the margin required for any F&O contract. So considering the margin and the M2M margin required, the trader may decide at any point he may not want to exceed holding more than **5 Nifty Futures contracts**, thus defining his risk limits, this seems fair enough and works really well while trading futures.

But does the same logic work while trading options? Let’s figure out if it is the right way to think about risk while trading options.

Here is a situation –

- Number of lots traded = 10 lots (Note – 10 lots of ATM contracts with delta of 0.5 each is equivalent to 5 Futures contract)
- Option = 8400 CE
- Spot = 8405
- Delta = 0.5
- Gamma = 0.005
- Position = Short

The trader is short 10 lots of Nifty 8400 Call Option; this means the trader is within his risk boundary. Recall the discussion we had in the Delta chapter about adding up the delta. We can essentially add up the deltas to get the overall delta of the position. Also each delta of 1 represents 1 lot of the underlying. So we will keep this in perspective and we can figure out the overall position’s delta.

- Delta = 0.5
- Number of lots = 10
- Position Delta = 10 * 0.5 =
**5**

So from the overall delta perspective the trader is within his risk boundary of trading not more than 5 Futures lots. Also, do note since the trader is short options, he is essentially **short gamma**.

The position’s delta of 5 indicates that the trader’s position will move 5 points for every 1 point movement in the underlying.

Now, assume Nifty moves 70 points against him and the trader continues to hold his position, hoping for a recovery. The trader is obviously under the impression that he is holding 10 lots of options which is within his risk appetite…

Let’s do some forensics to figure out behind the scenes changes –

- Delta = 0.5
- Gamma = 0.005
- Change in underlying = 70 points
- Change in Delta = Gamma * change in underlying = 0.005 * 70 = 0.35
- New Delta = 0.5 + 0.35 =
**0.85** - New Position Delta = 0.85*10 =
**8.5**

Do you see the problem here? Although the trader has defined his risk limit of 5 lots, thanks to a high Gamma value, he has overshot his risk limit and now holds positions equivalent to 8.5 lots, way beyond his perceived risk limit. An inexperienced trader can be caught unaware of this and still be under the impression that he is well under his risk radar. But in reality his risk exposure is getting higher.

Now since the delta is 8.5, his overall position is expected to move 8.5 points for every 1 point change in the underlying. For a moment assume the trader is long on the call option instead of being short – obviously he would enjoy the situation here as the market is moving in his favor. Besides the favorable movement in the market, his positions is getting ‘Longer’ since the ‘long gamma’ tends to add up the deltas, and therefore the delta tends to get bigger, which means the rate of change on premium with respect to change in underlying is faster.

Suggest you read that again in small bits if you found it confusing.

But since the trader is short, he is essentially short gamma…this means when the position moves against him (as in the market moves up while he is short) the deltas add up (thanks to gamma) and therefore at every stage of market increase, the delta and gamma gang up against the short option trader, making his position riskier way beyond what the plain eyes can see. Perhaps this is the reason why they say – shorting options carry huge amount of risk. In fact you can be more precise and say “shorting options carries the risk of being short gamma”.

Note – By no means I’m suggesting that you should not short options. In fact a successful trader employs both short and long positions as the situation demands. I’m only suggesting that when you short options you need to be aware of the Greeks and what they can do to your positions.

Also, I’d strongly suggest you avoid shorting option contracts which has a large Gamma.

This leads us to another interesting topic – what is considered as ‘large gamma’.

## 13.3 – Gamma movement

Earlier in the chapter we briefly discussed that the Gamma changes with respect to change in the underlying. This change in Gamma is captured by the 3^{rd} order derivative called ‘Speed’. I won’t get into discussing ‘Speed’ for reasons stated earlier. However we need to know the behavior of Gamma movement so that we can avoid initiating trades with high Gamma. Of course there are other advantages of knowing the behavior of Gamma, we will talk about this at a later stage in this module. But for now we will look into how the Gamma behaves with respect to changes in the underlying.

Have a look at the chart below,

The chart above has 3 different CE strike prices – 80, 100, and 120 and their respective Gamma movement. For example the blue line represents the Gamma of the 80 CE strike price. I would suggest you look at each graph individually to avoid confusion. In fact for sake of simplicity I will only talk about the 80 CE strike option, represented by the blue line.

Let us assume the spot price is at 80, thus making the 80 strike ATM. Keeping this in perspective we can observe the following from the above chart –

- Since the strike under consideration is 80 CE, the option attains ATM status when the spot price equals 80
- Strike values below 80 (65, 70, 75 etc) are ITM and values above 80 (85, 90, 95 etx) are OTM options.
- Notice the gamma value is low for OTM Options (80 and above). This explains why the premium for OTM options don’t change much in terms of absolute point terms, however in % terms the change is higher. For example – the premium of an OTM option can change from Rs.2 to Rs.2.5, while absolute change in is just 50 paisa, the % change is 25%.
- The gamma peaks when the option hits ATM status. This implies that the rate of change of delta is highest when the option is ATM. In other words, ATM options are most sensitive to the changes in the underlying
- Also, since ATM options have highest Gamma –
**avoid shorting ATM options**

- Also, since ATM options have highest Gamma –
- The gamma value is also low for ITM options (80 and below). Hence for a certain change in the underlying, the rate of change of delta for an ITM option is much lesser compared to ATM option. However do remember the ITM option inherently has a high delta. So while ITM delta reacts slowly to the change in underlying (due to low gamma) the change in premium is high (due to high base value of delta).
- You can observe similar Gamma behavior for other strikes i.e 100, and 120. In fact the reason to show different strikes is to showcase the fact that the gamma behaves in the same way for all options strikes

Just in case you found the above discussion bit overwhelming, here are 3 simple points that you can take home –

- Delta changes rapidly for ATM option
- Delta changes slowly for OTM and ITM options
- Never short ATM or ITM option with a hope that they will expire worthless upon expiry
- OTM options are great candidates for short trades assuming you intend to hold these short trades upto expiry wherein you expect the option to expire worthless

## 13.4 – Quick note on Greek interactions

One of the keys to successful options trading is to understand how the individual option Greeks behave under various circumstances. Now besides understanding the individual Greek behavior, one also needs to understand how these individual option Greeks react with each other.

So far we have considered only the premium change with respect to the changes in the spot price. We have not yet discussed time and volatility. Think about the markets and the real time changes that happen. Everything changes – time, volatility, and the underlying price. So an option trader should be in a position to understand these changes and its overall impact on the option premium.

You will fully appreciate this only when you understand the cross interactions of the option Greeks. Typical Greek cross interactions would be – gamma versus time, gamma versus volatility, volatility vs time, time vs delta etc.

Finally all your understanding of the Greeks boils down to a few critical decision making factors such as –

- For the given market circumstances which is the best strike to trade?
- What is your expectation of the premium of that particular strike – would it increase or decrease? Hence would you be a buyer or a seller in that option?
- If you plan to buy an option – is there a realistic chance for the premium to increase?
- If you plan to short an option – is it really safe to do so? Are you able to see risk beyond what the naked eyes can spot?

The answers to all these questions will evolve once you fully understand individual Greeks and their cross interactions.

Given this, here is how this module will develop going further –

- So far we have understood Delta and Gamma
- Over the next few chapters we will understand Theta and Vega
- When we introduce Vega (change in premium with respect to change in volatility) – we will digress slightly to understand volatility based stoploss
- Introduce Greek cross interactions – Gamma vs time, Gamma vs spot, Theta vs Vega, Vega vs Spot etc
- Overview of Black and Scholes option pricing formula
- Option calculator

So as you see, we have miles to walk before we sleep 🙂 .

### Key takeaways from this chapter

- Gamma measures the rate of change of delta
- Gamma is always a positive number for both Calls and Puts
- Large Gamma can translate to large gamma risk (directional risk)
- When you buy options (Calls or Puts) you are long Gamma
- When you short options (Calls or Puts) you are short Gamma
- Avoid shorting options which have large gamma
- Delta changes rapidly for ATM option
- Delta changes slowly for OTM and ITM options

*Special thanks to our good friend Prakash Lekkala for providing the Greek graphs in this and other chapters .*

hi, went through the chapter and found the presentation a little harried than the others. calculations were off the mark and in places no decimal points are incorporated. karthik, were you not involved in this chapter?

Raj, thanks for your feedback…can you please point out the errors, will make the necessary changes?

so what do you think the gamma of the Futures contract is? 😮 ans it pls.

Zero

The gamma of the future contract will be Zero.

Yes Sir.

Hello sir,

Thank you for helping us. Sir my concern is with the Delta vs. Spot curve for put option. As spot value increases the delta also increase.

Case 1 – Underlying moves up by 10 points

Delta = – 0.5

Gamma = 0.004

Change in underlying = 10 points

Change in Delta = Gamma * Change in underlying = 0.004 * 10 = 0.04

New Delta = We know the Put option loses delta when underlying increases, hence – 0.5 + 0.04 = – 0.46

Case 2 – Underlying goes down by 10 points

Delta = – 0.5

Gamma = 0.004

Change in underlying = – 10 points

Change in Delta = Gamma * Change in underlying = 0.004 * – 10 = – 0.04

New Delta = We know the Put option gains delta when underlying goes down, hence – 0.5 + (-0.04) = – 0.54

Kindly pardon me if I have misunderstood something. Please help me in this.

Shakti, thats right. As the underlying decreases, the PE option delta gains in value and as the underlying increases, the PE option delta loses in value.

Thank you sir, just got it. Here negative sign just shows that the if one gains other loses value.

It is really commendable work that you are doing.

My doubt is how is the gamma value arrived at?

Gamma value (in fact delta, theta, and vega) values are all calculated using a mathematical model called “Black & Scholes Options Pricing Model”. We will briefly talk about this in the coming chapters.

Hi kartik.

Very very thanks for this chapter. Although chapter has some minute printing mistakes of decimals and some calculation mistake(which doesn’t matters at all) but it is a very good and clear chapter which boosts my concept about gamma.

I have two questions-

1. In the topic estimating risk using gamma you have given-

New position delta = 0.85*10=25. What is means??? Please clarify

2. Suppose , for any underlying–

Spot price=8000

Strike price=8200

Premium=100

Option type=CE

After sometime,

Spot price 9000

Premium=800

If one square off his position at current price, will his position be square off because deep itm options have very less volume. Is any volume issue occurs???

Futures have gamma=0, since delta is always 1(answer to your question)

Glad you liked it 🙂

New position delta = 0.85*10=25 —–> this is an error it should be New position delta = 0.85*10=8.5

You can square off the position anytime you want…as long as there are volumes (counter party).

You are right on the value of Futures’s Gamma 🙂

So what if there is no volume my position will be still open?? In the meantime if market reverse should I had to cut position in loss??

If there are no volumes, then there is not much you can do. You should cut if you feel the need to and there is sufficient volume to do so.

I think I know today why they say that don’t trade options if you are a novice and blindly buy OTM options with the hope that you’d become rich overnight 🙂

I can appreciate complex mathematics Karthik – Would you suggest any book in particular (preferably by an Indian author who has kept indian indicies and stocks in perspective) for options? I am suddenly getting very interested and I will like to utilize the interval between which the chapters are posted here.

Couple of other generic questions:

1. Does it make sense to trade naked call/put options with say 1 lot nifty or is it just a bad idea altogether?

2. In your practical experience, are there folks who only trade options and nothing else?

3. In your practical experience, is it very difficult to make money with options? Also, what is better? Trading intraday or with 1/2/3 months time frame?

4. This one is really from the heart: While we know a lot of super rich value investors, why do we not hear of any super rich derivative traders? (Please do not take this question otherwise – Being an individual retail investors feels like a closed door with not much authentic information. Since you are hands-on in the field, you’d be the appropriate person to ask)

Really looking ahead!

Saurabh – Options trading is a different animal altogether. One needs to be aware of many different aspects involved. I’m really not sure which book to recommend, I found some of the books that I’ve read previously quite shallow. Maybe I’ve not updated my library so may not be the best person to answer this for you.

Coming to your other questions –

1) No harm trading 1 or 2 lots of naked options – lot size is not much so you don’t risk anything significant. But neither will this create any significant wealth for you. In fact I do this quite often just to test few random ideas.

2) Yes there are many people trading just options – you can trust me on this

3) You certainly can make money trading options – but you need to set your expectations right (ref section 1.3 – http://zerodha.com/varsity/chapter/background/). Trust me if you can consistently make 2% a month trading options you are doing a phenomenal job. Unfortunately most people perceive this a small return and aim for a higher return, in the process blowing up their account. So my take on this – aim for small but CONSISTENT return. Also, I prefer to trade with slightly longer duration than intraday. I avoid intraday because I don’t find the time and commitment it requires.

4) You have a valid point – I agree we all get to read about successful Value Investors but not many derivatives traders. I really dont know why. But this does not mean they dont exist. There are many traders who generate significant amount of money trading derivatives…cant speak on behalf of other brokers but we do have some really good traders with us. We had the opportunity to interview some of them here – https://zerodha.com/z-connect/category/zerodha-60-day-challenge

Good luck and please stay tuned. I can guarantee you that Zerodha will put up everything you need to know about Options trading, just give us a little more time 🙂

Thanks for the inputs Karthik.

Does zerodha provide a virtual trading a/c? It would be of great help if there is. I tried the one on NSE (Pathshala) but don’t get how it is showing my MTM as +ve when I in fact know that it is in the red. A simulated environment would really help!

Saurabh, we do not have a virtual trading platform as of now. But that is certain something we plan to do in the future.

sir what is naked options?

When you buy an option without any hedge, then its referred to as a naked option. All single option positions are naked. For ex : buying a call, buying a put, shorting call etc.

Thanks for the excellent work that you are doing Karthik Sir.

How many chapters have you planned for Options Module?

Not sure how many chapters but there are at least 5-6 major topics that needs to be covered. This may happen over the the next 3-4 chapters (or more).

Sir, why u removed quantitative concepts module?

We have it Keshav. Its just that we decided to include the taxation module we have removed that for time being. Will certainly have a module on that topic.

hi kartik

thanks for clearing doubt.

i like your new pic.

waiting for chapters on vega and theta. when will you upload???

Thanks 🙂

Working on the Theta chapter…should be up by next week!

Thanks for easy explanation on gamma. You had asked about gamma for the future contract. It is having fixed delta, 1 so no change in the delta means gamma of future contract will be zero. Please correct me if I am wrong.

Perfect 🙂

Hi Karthik,

Why Gamma of future contract would be 0?

It should be 1?

As new delta = 1(Delta)*0(Gamma) = 0

but if Gamma is 1 then

As new delta = 1(Delta)*1(Gamma) = 1

You do have a point, Amit. I’ll get back to you on this.

The change in delta is 0 (gamma). Therefore new delta = old delta + (gamma *delta).

i.e. new delta = 1 + (0*1) = 1

same ans Zero

Gamma of Futures will be ZERO due to nil change in value of DELTA which is 1.

Yes, thats right, Ajay.

Karthik – I have heard a lot about this open source software ‘Options Oracle’ by Samoasky technologies. What is it used for and how is it beneficial?

I’ve personally used Options Oracle extensively, I must admit the software was one of its kind. I guess they stopped supporting Indian markets and hence I lost interest..or something else happend which stopped me from using OO. Cant recollect the exact reason.

Some of the things I used to do with the software –

1) Calculate Option Greeks and Option Prices

2) Plot P&L of strategies upon expiry and before expiry

3) Stress test the strategy for change in inputs such as volatility

4) Plot Volatility cone and volatility smile

5) View max pain values

I will include all these topics in the coming chapters, except for Max Pain…which will be included in the next module.

Does PI support all the above mentioned features?

No, it does not for the moment. However we will probably have a tool to evaluate these parameters sometime soon.

Thanks karthik

You guys are doing an excellent job

What software do you use now

Any recommendation for beginners and pros

I use Kite.

Where can we find all these delta gamma theta in kite or in PI

can we find these in kite mobile app also?

Not as of now, but do check this – https://zerodha.com/tools/black-scholes/

Hi Karthik,

First of all; excellent ,excellent work…..I have read a lot of material (books, websites, platforms, trading mentors etc etc) but none of them have been as concise and simple as your content is. You can really “Teach” ..hats off. ….

Coming to my question:

1) If i am a regular nifty futures trader, trading say 10 lots on a regular basis, i can instead trade 20 lots of nifty ATM options (only buy CE/PE) for the same effect (positive or negative return) …..If my trade is in my favor and delta keeps on increasing, i need not adjust my position since the increased delta is improving my return……However, if it is going against me , i may need to adjust (reduce) my position based on the delta of the CE/PE i am holding???? If i am only buying ATM options, position going against me may also mean that delta is reducing ? and therefore my risk may also be coming down? It is more a question of the rate of change…..i.e the reduced position delta is within my initial risk range or not???

Thanks for the kind words and encouragement Prashant 🙂

I’m not sure if I’ve understood your question completely…but if it is what I think, then here are my thoughts –

If you buy an ATM option and the position starts to move in your favor the both Gamma and Delta works in your favor as the option transitions from ATM to ITM. However if you short options (ATM in this case) then more than the Delta you need to be worried about Gamma as you are essentially short Gamma when you short options …and ATM options have the highest Gamma value so you are taking on a large risk.

This also means you need to constantly tweak your position to ensure you are always short ATM option and not really ITM or OTM. This incurs logistical expenses…for that sense its better to just trade futures. However there are many trading secretaries (like Dynamic Delta hedging) which requires you to substitute options for futures. We will talk about it more in the subsequent modules.

Ok Thanks for your response…..For clarity, lets take the below scenario…..As of now, assume i am long 10 futures at 8471. I have my stop around 8400……..Now lets assume instead of futures, i have 20 option lots of 8450 CE…….When it goes in favor, it will probably give me more than futures….But if it goes against me, lets say Nifty closes at 8430 tomorrow, am i likely to lose more money than in options compared to what i would have lost in futures…Guess i am trying to understand what happens to delta when a position goes back into slightly OTM from ATM and then if the position needs to adjusted accordingly (in case of LOng CE @8450)

Long futures 10 lots = Long ATM calls 20 lots

In the example you have quoted you are comparing long futures 10 lots @ 8471 with 20 lots of ATM options ATM strike. ATM has a delta of 0.5.

So if the market moves from 8471 to 8430, then it falls by 41 points.

On Futures you will lose 41 * 10 * 25 = 10250

On Option you will lose 41*0.5*20 *25 = 10250 (approx)

Hence Long futures 10 lots = Long ATM calls 20 lots.

But after this move the story changes. The Option is no longer ATM …it becomes OTM, with delta of lets say 0.4. Consider the market moves 60 points up from 8430 to 8490 –

On futures you make = 60 * 10 * 25 = 15000

On Options you make = 60 * 0.4 * 20 * 25 = 12000

So as you can see once the option moves away from ATM status, it no longer becomes a surrogates for the futures contract. In order to maintain the equivalence you always need to adjust the option to ensure you are dealing with ATM options.

2.Values below 80 is OTM and values above 80 is ITM. Sir This is confusing. When ATM is 80 the >80 is OTM and <80 is ITM. Is my statement is Ok?

Oops, thats a mistake. Since its a call option, it should read “Values below 80 as ITM and values above 80 are OTM”. Thanks for pointing this out, will make the corrections.

What earlier printed was correct right. Because it is call (80CE) and hence Spot price below 80 the call becomes OTM and spot price above 80 makes call to be ITM.

Assuming the spot is at 80, strikes such as 60, 70, 75 etc are all ITM, and above 80 such as 85,90,100 are all OTM.

Sir we have range for delta +0 to 1 & -0 to -1. Similarly what is the range for Gamma so that we can judge high & low.

Its difficult to estimate the range for Gamma…from my experience a Gamma of 0.005 is considered quite high.

Is it possible to define gamma w.r.t. delta in place of underlying price as the second derivative may define based on the first derivative also apart from the base variable. Like distance, change in distance is velocity and change in velocity is acceleration. This may bring the delta calculation direct.

My second question is that why we have to worry more about gamma when options are at ATM or otherwise as gamma is constant for practical purpose………………..Why short position are more affected by gamma?

Thanks

Yes, you can treat Gamma as the 1st derivative as Delta, no harm with that. When the option hits ATM status, then Gamma hits maximum value. See the graph posted in the chapter. Also since Gamma is always a positive number, shorting options carry the risk of “Short Gamma’. Hence I say short positions carry ‘short gamma’ risk. However this should discourage you for shorting options, juts bear in mind the fact that when you short Options, you are short gamma.

Good work Karthik. Really liked the way the concepts has been put across in a very simple language. Is it possible to provide a module to explain starting from TA on an underlying to identify the direction of the underlying and thereby identifying a strike price using greeks.

Great idea Amit, thanks. Towards the end of this module I will include a case study based on your suggestion.

In extension of Amit post: Actually the spot movement depends on many factor like TA, fundamentals and current news, global developments etc. This is a normal concept. I want to know is it possible that TA will be always dominating other factors? How to judge the more effective factors. At times we have seen that even after the quarterly results are good the script price goes down and vice versa. Is it that there TA was having more power? Examples are SBI, Infy, Kotak B etc.

You always need to take a holistic view. There are many factors that affect the stock price form a short term perspective, although only business fundamentals matter in the long run. As a trader you need to develop a sense for all these factors and never isolate a certain factor as more dominant. How to judge these factors and assign a weight to the price movement is something you will develop as you spend more time in markets.

Thanks,

But options and future are valid for 1 month only or future may be for few months which I thinks is shot term and we have to analyse the market like a short term trader. Hence for Options all factors will matter. How to slowly rope in all factors may be of option’s trading. This was my point.

Understood your point, one of the readers (I guess Amit) suggested that I do a case study where I consider all points and factors and plug things together. I think thats a great idea I will do it towards the end of this module. That should answer most of your concerns.

Hi Karthik…

When would you upload option strategies module??….I am eagerly waiting for the same…..

The current focus is to finish Option Theory…few more chapters here…once we are done with Options Theory, we will start work on Options Strategies. I guess sometime next month we should get started on Options Strategies.

Hi Karthik,

Thanks for reply… and also I would like to thank you for such good quality, easy to understand study material by you on Varsity. I never seen such material on internet and too at one place. I am new to share market, I was doing trading blindly, now stopped everything and doing study with Varsity modules. Really thanks for your great efforts. Please keep it up…God Bless You…:)

Regards,

Abhijit

Thanks for your kind words Abhijit. It is indeed both encouraging and motivating for us. Please stay tuned for more.

Hi Karthik….

When would you upload Option Strategies Module?? I am eagerly waiting for the same….

Regards,

Abhijit

The gama decreases when a call option transits from ATM to OTM and ATM to ITM. due to the lower gama the change in premium is minimal with respect to the change in underlying. since, the ITM call options have a higher delta the change in premium in points term is higher even though the gama plays the drag. would this be a correct assessment karthik?

You said “The gama decreases when a call option transits from ATM to OTM and ATM to ITM. due to the lower gama the change in premium is minimal with respect to the change in underlying” —-> This is correct, however do remember in terms of absolute points change it maybe minimum but % wise, it will be a reasonable number.

“since, the ITM call options have a higher delta the change in premium in points term is higher even though the gama plays the drag” —–> Right on. However Delta is highest when Options are near ITM…but at ITM gamma is lower. ATM delta is around 0.5, but the sensitivity at this point is high as the gamma is the highest at ATM.

Gamma of futures contract should be “zero” as the delta of futures contract does not change at all so the rate of change is constant so the Gamma of futures should always be constant and because change in delta of futures contract because of change in spot price change is zero so the gamma of futures contract should be zero

Perfect!!

There is a mistake from you in chapter number 13.3.

You wrote that when the spot price is below 80, the call option with strike 80 is in the money and above 80 is out of the money. It should be other way around. Spot above 80 should be in the money while below 80 should be out of the money.

PLEASE CORRECT THIS MISTAKE>

Not a mistake Amarjeet, it is correct.

We are talking about a call option here. So strike is 80, spot is 80…so 80 is ATM, all strikes below 80 (like 70,75) are all ITM and above 80 (85, 90) are all OTM.

Awesome is the word for your efforts, knowledge and presentation skills Karthik, I am trading (or I must say gambling 🙂 ) options since 2007 with absolutely no knowledge of all these factors and now I know why am I in huge loss :). I am still unable to grasp all of it but this is the best thing so far and my dream of becoming full time trader now has a new hope !!!

Question :- When does the delta change for given option? for example if spot is at 8000 and 8050 ce is OTM with delat say 0.3 and spot moves 100 points to 8100 in 4 hours making 8050 ITM at what point will delta change? is it time dependent i.e end of market or start of market or is it price dependent i.e every 20 points etc?

Thanks for the kind words and appriciation 🙂 I hope you find all the success in trading and everything else.

About your query – Delta (and other greeks) changes real time as and when the markets move.

Hi

When i go to http://www.moneycontrol.com/stocks/fno/marketstats/options/gainers/index.php

and filter for top gainers , all options , CE , all expiry . I seem to get companies with phenomenal growth for the day (eg 14900% in a day for Bajaj auto CE 2700 today )

but when i check that same option at that same strike price and same expiry i get completely different numbers in the option chain for Bajaj Auto.

Am i doing something wrong ?

These numbers are different every day across moneycontrol and NSE option chain .

Mehul – I’m not sure why this happens, I would suggest you stick to NSE website, they provide the most reliable market information.

thanks for your reply one more question/confusion, point 3 &5 below the greeks graph says

“Notice the gamma value is low for spot values between ATM and ITM (80 and above).” — point 3

“The gamma starts to decrease when the strike starts to transition from ATM to OTM (80 and below)” — point 5

Should it not be ITM (80 and BELOW) for point 3 and

OTM(80 and ABOVE) for point 5?

or am i really confused?

Hey, thanks for pointing this out. I had kind of messed up this narration. Have fixed it now, please do have a look to check if it makes sense.

(y) looks good now , thanks

Thanks for pointing it!

Sir, Today Heromotor spot price went up from 2714 to 2738 almost 24 rs up. but ce 2850 for July hardly changed from 4.6 to 4.65 (.05) only whereas ce 2850 for August rose from 33.0 to 45.0 significant rise. Why its so. Cause July ce will have less time value hence IV change shall be % wise more and August ce will have more time value so effect of IV shall be less % wise. Also, what about IV change both should be same or not? This is crucial from selecting not only strike price but also expiry date also. Please elaborate. –Thanks

Yes, what you said is true – we have less time for expiry in July series where as the August series has more time to expiry. Strike selection is an important topic, will certainly talk about this.

The gamma for Futures (also other cash products) where delta is 1 meaning the rate of change in price is in perfect correlation to the change in Price of the underlying, would be Flat, since there is no curvature on the Delta curve during the life of the product.

As the vehicle is moving at a constant speed, gamma for Futures would be Zero :p:p

Please correct if wrong :d

Yup!

Zero

As we know from elementary mathematics that ‘derivative’ of a constant (i.e. delta = 1) is 0.

Dear Mr Rangappa,

At the end of Para 13.3 you made two statement as given below:

(a) Never short ATM or ITM option with a hope that they will expire worthless upon expiry

(b) OTM options are great candidates for short trades assuming you intend to hold these short trades upto expiry wherein you expect the option to expire worthless.

I couldn’t understand the basis of these statement.

Would be grateful if you could explain it.

Both the statements hinges on the same fact – towards the expiry OTM and ITM options have a great chance to remain OTM or ITM, hence they can expire worthless….therefore they are great candidates for shorting. Whereas ATM could be a bit tricky…it has a 50 – 50 percent chance of expiring as a worthy contract/not worthy contract…hence no point taking the risk to short these options.

Thank you for your explanation. Now I feel how silly my doubt was. ???

🙂

Dear Karthik,

After getting inspired I am planing to write Call options that are slightly OTM.

Could you please tell when exactly an option is considered to be ATM. Is it when strike Price falls within some price band around spot price say when Strike Price = Spot Price ± some %age of Spot price ? What is that %age ?

What ideally should be delta, gamma and theta values to write OTM call options ?

ATM is when the strike price equals (or approximately equals) spot price.

Also please dont write options early in the series, wait for few…its best to write options after 15th of …also please avoid writing ATM options.

Good luck.

Hi sir

I am really thankful to you for providing so many insightful articles. Its very easy to read and best part is its applicability in the real scenario. You are amazing.

I have one query. In 13.2 example … since we are short on 10 lots Nifty 8500CE so Delta would be -ve as i have done below. Please clarify.

Number of lots = 10

Position Delta = -10 * 0.5 = – 5

Perfect!

CONCERN REGARDING EXAMPLE MENTIONED IN POINT 13.1 :-

1) first we consider 70 points upwards , premium appreciates .

instead of considering a 50 point downward movement . let us consider a 70 point drop .

in this case the underlying is back to original state with no profit & no loss .

but when we calculate new premium , it is a t a loss and depreciates to 36.85 ….. am i correct or have i made a mistake ?

2) CASE-2 :-

the underlying falls 70 points and gains back 70 points…. again no profit ,no loss

but in this case also , the premium is at a loss at the value = 34.75 .

PLEASE DO CORRECT ME IF I AM WRONG .

in this kind of scenario , why & when should anyone consider option trading other than spot or future markets ?

thank you

You need to factor in the fact that with the change in underlying both the delta and Gamma changes. The calculations in the next step should be considered with the new values in perspective. Hope I’m not confusing you more 🙂

Since the derivative of a constant is zero .

Delta for the future contracts is constant and hence the gamma for future contract would be zero

Alternatively – If Delta = Gamma * change in the spot

so delta = 0*Change in the spot = 0

Perfect!!

Also i wanted to know that does gamma have a range like that of delta ?

Not really, Gamma peaks for ATM options and cools off for ITM/OTM options. Hence the gamma graph looks like an inverted parabola.

dear karthick,

i have a logical doubt . suppose the nifty spot is trading at 7800 , and i decide to buy 7600 call option it is deep itm contract. BUT IF IAM WRITING THE SAME 7600 CALL IT WOULD BE AN OTM CONTRACT ISNT IT. THE CONTRACT WHICH IS ITM FOR AN OPTION BUYER WOULD BE OTM FOR AN OPTION WRITER ISNT IT

No!!

A option is either ITM, ATM, or OTM and it remains the same for both option buyer and seller. In the example you have quoted the option will be an ITM option for both buyer and seller.

This is in response to your trick question on GAMMA.

I feel GAMMA does not apply to futures as the DELTA is constant ie 1 for FUTURES.

Please let me know wether I am right or wrong.

Bingo 🙂

several time i see in some website “don’t short put option (normally)” , can you please explain….

Yes, simple reason being that the panic spreads faster than greed, in other words its much faster for the market to fall 100 points than go up 100 points. Hence shorting options can be a bit scary.

Dear Karthik Sir Thanks for yet another good article on options on scientific background. You triggered my memories on Differential Calculus and Physics. The delta vs spot_price curve looks to have a perfect mathematical pattern. I found the curve y = 1 / (1 + (1/(x^4))) is best matching the delta vs spot_price curve. Let O be Deep OTM, A be ATM, I be deep ITM and S be spot price. Then x = ((O – S)(A -I)) / ((O – A)(S – I)). If you plot this, you can see the curve created matching delta curve. So gamma is first derivative of Y = 1 / (1 + (1/(x^4))) which is Gamma = (4(x^3)) /( ((x^4) + 1)^2)

Yes Gamma is the 1st order derivative…in fact you can differentiate this further to get the 2nd order derivative :). 2nd order is used to hedge posistions especially when you are running a huge trading book. For small retail positions this is not really required.

Above you mentioned ” Notice the gamma value is low for OTM Options (80 and above). This explains why the premium for OTM options don’t change much in terms of absolute point terms, however in % terms the change is higher.”, I get that premium doesn’t change much in terms of absolute points because of low delta but how does low gamma affect relative change in premium?

Well, if the gamma is low, then the premiums don’t change much. However if the volatility increases drastically or if the market moves in favor then option premiums for low gamma options tend to move…this is when you will see OTM options doubling in value. Recent example was the way L&T options reacted to a 14% increase in the stock price.

Hey Karthik,

Your every response to public doubts and the articles encourage people to trade before they opt out due to risk taking in markets.

I got confused with the below points, hope you’ll rectify

1. In your 1st two example showing a change in the delta with respect to Gamma with 70 points up (in each) changes the moneyness from OTM to ATM and lastly to ITM giving a premium of 80.25 keeping the New Delta at 0.65.

My question if Nifty changes by 140 points up directly (irrespective of 70, 70) although the moneyness becomes ITM from OTM. But giving a premium of 68 at Delta 0.65.

How to get a proper view on this ?

2. Every Underlying or Index has it’s lot size stated on NSE website. Can we choose lots below the stated. Say Nifty has 75 market lot, can we take 20 lots for trade or we have to trade on 75.

The directional view has to be developed based on TA, FA or say quants. Check this – http://zerodha.com/varsity/chapter/getting-started/

No, you cannot change the lot size, you will have to go with what the exchange prescribes!

Sorry Karthik, if I have confused you with my confusion. My question was not about the directional view rather it was on the premium change that took place from OTM to ITM in your example.

Nifty Spot = 8326

Strike = 8400

Option type = CE

Moneyness of Option = Slightly OTM

Premium = Rs.26/-

Delta = 0.3

Gamma = 0.0025

1st example

Nifty spot raised 70 points up i.e. (8326+70) = 8396

@8396

Change in Premium =0.3 * 70 = 21

New premium = 21 + 26 = 47

Change in delta =0.0025 * 70 = 0.175

New Delta = 0.3 + 0.175 = 0.475

New Moneyness = ATM

2nd example

Nifty spot raise another 70 points up i.e. (8396+70) = 8466

@8466

Change in Premium = 0.475 * 70 = 33.25

New Premium = 47 + 33.25 = 80.25

Change in delta =0.0025 * 70 = 0.175

New Delta = 0.475 + 0.175 = 0.65

New Moneyness = ITM (hence delta should be higher than 0.5)

Here in the above two example 8400 Call option has moved from Slightly OTM to ATM and then to ITM giving a total premium of 80.25.

Now if Nifty change for 140 points up in one step rather in two as above, say

Nifty Spot = 8326

Strike = 8400

Option type = CE

Moneyness of Option = Slightly OTM

Premium = Rs.26/-

Delta = 0.3

Gamma = 0.0025

Nifty moves up by 140 points i.e. (8326+140) = 8466

@8466

Change in Premium =0.3 * 140 = 42

New premium = 42 + 26 = 68

Change in delta =0.0025 * 140 = 0.35

New Delta = 0.3 + 0.35 = 0.0.65

New Moneyness = ITM

Why there is a big difference in the case of premium when the OTM transits to ITM in both cases? So my question is how to rectify such confusion, not directional view?

My bad, I completely mistook your question. There are two explanations for this –

1) Mathematical explanation – Technically speaking the change in premium, delta, and gamma are all defined for 1 point change in the spot price. So when I say there is a 70 point change in spot, I tend to directly multiply the 70 points change with delta (or gamma) to get the premium value..but note this is just an approximation. To get the true value for a 70 point change in spot, I will have to calculate the change in premium by changing the value of delta (and gamma), for 1 point at a time….and I will have to iterate this 70 times. This is when when i get true value of the premium. In fact gamma/delta are instantaneous values and I will have to do this one step at a time. An alternate way to do this is would be by integrating (recall your school calculus) over the change in premium.

2) Easy explanation – Note, when the spot price changed 70 for the 1st time, the delta changed from 0.3 to 0.47 and for the 2nd 70 points, the change in premium occurred on a higher delta, therefore higher premium. Whereas when you took the 140 point change directly, this happened on a smaller delta i.e 0.3, thus leading to a lesser premium when compared to two 70 point change

Hope this clarifies.

Calculus? You are kidding right!

But thanks, somewhat you have put me in one step further to dealt with my confusion although I still have to ask you for some more recognition

Say at 10 am = Bought 8400 CE @ 26 (Slightly OTM), spot 8326

11 am = Spot goes to 8396 @ 47 (ATM),

12 pm = Spot goes to 8466 @ 80.25 (ITM)

or else,

at 10 am = Bought 8400 CE @ 26 (Slightly OTM), spot 8326

12 pm = Spot goes to 8466 (140+) @ 68 (ITM)

So if I want to square off my position at 12 pm what will be the consequence according to the above follow up?

Not kidding 🙂

Calculus plays an important role in derivatives!

Either ways, the same explanation that I gave above holds true. Also remember when such a rapid move happens on a intra day basis the effect on premiums will be much higher.

I have not disrespected your ways, it’s me poor in calculus. :'(

It means if price movement rests its value changes but during the movement, no value get affected? And if the movement lasts for less time the change in premium is high? Am I wrong somewhere?

Sorry Nil, I’m bit lost on what you just said – can you please break this down for me? Thanks.

1. When spot price starts to change, the other values of an option get affected once the spot price reached a higher/lower value than earlier.

2. The values don’t change until the spot price reach a predetermined price (either high or low)

3. If the spot price shows a big movement within few moments then the premium changes rapidly or price movements in large periods gives lower rate of premium change

Summary: Spot price 8326 changes 70 points twice within less time than the change of 140 points.

So, Big movements within less time , Higher premium

Big movements in higher time, Less premium

Hope you have understand my confusion.

Looking for your reply

This is somewhat true – “Big movements within less time , Higher premium

Big movements in higher time, Less premium”.

This one is not correct – “The values don’t change until the spot price reach a predetermined price (either high or low)”

Thank you, Karthik. Your quick response makes me more enthusiastic to tackle further. Hope you won’t mind if I come back to you again.

Please do fee free to post as many queries as you want, it will only enrich the forum!

Hi Karthik,

Thanks for your way of teaching… it’s good.. I missed the opportunity to read much earlier. Now come to the above point…

Problem is : There is a difference in premium when calculating of movement of 70pt + 70pt & in single stroke 140pt.

As per your one of the Answer the Delta movement is real time… If we calculate for every point movement from 1 to 140 separately

we will get the correct Premium… right?

Thanks.

Yes, the continuous calculation is the best approximation to the actual value.

I have doubt (don’t know if it is already answered)

How do we calculate Gamma and Delta in first place??

Its derived from the B&S model.

Thank you Sir…

Welcome!

Sir since ITM is similar to future contracts, is it wise to trade them like futures using technical analysis with a lower margin ?

Thank you.

They behave similarly but they are not the same 🙂 …having said that, yes you can attempt to do that for deep ITM options.

Karthik

Please suggest if this summarization is correct understanding:

Type of Option Long or Short Market Status Delta & Gamma Effect Long / Short Gamma

=================================================================================

Call Long Moves Up Delta + Gamma X (+Points) Long Gamma

Call Long Moves Down Delta + Gamma X (-Points) Long Gamma

Put Long Moves Down -Delta + Gamma X (-Points) Long Gamma

Put Long Moves Up -Delta + Gamma X (+Points) Long Gamma

Call Short Moves Up Delta + Gamma X (+Points) Short Gamma

Call Short Moves Down Delta + Gamma X (-Points) Short Gamma

Put Short Moves Down -Delta + Gamma X (-Points) Short Gamma

Put Short Moves Up -Delta + Gamma X (+Points) Short Gamma

I have difficulties in understanding this one, maybe I’m missing something here. But my gut says you could be right 🙂

In “Case 1 – Underlying moves up by 10 points”, the new delta should be -0.5 – 0.04 = -0.54 as delta is loses its value when the underlying price goes up so its value must decrease. It is also clear from graph of delta vs spot price for put options that value will decrease. Similarly in case 2 answer should be -0.46.

Delta of a Put option decreased when the underlying increase, hence-0.5+0.04 = -0.46 is correct. Remember, for Put option, delta is negative to capture the effect of decrease in delta for increase in underlying.

Hi

Right now I am holding 12900 qty of option 9500CE at the average price of rs.3.00. But currently the price is rs.1.15. Can you suggest what can I do now.can I hold it or sell it. Another 7 trading days only available for match. The loss is 23 k now.

Vijay, this really depends on your conviction. If you feel the markets can make a move higher then 9500, then please do hold, else sell it and book your loss.

On Sec 13.2 Estimating Risk Using Gamma

Position – Short

When the underlyning moved by 70 points would the position not slightly become OTM for him and delta of the over all position be reduced rather going up from 0.5 to 0.15 rather than 0.85

He is short call and the assumption is that Nifty moves higher by 70 points, so the option becomes ITM.

Hello Sir, I have the same query in Section 13.2(Estimating Risk using gamma)

As we are shorting the call option and Nifty is increasing by 70 points, won’t the moneyness change from slightly ITM to OTM and hence the delta be less than 0.5?

No Sanat, think about it from the strike and the spot perspective. With 70 point increase, the 8400CE becomes more ITM right? So the delta actually increases.

New Delta = We know the Put option loses delta when underlying increases, hence – 0.5 + 0.04 = – 0.46.

I think here delta= -0.5-0.04=-0.54.

Yes, Puts lose delta when market moves up.

New Delta = We know the Put option gains delta when underlying goes down, hence – 0.5 + (-0.04) = – 0.54.

I think here should be -0.5+0.04= -0.46

Makes sense, I guess someone earlier had posted a reply as well. Request you to double check. Thanks.

The Gamma of a futures contract would be 0 right?

(As the differentiation of a constant is always 0)

Yup…this also explains why the delta of a futures is a constant 1.

In the example of calculating risk using Gamma, shouldn’t we consider negative sign before the number of lots because we have taken a short position?

i.e. position delta = -10 * 0.5 = -5.

then, when the market moves against me, new gamma = 0.05*70 = 3.5.

therefore, shouldn’t the new delta be = -5+3.5 = -2.5?

Please correct me wherever I’m wrong.

No gamma is a positive number…and remember, we are only trying to estimate the risk in terms of number of lots here.

sir,

how the delta and gamma are calculated ?

Black & Scholes model helps you calculate these values.

Sir,

Does premium also comes to zero on the day of expiry?

No, the value of the premium will depend on the intrinsic value of the option.

hello karthik,

i have a question which may sound funny. i have gone through all chapters till now but there are too many mathematical calculation & seriously looks horrible to me (not a academic person at all). my question is that-

“suppose i am very bearish on a particular contract and i decides to buy a way far out of money put with next month expiry (since i am extremely bearish on it) which is available at almost free of cost lets say may be around Rs. 0.80 – 1. so before initiating the trade should i look for delta & gamma, when there is nothing on stake.

No, if you are convinced about your view, you can do this….i.e buy way OTM option with ample time to expiry.

As we have seen position of ATM options is most sensitive to changes in underlying therefore the effects of gamma on it but why is Gamma of an ATM option highest?

Also I wanted to know why theta of a deep put option is positive? (Though it should have been posted in other chapter, I am posting it here for the sake of convenience.)

You actually answered it yourself 🙂

Think of gamma as a representation of the sensitivity of an option to the underlying’s price movement. ATMs clearly are the most sensitive. Given this, the gamma is highest for ATMs.

About Theta – not true. All options lose money with respect to time.

Karthik,

This is an excellent series. I found it only in Sep 2017 and I am reading it for the ‘n’th time, just to get my fundas clear. I really appreciate your patience in answering all the questions too ! Hats off to you ! (I have just opened an account in Zerodha 🙂 )

Considering that this article was written in July 2015, I hope it is not too late for me to ask these questions:

1. I don’t think I have understood the difference between short gamma and long gamma. Is it that if you have taken a long position, it is long gamma and if you have taken a short position, it is short gamma ?

2. Let us say that an option is ATM, where the gamma is the highest. Now whether the price moves up or down, the gamma is going to decrease in the same way (because the gamma curve is like a bell curve – I have assumed it to be symmetrical about the ATM). With this, if I have shorted the option, the risk of price going up is the same as the reward of price going down, isn’t it ? So why is it dangerous to short an ATM option, considering that the reward is equally good ?

One reason I can think of is that as the price increases, the Delta also increases and hence it has a cascading effect (thus increasing my losses, if I have shorted) whereas when the price falls, Delta decreases so as to minimise the overall effect a bit, thus reducing my profits a bit. In other words, the losses I incur by a move of x points upwards in the spot price will be more than the profits I make by a move of x points downward. Is it ?

Welcome to the family, Chengappa!

1) Yes, from the gamma perspective, long position is often called long gamma and short positions as short gamma

2) Since ATM options have the highest gamma they also tend to be the most sensitive options. It’s like this – assume you are short simultaneously on an ATM option and also short on an OTM option. Now if the market moves against you, then obviously you will lose money on both these short positions…but you will lose much more on the short ATM position compared to the OTM option.

Karthik,

I understand that the unfavourable market movement affects the ATM options more than OTM options because of high gamma of ATM. For example, if I have bought an OTM call and an ATM call, if the price comes down, the drop in premium is more for the ATM call, right ?

So let us say I have bought an OTM call and after a day, market moves favourably and now my option is ATM. I expect the price to go up further. Is it better to:

1. Leave it as it is (and risk the premium coming down steeply if the price comes down)

2. Square off the ATM call and buy an OTM call (I can even book the profit and but an OTM call with the original amount)

Thanks,

Chengappa C B

Yes, the ATM call drops more as the ATM option is most sensitive to directional movements i.e Delta

1) Depends on your trade set up and the targets you have set. Also, if you are holding an option which has transitioned from OTM to ATM, then you will have enough cushion in terms of profits.

2) Again, depends on your risk appetite 🙂

In the options calculator, what values should be taken as implied volatility and Interest? On the specific stock derivative on nse webpage their is a dash in place of value for volatility. Please enlighten. 🙂

You can check for IVs in the Option Chain page on NSE. They publish the IVs for individual stocks / strikes – https://www.nseindia.com/live_market/dynaContent/live_watch/option_chain/optionKeys.jsp?symbolCode=-10002&symbol=NIFTY&symbol=NIFTY&instrument=-&date=-&segmentLink=17&symbolCount=2&segmentLink=17

And the interest value?

Take the 91-day t-bill as a reference rate.

Thank you karthik sir.. indebted for your guidance on truly each and everything! ?

It’s a pleasure!

Sir you are too good! Thanks a ton!

Happy learning!

Pretty sure your first diagram delta vs stock price is wrong for the put delta.

Put delta doesnt start at 0 and move to -1 it starts at -1 and moves to 0.

The two curves should be shifts of each other not mirror images.

Not really. Read this chart starting from the ATM position.

Dear Karthik Rangappa,

First of all, thank you very much for putting up varsity. I learned a little bit of FA and TA through some classes. Futures and options classes are priced too costly and was searching for alternatives. That is when I landed here. When I finished all your options module, to my surprise, I noticed that I did not even take a single line of notes for the first time in learning anything in my life. All just went, straight into the head ;). Such was the manner how the concepts are explained. Referred many of my friends to this site.

I will be doing my first options trade next week :). So I am doing a quick recap of all the modules. While doing so, I also noticed that there is a slight confusion in the delta vs spot price figure. May be you need to remove the spot price caption at the bottom. Going by delta vs spot price in the figure, it conveys that as the spot price increases delta of the put option goes from 0 to -1. I think this is what Fbish pointed out. In such case for put option, the call option delta curve would just shift down.

If we want to go by OTM, ATM and ITM labels, then we may need to remove spot price caption below. It may lead one to interpret that spot price increases from left to right.

Thanks again Karthik Rangappa and Team Zerodha. All your sincere efforts are highly appreciated, deeply regarded and will be remembered through out my journey in the markets.

Vetriselvan, thank you so much for such kind words. I’m really happy you liked the content here.

Quite a few people have pointed this on the spot vs Delta chart. The trick is to start from the center of the graph and then look to the right (where the spot increases) and then to the left (where the spot decreases)…and observe the behavior of both Call and Put Delta. Anyway, I will see what I can do to make it easier.

Anyway, good luck for your very first options trade. Hope you learn and earn well!

Thanks for the reply and your wishes :).

Starting from the center makes it easier.

You may consider putting separate labels for put and calls along the curves. Starting from the left for calls, it would be OTM, ATM and ITM and for puts it would be ITM, ATM and OTM with blue and red colors. Alternatively, you may just remove the labels and draw arrows from the centers towards the left and right saying decrease and increase in price respectively.

Thanks Vetriselvan, I will try and do that 🙂

Thank you.Your material is simple to understand.

Please clarify my doubt

Initially, you are assigning values for delta as 0.2, 0.8 etc.. for Delta 0.05, 0.025 etc..

How can we fix those values? Are those are estimated values?

kindly reply me

Thank you

Rajesh – I’m unable to understand this bit – “assigning values for delta as 0.2, 0.8 etc.. for Delta 0.05, 0.025 etc..”, can you please rephrase this?

Hi,

Gamma for the future contract would be zero as delta for future is constant.

Yes, the delta of Futures is 1.

Hi

Here we are calculating delta change considering 70 points change in spot price.

for eg current delta is .3 and if gamma is .002 so new delta will be =.3 +(.002*70) equals to 0.44

Now I am sure in real world delta calculation happens for every single point change in spot price so for every point change in spot we use to get new delta as per calculation explained above. Am i right?

The delta calculation explained here is only an approximation. Remember, when we say 70 point change, we are talking about ‘direct’ change of 70 points. In reality, it does not work that way.

Very well explained sir… last line is very true 😛 lots to read before i go to sleep 😛

Good luck and happy learning, Azeem!

Great work Karthik!

I had a concern though, the statement ‘when you short options, you are shorting gamma’ is still unclear. If you could further delve into this aspect and enlighten us.

Thank you for the amazing write-up.

This is quite straightforward, Ashish. Gamma is always a positive number – and not like the DELTA which can take -ve value based on the position you take. So when you go long on an option, you are also long on the gamma, likewise, when you are short on an option, you are also short gamma.

Delta is additive i.e. we can add delta, what about Gamma and other greeks ? If they are also then please give example also.

You cannot really add the other greeks like Delta.

Hello Sir,

Sorry for troubling you with many questions. I am new to options in fact to the market.

I dont get it when you say long gamma and short gamma. I understood, ATM options have high gamma as the delta is in take off and acceleration phase.

“In fact you can be more precise and say “shorting options carries the risk of being short gamma”.

What does this statement mean actually sir??

Thank you so much for responding all queries.

Aishwarya

Gamma, unlike delta, is only positive for both long and short options. The gamma dictates the rate at which the delta moves. If you are short on an option, then essentially you are also short on Gamma. Like in any position, if the position starts moving against you, you have the risk of a loss. Its just that short option position carries significantly larger risk compared to long options. I’ve only tried to express this risk in terms of the Gamma.

Got it now sir, thank you so much

Welcome. Happy learning, Aishwarya!

Hello Karthik,

From the last graph of gamma vs spot price, can we say as strike price increases (for any option call or put, buy or sell) the maximum gamma value decreases?

Yes, this increase has to happen with respect to time and speed of the market.

Hello karthik, In one of the examples above options = 8400CE And position = short . But we buy a call option when we expect the price to go up, so shouldn’t the position be long ?

If you are short on the call option, then you essentially expect the prices to go down. Likewise, long put. If you are short on the Put option, then you expect the price to go higher, likewise, long call.

So does this mean that now he is going to suffer a loss or his profit is going to decrease as the price is going to decrease ?

Yup.

Thnx a lot

Cheers!

Hello sir, according to the first graph when the spot price increases the delta for put option becomes more negative but in case I (one) of the example as the price moves up by 10 points The Delta becomes less negative ?

BTW thank you so much sir for sharing your wisdom with us ?

Welcome! Keep learning 🙂

This depends on which option and which position you are looking at. As the price moves higher, long call and short Put gains more delta. If the price drops, short call and long PUT gains delta.

the gamma of the futures contract is zero.

thanks

Yup, and hence the delta is fixed to 1.

kindly post the link for quants

Which quants, Rupali?

Hi,

I had a question regarding the movement in the premium wrt delta, as you said gamma is acceleration so shouldn’t the delta change at every tick in the underlying. Which would form an arithmetic progression with gamma as the common difference.

Delta =.3

Gamma =.0025

So, with every tick up in the underlying the new premium should move by

.3 + .30025+.30050…..So on

In fact, this is how it works, Animesh. It is on a continuous basis. For sake of simplicity and ease of explaining, I had to take a step approach where I’ve assumed the price moves in steps.

Hey thanks a lot for clarifying .

Good luck!

Hi karthick, I want to learn about stress testing and backtesting. Can you please help me into this?

Check out https://www.streak.tech/ for backtesting, Santosh.

Thank you and what about Stress Testing…?

Stress testing is a bit complex, involves multiple scenario generations. I’m not sure of any platforms which can do this.

What is the max and min value of gamma? Like you defined delta value of OTM, ATM and ITM

Gamma can hit close to zero on the lower end, but there is no upper cap (theoretically).

But for ITM gamma becomes saturated..so if there is no upper cap then it should not become saturated..please correct me if m wrong!!

In fact, Gamma has a bell shape curve. At its peak, it starts to decline.

Hi Karthik, I saw that options oracle started supporting NIFTY, BANKNIFTY and NSE stocks – http://www.pasitechnologies.com/2015/08/happy-independence-day-to-all-indian-as.html

Is that correct?

I;m not sure, Pradeep. Have you checked out Sensibull?

ATM CALL OPTION 100CE HAS A DELTA OF 0.5. WHEN THE ATM OPTION MOVES TO ITM,(SPOT PRICE RISES TO 110 FROM 100). THE DELTA CHANGES TO 0.65.THE DELTA HAS CHANGED BY +0.15. IS THIS CHANGE BECAUSE OF GAMMA

Yes, the rate of change of Delta is captured by Gamma.

derivative of a constant is zero so futures with delta “1” will have gamma value “0”.

Perfect!

Futures have a delta of 1 and therefore a gamma of 0.

Really an awesome experience learning this!

If only other academia had such clarity!!

Souvik, I’m really glad you liked the content here. Happy learning!

Hi Karthik,

I don’t know how to thank you for pulling me towards stock market trading! Every chapter loads my brain with lot of new content. It is so refreshing to learn lot of new things. Keep up the good work. It might be exaggerating to say, but it is truth, there are hardly better teachers than you in the real world. You are awesome! Content is awesome in every sense! And kudos to you for replying to every comment with such love!

Thanks a ton!

Hey Avinash, thank you so much for the kind words. I’m glad you are finding your time worth while here 🙂

Happy learning and good luck 🙂

Sir please write a complete chapter on hedging using put option. Lot of doubts on it. Can I buy 2 put options or complete lot of 75 fir nifty.

The futures have a delta of 1, so to completely hedge this, you need to ensure the delta is -1 from the options position. I will try and write something ard this soon 🙂

Gamma for Future is 0 as Delta for future is 1 every time. Since it’s constant, it there is no change in delta. Hence, since gamma value changes delta value when price of underlying is changing, gamma is 0.

Mathematicaly, derivative of a constant function is zero.

My question is then if delta for future is 1 why don’t equal number of points go up or down on a future of a stock and it’s spot?

Also on practical examples, since the above is true, gamma won’t be zero since delta is not constant always.

That’s right, the gamma of Futures is 0.

Btw, Futures and spot move in tandem.

Hi, Varsity is just amazing guys! Keep up the good work!

I have a question in this chapter. I understand that the risk position changed from 5 to 8.5 in the above example when a trader is shorting his position on call options. However if a trader has a long position on call options, then to my knowledge whatever be the change in the gamma, the risk remains to the extent of the premium paid right? So basically a change in Gamma against my long call position will not make much difference as the risk is only and only the premium amount and nothing more than that. Is this understanding correct?

Yes, when you are long, the gamma risk is contained. In fact, when you are short, the gamma risk is the highest.

hi Greetings, Thanks for the excellent stock market lessons , The gamma of the Futures contract is Zero 🙂

Yes, Kuldeep, the gamma of futures is 0, hence the delta is 1 🙂

Sir Is there a way to publish it in epub format or mobi format to read in a kindle because pdf format is not supported well on kindle

Need to look into that, Mayank. Thanks.

Hello sir…

My question is THAT you said going short on ATM is risky as slight increase in the underlyimg changes the delta by greater margin(which is not possible in deep ITM and deep OTM).

BUT same thing is applicable for going long also,If underlying prices fall.

Then going long is as as risky as going short.

Then why you warn in going short if both are equally risk…..Or is it just because we already presume market to be bullish?

You quote [Note – By no means I’m suggesting that you should not short options. In fact a

successful trader employs both short and long positions as the situation demands.

I’m only suggesting that when you short options you need to be aware of the Greeks

and what they can do to your positions.]

Please explain this.

And sir your varsity project is really good and upto the mark.And i really wonder that its free..Although i have acxount on zerodha but still you are doing a great job sir.

When you short options, you are also short on Gamma, which is the rate at which the delta changes. When the position goes against you, the gamma too goes against you. This does not happen when you go long, Edward. For this reason, the risk of writing options is higher.

Gamma for futures contract will be zero as there is no change in Delta, and when delta is constant then there in no question of Gamma Having non zero value.

Thats right, Pradeep.

Hi Karthik,

I have been wanting to write you for quite some time so here I go today. Many thanks for writing these lessons/chapters. They are all awesome. Since I wanted to understand options, I straightaway went to options. They are all written so well and with such depth that I haven’t seen in many study materials those are on net. Thanks a lot for taking pains to write each and every module, chapter, and so on. I really appreciate it. Thanks to Zerodha too for making it available on-line absolutely free of cost! Gratitude folks!!

Now the question- I could not understand why different gammas has different values at peaks (i.e. at ATM) for different strikes? I could not find this question in the long list of questions asked before? And How are these values derived? meaning what makes 80 CE ITM Gamma value 0.004 and 120 CE ITM Gamma at 0.003 (referring to gamma vs spot graph featured above) ?

Do I get an email notification when my question is answered? would appreciate one.

Thank you in anticipation Karthik.

Thanks for the super kind words, Abhijit.

These are three different strikes, hence the gamma value changes. But the point to note is that the gamma peeks when the strike reaches the ITM status and this is true for all options (call or put) and across all strikes.

No email notifications, the comments run up to 100’s and it will soon start annoying you 🙂

Hi Karthik,

Enjoying reading through!!

Now, here is trick question for you – In the earlier chapters, we had discussed that the Delta of the Futures contract in always 1, so what do you think the gamma of the Futures contract is? Please leave your answers in the comment box below 🙂

Would the Gamma be “0” for a Future Contract?

Thats right!

Gamma of future is always 0 as delta is always 1

Yes sir, thats right.

Basically!!!!! Where can we find the delta and gamma values for the options.

Any option calculator will give you this information.

I dont know any option calculators as i am noob in stock market, What would you suggest as a option calculator (like is there any site or application)

You can check this, Hari – https://sensibull.com/

sir ,

I am trying to find delta and gamma of USDINR spot 71.80 , strike CE 71.75 ,but delta showing 1 , it should be 0.5 ? (using option calculator of pi , voltality 0.004 , interest rate 6.50 )

I think your volatility input seems a little off. Yes, nevertheless it should be around 0.5. Can you please try here – https://zerodha.com/tools/black-scholes/

yes sir , it should be implied volatility , i was trying to calculate volatility through pi option calculator , thats why wrong calculation , thank you sir

Good luck, Nitin.

How to calculate gamma…. Considered as 0.0025

You could use any basic B&S calculator to get the exact value of Gamma. I’d suggest you check this – https://sensibull.com/

Sir varsity app is good I liked the related links,expert opinion and quiz part even I took the certification of technical analysis and completed it successfully on 1st attempt with 220points.But disappointed that there is no comments section here I learnt most things through comments section in varsity web please include comments section here also.

I’m glad you liked the app, Srinath 🙂

Including the comments can be a huge task. But will bounce off the idea with the team.

https://drive.google.com/file/d/1kZ6D6Jy6noAt-Km8qrbgsg7fWG0q5e2Y/view?usp=drivesdk

Sir Gamma and theta are always positive numbers for both calls and puts but why here they are negative and what is values of Greeks indicating here.

These are just reporting conventions, Srinath. Negative theta indicates the number of points it decays by each passing day, since its technically a loss, its shown in -ve. Gamma is -ve for put when the spot moves up. Hence -ve.

Sir here ur saying Gamma is -ve for puts when the spot moves up but in this module u have stated unlike delta Gamma is positive for both call and put.

You can consider it as positive and it gets deducted (for PUT option) when mkts go up.

hi Sir,

what is the reason for ATM to have highest gamma? Why can’t the gamma be same for all the moneyness ?

ATM options have the highest probability of transitioning to ITM, hence the gamma is highest.

Sir,

In Gamma (Part2) 5th page,

It has been mentioned that trader is short 10 lots of Nifty Call option and Delta = 0.5.

Query 1 – For Short call – Delta = -0.5 right?

and

Query 2- If Nifty moves 70 points against him, then Change in Delta = 70×0.005 = 0.35..So New Delta = -0.5+0.35 = -0.15 right ?

So New Combined Delta = -0.15×10 = -1.5 right?

Why does Delta has been taken as 0.5 instead of -0.5 as mentioned in Query1 for Short Call and therefore New Delta instead of -0.15 arrived at 0.85.

Please clarify the above 2 queries.

1) Yes, provided you’ve shorted ATM calls

2) Yes

The algebraic sign is to differentiate short versus the long.

How the gamma values 0.0025 and 0.004 were taken

You get that from the Black & Scholes formula.

Hi Karthik,

In the section 13.2 shouldn’t the positional Delta be -10*0.5 = -5? And when the position moves against, it means the spot moves +70 meaning, it is moving towards the saturation side and hence new delta=0.5+0.005*70=0.85. And new positional delta = -10*0.85= -8.5

Can I say for a Futures contracts Delta is always +1 and positional Delta is +1 when it is long and -1 when it is short?

Rajesh, I think someone else had a similar query on the delta value, have posted a reply. Can you please check the comments section please?

Yes, futures delta is always 1.

The trader is short 10 lots of Nifty 8400 Call Option; this means the trader is within his risk boundary. Recall the discussion we had in the Delta chapter about adding up the delta. We can essentially add up the deltas to get the overall delta of the position. Also each delta of 1 represents 1 lot of the underlying. So we will keep this in perspective and we can figure out the overall position’s delta.

Delta = 0.5

Number of lots = 10

Position Delta = 10 * 0.5 = 5

sir it would be -5. short 10 lot i.e -10*0.5 = -5

Yup, but the delta is additive. You need to add this to the delta value that existed before the change. This will give you the new delta.

Dear Karthik ji,

i want to know the difference between shorting a call option and buying a put option, How it is difference from view of risk and profit.

Suppose today Nifty 50 was around 11525-30 about 14:00 . and i am sure that nifty will drop at least upto 11500. Now what should i do if i am in intraday trading. Selling Call option Nifty at 11600 or buying Nifty put option of 11400. i am new in options and today it was my 2nd trade plan. I know about shorting Equity. but not sure in this position how a trader should plan?

thank you

The difference is in your expectation of the volatility. If you think the volatility is high and you expect the volatility to go down (and also expect the market to go down), then you are better off writing a call option and pocketing the premium? Or if you think the other way, i.e volatility is low, expect it to go up (and the market to go down), then you are better off buying the put. This is because if the volatility is high, the premiums are expensive so you should be looking at selling. If the volatility is low, premiums are cheaper, so you are better off buying the premium.

If you are trading intraday, I’d suggest you trade with futures for a bit, till you get a complete hang of the options market.

Thank you karthik ji

Good luck!

What is gamma-vega covariance factor?

Hmm, I’m not sure about this, Vidit. Let me check.

Hey there!! Karthik

When you say, “An inexperienced trader can be caught unaware of this and still be under the impression that he is well under his risk radar. But in reality his risk exposure is getting higher” in the view of a trader shorting ATM options, which have high gamma, which means they have greater risk, i understand all of it, the one thing i need to clarify is,

when you say risk, i believe that it’s risk related to volatility, how quick can the premiums change, and this factor doesn’t change the fact that the maximum amount one can lose no matter what is the premium or (premium*no.of lots), so in a trade shorting ATM option or high gamma option if one is aware of the fact that they should risk more than a trade involving low gamma option coz high gamma premiums move faster, one can be confident enough to take a short trade on ATM options (high gamma options) right?

It is actually the risk related to the delta, the change of delta (which is dictated by gamma) and its overall impact on the position. Higher the gamma, higher is the risk. Of course, volatility is also a risk factor, depends on your position…but that is out of context in this discussion. Btw, the maximum amount that you can lose in a long position is restricted to the premium paid and for short positions, its the margin blocked.

Yeah! That’s right, thank you

Cheers!

Shouldn’t the line “2. Strike values below 80 (65, 70, 75 etc) are ITM and values above 80 (85, 90, 95 etx) are OTM options.” read as “Strike values below 80 (65, 70, 75 etc) are OTM and values above 80 (85, 90, 95 etx) are ITM options.”

My bad. As I read again the the sentence makes sense. Probably stating the same as “CE options below 80 (65, 70, 75 etc) are ITM…..” will make it more clear

Thanks, will try and fix that 🙂

In this example you have given above..

“Now, assume Nifty moves 70 points against him and the trader continues to hold his position, hoping for a recovery. The trader is obviously under the impression that he is holding 10 lots of options which is within his risk appetite…

Let’s do some forensics to figure out behind the scenes changes –

Delta = 0.5

Gamma = 0.005

Change in underlying = 70 points

Change in Delta = Gamma * change in underlying = 0.005 * 70 = 0.35

New Delta = 0.5 + 0.35 = 0.85

New Position Delta = 0.85*10 = 8.5”

What will happen if that 70 points move in trader’s favour?? Please explain!!!

It means that the option transitions more into a ITM option, which means the delta goes closer to 1 and starts behaving like a futures instrument.

Hey Karthik !

Really great work.

I just had a quick doubt …in the section “13.2 – Estimating Risk using Gamma”. When the trader is trading 10 ATM CE . I understand his delta per lot would be 0.5 since it is an ATM CE. However, Shouldn’t his overall position Delta should be -ive 5 since he is shorting CE ( 0.5 * -10).

Either we consider the sign with Position or with Delta.

My long Call Options have a delta between 0 to 1

My long Put Options have a delta between 0 to -1.

So by that logic, when I am shorting, either Delta sign should change or sign in front of potion should change ( to indicate I am short).

Extrapolating above logic equation in section 13.2 should like this according to me :

Delta = 0.5

Number of lots = 10

Position Delta = -10 * 0.5 = -5 or Position Delta = 10 * -0.5 = -5

Also, if you look from another perspective….When you are long Future, your direction expectation is “Spot going up” and when you are Shorting Calls, your direction expectation is ” Spot not going up or going down” so that you get to keep the premium when option expire worthless. CONSIDERING both bets are on opposite direction shouldn’t their position Delta be of opposite sign too.

I am a bit confused with this part. Some clarity would be great. 🙂

Hoping to hear from you

When you are long futures, the directional expectation is that the spot will go up. This is same as long call. When you are short call, you expect the market to not go up. Similar to shorting futures. So different signs 🙂

[…] 13. Gamma (Part 2) […]

Hello Karthik

You have asked a question and asked us to write our answer in comment box. That’s why I am trying to answer to your question

“What will be the Gamma for future?”

I have paused studying further and trying to answer to your question first. Let me know whether I am right or wrong

Ans. : Since delta of future always remain 1 then there should not be question of Gama I think. So No Gama

Regards

Satish Baichwal