## 21.1 – Background

So far in this module we have discussed all the important Option Greeks and their applications. It is now time to understand how to calculate these Greeks using the Black & Scholes (BS) Options pricing calculator. The BS options pricing calculator is based on the Black and Scholes options pricing model, which was first published by Fisher Black and Myron Scholes (hence the name Black & Scholes) in 1973, however Robert C Merton developed the model and brought in a full mathematical understanding to the pricing formula.

This particular pricing model is highly revered in the financial market, so much so that both Robert C Merton and Myron Scholes received the 1997 Noble Prize for Economic Sciences. The B&S options pricing model involves mathematical concepts such as partial differential equations, normal distribution, stochastic processes etc. The objective in this module is not to take you through the math in B&S model; in fact you could look at this video from Khan Academy for the same –

My objective is to take you through the practical application of the Black & Scholes options pricing formula.

## 21.2 – Overview of the model

Think of the BS calculator as a black box, which takes in a bunch of inputs and gives out a bunch of outputs. The inputs required are mostly market data of the options contract and the outputs are the Option Greeks.

The framework for the pricing model works like this:

- We input the model with Spot price, Strike price, Interest rate, Implied volatility, Dividend, and Number of days to expiry
- The pricing model churns out the required mathematical calculation and gives out a bunch of outputs
- The output includes all the Option Greeks and the theoretical price of the call and put option for the strike selected

The illustration below gives the schema of a typical options calculator:

On the input side:

**Spot price** – This is the spot price at which the underlying is trading. Note we can even replace the spot price with the futures price. We use the futures price when the option contract is based on futures as its underlying. Usually the commodity and in some cases the currency options are based on futures. For equity option contacts always use the spot price.

**Interest Rate** – This is risk free rate prevailing in the economy. Use the RBI 91 day Treasury bill rate for this purpose. You can get the rate from the RBI website, RBI has made it available on their landing page, as highlighted below.

As of September 2015 the prevailing rate is 7.4769% per annum.

**Dividend **– This is the dividend per share expected in the stock, provided the stock goes ex dividend within the expiry period. For example, assume today is 11^{th} September and you wish to calculate the Option Greeks for the ICICI Bank option contract. Assume ICICI Bank is going ex dividend on 18^{th} Sept with a dividend of Rs.4. The expiry for the September series is 24^{th} September 2015, hence the dividend would be Rs.4. in this case.

**Number of days to expiry** – This the number of calendar days left to expiry

**Volatility **– This is where you need to enter the option’s implied volatility. You can always look at the option chain provided by NSE to extract the implied volatility data. For example, here is the snap shot of ICICI Bank’s 280 CE, and as we can see, the IV for this contract is 43.55%.

Let us use this information to calculate the option Greeks for ICICI 280 CE.

- Spot Price = 272.7
- Interest Rate = 7.4769%
- Dividend = 0
- Number of days to expiry = 1 (today is 23
^{rd}September, and expiry is on 24^{th}September) - Volatility = 43.55%

Once we have this information, we need to feed this into a standard Black & Scholes Options calculator. We do have this calculator on our website – https://zerodha.com/tools/black-scholes , you can use the same to calculate the Greeks.

Once you enter the relevant data in the calculator and click on ‘calculate’, the calculator displays the Option Greeks –

On the output side, notice the following –

- The premium of 280 CE and 280 PE is calculated. This is the theoretical option price as per the B&S options calculator. Ideally this should match with the current option price in the market
- Below the premium values, all the Options Greeks are listed.

I’m assuming that by now you are fairly familiar with what each of the Greeks convey, and the application of the same.

One last note on option calculators – the option calculator is mainly used to calculate the Option Greeks and the theoretical option price. Sometimes small difference arises owing to variations in input assumptions. Hence for this reason, it is good to have room for the inevitable modeling errors. However by and large, the option calculator is fairly accurate.

## 21.3 – Put Call Parity

While we are discussing the topic on Option pricing, it perhaps makes sense to discuss ‘Put Call Parity’ (PCP). PCP is a simple mathematical equation which states –

**Put Value + Spot Price = Present value of strike (invested to maturity) + Call Value**.

The equation above holds true assuming –

- Both the Put and Call are ATM options
- The options are European
- They both expire at the same time
- The options are held till expiry

For people who are not familiar with the concept of Present value, I would suggest you read through this – http://zerodha.com/varsity/chapter/dcf-primer/ (section 14.3).

Assuming you are familiar with the concept of Present value, we can restate the above equation as –

P + S = Ke^{(-rt)} + C

Where, Ke^{(-rt)} represents the present value of strike, with K being the strike itself. In mathematical terms, strike K is getting discounted continuously at rate of ‘r’ over time‘t’

Also, do realize if you hold the present value of the strike and hold the same to maturity, you will get the value of strike itself, hence the above can be further restated as –

**Put Option + Spot Price = Strike + Call options**

So why should the equality hold? To help you understand this better think about two traders, Trader A and Trader B.

- Trader A holds ATM Put option and 1 share of the underlying stock (left hand side of PCP equation)
- Trader B holds a Call option and cash amount equivalent to the strike (right hand side of PCP equation)

This being the case, as per the PCP the amount of money both traders make (assuming they hold till expiry) should be the same. Let us put some numbers to evaluate the equation –

Underlying = Infosys

Strike = 1200

Spot = 1200

Trader A holds = 1200 PE + 1 share of Infy at 1200

Trader B holds = 1200 CE + Cash equivalent to strike i.e 1200

Assume upon expiry Infosys expires at 1100, what do you think happens?

Trader A’s Put option becomes profitable and he makes Rs.100 however he loses 100 on the stock that he holds, hence his net pay off is 100 + 1100 = 1200.

Trader B’s Call option becomes worthless, hence the option’s value goes to 0, however he has cash equivalent to 1200, hence his account value is 0 + 1200 = 1200.

Let’s take another example, assume Infy hits 1350 upon expiry, lets see what happens to the accounts of both the trader’s.

Trader A = Put goes to zero, stock goes to 1350/-

Trader B = Call value goes to 150 + 1200 in cash = 1350/-

So clearly, irrespective of where the stock expires, the equations hold true, meaning both trader A and trader B end up making the same amount of money.

All good, but how would you use the PCP to develop a trading strategy? Well, for that you will have to wait for the next module which is dedicated to “Option Strategies” J. Before we start the next module on Option Strategies, we have 2 more chapters to go in this module.

### Key takeaways from this chapter

- The options calculator is based on the Black & Scholes model
- The Black & Scholes model is used to estimate the option’s theoretical price along with the option’s Greek
- The interest rate in the B&S calculator refers to the risk free rate as available on the RBI site
- The implied volatility can be fetched from the option chain from the NSE website
- The put call parity states that the payoff from a put option plus the spot equals the payoff from call option plus the strike.

When can we expect Option Strategies Module..?

Very soon, another 2 chapters in the current module and we move to Options Strategies.

sir,what happens to overnight futures position in case of stock split like adani ent,idfc today

The F&O positions get adjusted accordingly, check this – http://www.nseindia.com/content/circulars/FAOP30855.pdf

I notice that the delta of 280 PE is -0.873. But, only deep ITM have such high deltas, right?

Where did you get this value from Ajay?. Delta should be less than -0.5.

Think i got my answer. By the way, eagerly waiting for the next chapter. 🙂

Next chapter (22) will be uploaded next week Ajay.

sir,why should we use calender days in calculating theoratical option value,when trading days excluded whats use,enlighten me

Well, the number of days is treated on something called as the ‘day count convention’…NSE adopts a day count convention called as ‘actual by actual’ according to which you need to take 365 days.

Hi In the black scholes option calculator the input for IV is one but the theoretical prices for both put and call are computed based on that one IV INPUT Whereas in reality the IV puts and call for the same strike differ, so using which IV can be better? Can we use the VIX % instead?

Vix is a good approximation for Nifty. For stock specific IV check the stock’s option chain for IV.

As per Khan Academy video the Implied Volatility (IV) is not an input to Black-Scholes (BS) formula. The input to BS formula is standard deviation of log returns. In fact the IV is calculated by applying BS formula in reverse, see the link to khan academy video that explains how IV is calculated:

https://www.youtube.com/watch?v=VIHldsSmASU

I believe the BS formula if fed with standard deviation of log returns would give provide (predict) option price which may differ slightly form the actual price that is settled in market.

Sunil, yes I’m aware of that. In fact check this http://zerodha.com/z-connect/queries/stock-and-fo-queries/option-greeks/how-to-use-the-option-calculator . From what I’ve noticed people tend to get confused with reverse engineering BS model to calculate IV’s, so we decided not do it with the our version of BS calculator. We are trying to keep this very simple and intuitive.

Hello Karthik,

We have learned so far that when you buy ATM options , delta is in the region of 0.5-0.6 and as the trade goes in favor , delta increases and therefore for every 1/- move on the stock/index, we get higher (>0.6 ) move on the option…………I want to understand the opposite side…..

When i buy ATM options and the positions go against me on the same day, i am assuming that delta will reduce and i will lose less than 0.5 or 0.6 pts in relation to a 1 pt move against me…..Let me explain with an example….Suppose i go long on 7900 CE when nifty breaks through 7940 and then i decide to keep a 40 pt stop loss. I expect to lose around 20 pts (give and take a couple of points) in options if my SL is trigerred. However my observation is that often i lose close to 40 pts in options as well. What can i attribute this loss to? Most times, SL gets triggered on the same day, so time value impact is minimal…..I am guessing vega plays a role but at all times???? What could i be missing?

Regards,

Prashant

Prashanth – When underlying moves by one point, the premium is expected to move to the extent of delta. So if the delta is 0.6, then for every one point move in the underlying, premium is expected to move by 0.6 points.

I’m elaborating your case here – You buy 7900CE (ATM), premium is 180/-, Delta is 0.5. Spot moves to 7940, 40 points increase..so new premium will be old premium plus delta times movement in the underlying. Hence new premium is 180 + (0.5*40) = 200. However now that spot is at 7940 (slightly ITM) delta is 0.6 (approximate value). While you have a 40 point SL on underlying the premium will react a bit differently. So if market falls by 40 from 7940, then you will lose 40*0.6 = 24 points. So…that would take the new premium to 200 – 24 = 176 points.

Besides, as you mentioned, Vega has a massive impact on options premiums.

Next chapter pls..

Next week.

Nowadays U r taking too much of time (abt 15days),pls reduce the time at least to 1week..

Keshav – you dont want me to write rubbish right? So please give me the time, I will make sure the content is worth your patience 🙂

Dear karthik,

i think some small typos in 2 places one in icici option input eg.& prashanth nairs Q&A

icici option price calculation interest rate typed as 4769% inteaad of 7.4769%•

prasanths case,

regarding premium calculation 180 + (0.5*40) =220,this is not 220,but 200 and calculation is right 220 – 24 = 196,but as per eg.we should subtracct from 200-20=180.

Ah, thanks for pointing this, will look into it.

Karthik, good efforts thanks, i hope you are well aware the greek calculatore, in

ODIN Diet, when you select paricular stock or strike and click CTRL + pg up, a window pop up with BS calculatore, which have all input information as default ,you just click on calculate and will get all output, hope you also can do that.

Not sure how it works on ODIN diet, but if you are using NEST you may want to check this – http://zerodha.com/z-connect/queries/stock-and-fo-queries/option-greeks/how-to-use-the-option-calculator

Karthik,you are a very innovative person and trying to give latest and best trading system to your client, hence request to look in to that system, i am sure you will appreciate.

Will do, thanks.

When you will post “Option strategy” in Varsity? any specific timeline?

Just uploaded the last chapter in this module – http://zerodha.com/varsity/chapter/case-studies-wrapping-it-all-up/

Starting work on next module soon.

Very good explanation in a simple way. In MBA i studied Derivatives during my higher education, but it was all theoretical and also difficult to implement in real world. This explnation was really help. But i have some doubts.

https://zerodha.com/tools/black-scholes in this page you are telling to calculate historical volatility to calculate option price, where as in this web page http://zerodha.com/varsity/chapter/greek-calculator/ you are telling to calculate option price using implied volatility. Could you pls explain

I’m glad you liked the explanation 🙂

The historical volatility is a simple “Quick & Dirty” approximation.

For Nifty options,what can be the dividend.

Depends on Nifty itself. Check this for data – http://www.nseindia.com/products/content/equities/indices/historical_pepb.htm

as per your link nifty ‘s today’s dividend is 1.51 right?

Yes.

For Nifty Premium calculation In BS options, in the Spot (underlying) option whether nifty index value or current month future value to be entered?

Spot is fine.

Does the theta derived in BS clculator denotes the decay of premium per day .Is it so.The varsity article doesn’t mention that.

Yes, theta is the decay in premium value attributable to passage of time, provided all else is equal. Let me check this again on Varsity. Thanks.

Which module covered Rho ?

Not covered Rho, as Rho indicates the change in premium wrt to change in interest rate. Interest rate does not change that often, hence decided to skip this Greek.

Sir,

Can i get Balck schole option formula in excel spread sheet so as its is convenient to home work on it

Regards,

Mayur

Check this – http://www.stern.nyu.edu/~igiddy/spreadsheets/black-scholes.xls

Hello sir,

I am satish srinivasan and I am trading in my sister’s account.Till date I haven’t succeeded in trading and I haven’t asked anybody’s help I don’t know who is the technical person who is supporting traders at zerodha my personal wishes to him.I hope if you lend your hand to me it will be very useful. I hope a conversation with a wise man around a table is as good as reading thousand many books.

Dear sir,

If you are reading this, I think I am close to you.If I could able to come this far, I think I can come little further.I will keep an eye out for you. I will be hoping that this letter finds you.

Satish – not sure with whom you need to speak. We will be more than happy to respond to queries posted here, so please do not hesitate asking questions here.

What’s Rho?

Rho is the rate of change of premium with respect to change in interest rate.

sir, i just calculated option Greeks of usd inr and current call option premium is 0.2700 but in option calculator show option premium is 0.1600 is it ok or is there any mistake ? and also in theta put option have no theta please explain !!!

Well the option calculator gives you the theoretical option price of an asset based on the factors playing out in the market. It is not necessary that it should match the current market price.

Not sure about the Theta, will check and get back. Thanks.

sir,

in volatility box actually which volatility have to enter, call option iv or put option iv? please explain

In fact you can use ViX values (for Nifty) for both Calls & Puts.

Dear Sir,

Regarding using of vix values for both call and put, I would like to seek your clarification that can I use the same vix volatality ie suppose today which is showing 17.35 at that particular moment of entering into a strategy for both call and put same vix. thanks and regards. r v n sastry

Yes, you can use the same ViX values to get the approximate Greek values.

What is options smile

Explained here – http://zerodha.com/varsity/chapter/greek-interactions/

Refer section 20.1

1. In RBI site 91 day T bill is blank, what does it implies?

2. where to find wipro is going to give in feb month or not, to enter dividend on B&S calsulator?

You need to enter in a value – the interest rate of the T bill. This is available on the RBI website.

Dividend info is available as and when its made available.

T bill value is empty in rbi website I have encircled that

Oh, in that case you can take the 180 day bill rates.

tatamotors

spot-340

strike-360, contract expiry- 25 feb

actual premium obtained from nse website or 360CE-7.70

I have attached the snapshot of values got by B&S calculator

Delta-.357,Gamma-.0089

Now suppose spot moves by +25 points and new spot is 365.

so the below calculations-

new premium- 7.70 + 25*(.357) = 16.63

new delta- .357 + 25*(.0089) = .579

My question is delta is constantly changing with change in underlying(stock), so from what point onwards premium should be calculated with new delta and not the old one? Means if calculate premium with delta .357 different value of premium will come, and if I stop in between and calculate premium after increase of 10 points( of stock) then new delta value will come and premium corresponding to this will be different

This is a tricky problem Rohan. In reality the Delta is a continuously evolving variable and it does not stop to change till expiry. For all practical purposes, its best if you define your timeframe and evaluate the deltas at that period.

If I enter values in B&S calculator it gives values of delta,gamma etc for both call and put options for given spot ( 1200) and strike (1220).

But if IV of call and put option is different than what should be entered in calculator? I have encircled different IV’s for same strike

I assume you are talking about the B&S calculator on Zerodha. We’ve put up a very basic version of the calculator. You need to be aware of which option you are calculating for and enter the relevant IV.

sir,

i enter all data for getting option greek for USDINR 68.75 CE . 25 FEB EXPIRY. AND I GOT THE OUTPUT BUT I THING IT IS NOT CORRECT DATA BECAUSE IT SHOWING GAMMA OF : 1.6398 PLEASE FIND THE SCREENSHOT AND PLEASE EXPLAIN .,

Thanks for posting this, Gamma of an ATM option invariably shoots up as we approach expiry. However I think this gamma value is extremely high. Let me dig in deeper and get back to you as soon as I can. Thanks.

Thanks for the quick reply,…and i am waiting for the more information…

Sure, thanks.

today (25.02.2016) i look the nifty option chain but i cant see any strikes IV , In IV column showing blank, please find the screenshot and please explain

Not sure why, you will have to speak to NSE for this.

how to find Intrest and volatility parameter values on dialy basis, is there a way to get/find them, answer to this will be much appreciated

Interest rates don’t change daily, so that should not worry you much. For stock specific volatility information I’m not sure where we will find it…maybe you will have to calculate it yourself. From my experience, knowing the rough volatility figure is good enough, unless you are dealing with some volatility sensitive trades. For Nifty, I’d suggest you check ViX, that will give you an approximation.

Hi sir by using block and scholes calculator for nifty vix i have give as input for volatility % , but if i do same thing giving vix as input to volatility % in case of bank nifty theoretical values are far different from actual price , here what should we given as input to volatility in case of bank nifty .thanks in advance

You can use ViX value for Nifty but not bank Nifty. I’d suggest you look under ‘other information’ here for Bank Nifty’s volatility numbers – https://www1.nseindia.com/live_market/dynaContent/live_watch/get_quote/GetQuoteFO.jsp?underlying=BANKNIFTY&instrument=FUTIDX&type=-&strike=-&expiry=28APR2016

Hey, Karthik.

1.How does RBI interest rate effect options? Can you share some details on it?

2.How to find dividend for stock rather than Index as you have posted in earlier reply.

The effect of interest rates are captured by a Greek called Rho, I skipped discussing this as Interest Rates dont change frequently. In general interest rate and options premium have an inverse relationship.

You will have to keep track of corporate events for info on dividends, bonus, splits etc.

Can you refer any site where I can track of corporate events for dividends, bonus, splits etc of each stock in NSE/BSE? I have searched in many but didn’t get any appropriate result.

Thank you

Moneycontrol has this option, check this – http://www.moneycontrol.com/company-facts/itc/board-meetings/ITC#ITC

thank you. I searched in money control but didn’t get at that time.

Sure, good luck!

In the NSE option chain, the Interest rate considered is 10% (Note at the bottom).

Why is it different from RBI [91 day T Bill] Interest Rate?

Isn’t it appropriate to consider the interest rate mentioned in NSE, because that is the basis we pay as premium ultimately while trade?

Also do we have to separately calculate the Daily Volatility, although it is mentioned in NSE Quote Page? Can we take the same value while calculating the premium (for Options) or stop-loss (for Futures) – I understand that knowing how to calculate is a better to understand the concept as covered in Chapter 7.

Ah! I never noticed the interest rate bit in the option chain. Thanks for pointing that out. Not sure why NSE assumes 10%, it does not make sense to me. Also, there is no harm taking the values from NSE…although its good to know how to crunch the number!

Well, Thanks to you for such wonderful modules and in-depth explanation!

I tried to calculate the premium and Greeks based on the description in the module, using Zerodha Black & Scholes Options calculator, but it was not matching the NSE option chain. When we put the values of Interest rate and volatility as per NSE website, the figures mostly match.

Yes, we have taken the interest rates as per the t-bill rates.

Dear Karthik,

When we put all data in Black & Scholes calculator we get the present premium of the stock/index. But how to calculate the future premiums. For example; shorting Nifty 8800 CE at 62/-. If Nifty rises to 9000 what will be the premium. How to calculate.

Thanks

You can do that using the Delta, this will give you an approximate value.

While going thro NSE website to read volatality of Bata, nothing is mentioned in the column. In that case what fig. need to be put in Black Scholes formula.

Yes, if you are referring to the Implied volatility. If you are talking about historical volatility, I’d suggest you use the the ‘=STDEV’ function in excel.

Karthik, firstly thankyou for the great explanation. and i have a small doubt, in the above video there is only B&S call option formula THEN what is the formula for B&S put option ?

Thanks&Regards

The calculation for Put option is quite similar Rakesh.

Karthik, Im very confused about IV and vega

actually my doubt is , in the B&S formula should i input IV which is shown in options chain(IS THAT IMPLIED VOLATILITY NOT VEGA )?

how is that IV calculated for different strikes? is it same as theSD calculation?

Please karthik please clear the doubt

Thanks&Regards

Yes, it is IV.

I would suggest you read this post to know how exactly you can use the B&S calculator – http://zerodha.com/z-connect/queries/stock-and-fo-queries/option-greeks/how-to-use-the-option-calculator

Hi Karthik, can we calculate the IV of a specific strike through using the LTP’s (premiums) of past 1year of that strike and can we find out SD or IV of that particular strike ?(yes or no). correct me if im wrong.

Thanks&Regards

IV is more like the volatility at this moment…its kind of forward looking. Moment we look at volatility we are referring the the ‘realized/historical’ volatility.

Hi Karthik, Is there any link on Zerodha where we can find options strategies based on our view on market, acceptable P/L range, etc like it is provided in following link:

http://www.theoptionsguide. com/option-trading-strategies.aspx

I think it is good, may be little improvisation possible, considering Greeks as well.

Nothing as of now Santosh…but don’t be surprised if we have something like this soon 🙂

Thanks Karthik, I am sure you guys will definitely come up with something better than that. All the best. 🙂

🙂

Hi Karthik,

Great Explaination !!!! thanks alot.

I have following queries

1) from where do i get the value of ViX

2) When i calculate Option Pricing using BS Calculator with IV of Call option with 10% interest rate and IV Put option with 10% interest rate (different IV for Call and Put from NSE option Chain with 10% interest rate) then Greek values of BS calculator matches with NSE Option chain. But when you put 91 day Tbill interest rate then values doesn’t matches. Why do so?

1) India ViX values are available on NSE, please do take a look at their website.

2) That’s because NSE considers 10% interest rate values.

Hi Karthik,

I have gone through this module….you have done wonderful job ……

As i am newbee to options ….Pls correct me if i am wrong .After reading all the chapters what i have concluded is the options trading requires all Greek consideration as well as view on the broader market(if trading on the Nifty)/underlying assset. isn’t it?

Every chapter is specific to individual greeek and very much clear. When it comes to trading , i couldn’t able implement.

Can you list down the mechanical rules while trading options. Ex : If i want to trade only on Nifty index then how to start building trade plan.

Thank you !!!!

Hello Sir, After reading all related chapter of option,Its really wonderful.Thanks alot for ur effort

Doubt: After doing technical analysis,I put the stop loss according to the my spot price .i.e i calculate the stoploss price and see the delta value…and according to that i m trying to use it but failed to do successfully because i am not able to correctly estimate the the combination all the Greek at once.there is any calculator for intraday or positional position to solve my problem..I tried black and scholes calculator and not able to understand how to calculate the target/stopploss using greek value.Please guide me sir…Thanks in advance.

Avinash – If you wish to identify SL price, I’d suggest you stick only to technical analysis. As far my experience goes, apart from vega, no other greeks helps you identify sl/entry prices.

Dear Karthik

I have a question on period or duration of Implied Volatility. When we calculate historical volatility, we calculate it for a particular period like – daily or annual or 30 days etc.

Does Implied Volatility refer to any particular forward period ? For example, If Implied volatility of Bank Nifty Call Option 24 Nov 2016 is 24% , does it mean market is expecting a volatility of 24% in the index value of for the next year or only till option expiry date ?

Yes, it does. If the IV is 24%, then its the market’s volatility expectation (at this very moment) for the next 1 year forward.

Hi Karthik,

I was trying to use the option calculator and stumbled upon this strange thing on NSE website while looking at different nifty strikes for Jan 2017. This 8250 PE for Jan series shows a net change of +118 points and 7750 PE shows +44 points but for almost all other strikes the net change was in negative. can you help me understand?

This must be the option chain 🙂

Different strikes behave differently for the same movement in the underlying. The option chain summarizes these changes along with other changes. Understanding option chain requires you to have some background in options. I’d suggest you start from chapter 1.

Thanks Karthik, your teachings changed our approach to the trades with conviction.

I have a query,

30-Jan,idea cellular,call 95CE SPOT WAS AT 78,IV:45,delta 0.05,gamma:0.012(as per zerodha option calc) now spot has moved by 20 points to 98,delta is supposed to be 0.6 to 1.but manual calc of new delta shows 0.29 or 0.3. (0.05+0.012*20)Why is that? Am I missing something

Yes, since the spot is at 98, 95CE is ITM and the delta is likely to be 0.7 or higher. Not sure why the calculator is not reflecting this value. Can you please check again?

Daily volatility calc as per excel is different from number shown on nse,difference observed was 14 -15 bips,similar difference is observed for annualised volatility as well.IS THIS NORMAL

Yeah, I guess it is because of the date selection.

Hello kartik how to calulate implied volatility in excel

Not sure, you will have to adopt one of the models which will help you calculate the same.

Hi karthik sir

i got an problem while understanding B&S calculator

I tried it eith nifty 50 figures such as

Strike 9350, spot 9198, premium is 32,Expiry 27/4/17

And according to formula premium arises at 22.76 for calls and 147.78 for Puts

sir i wanna ask you is this future value for premium or current fair valye which should be????

If this future value then for which date

Thanks

Have a nice day

It is the fair value of the premium for the give strike and spot value.

Thanks for everything…….

Welcome!

Dear Karthik,

What’s the formula to calculate the call and put options Gamma, Theta & Vega using excel.

Regards,

Sonjoe Joseph

I’ve not gotten into the formula as it can deep dive into quants. But just to give you a direction – the formula is a 2nd order differentiation of Black & Scholes formula.

Hello Sir,

I tried to calculate option greeks using https://zerodha.com/tools/black-scholes/

But it is giving different premium values.

Here are the screen shots. Please have a look.

for call https://www.indishare.me/06atgb24fp0h (when IV is used for call i.e 9.44)

for put https://www.indishare.me/l1jgg3zzh57p (when IV is used for put i.e 10.23)

and this is from nse https://www.indishare.me/jguznjki6vlw

It is giving some different values. Please let me know what mistake i am making.

Not sure why the difference, but I’d like to believe our calculator is accurate.

means input values are correct?

also i wanted to know that IV will be according to call and put? right?

IV should be same for both call and put for the given strike. However, you may notice some difference here.

Hello,

what are all the ways to find ( PCR is steadily rising and declining)?

You will have to stick to regular PCR techniques. Its been tried and tested, cant go too wrong 🙂

Hi,

I am still in the process of learning. Can you please tell me how many days before Ex-Dividend date I need to buy the stock and keep so that I can enjoy the dividend. Is this possible or else do I need to keep it for 1 complete year so that I get the dividend. I am confused. Also I see that there is lot of buying and selling happening when the Ex-Dividend date is nearby and on that day. Can you please brief on this please.

You need to buy the stock before the Record date. I’d suggest you check this – https://zerodha.com/varsity/chapter/five-corporate-actions-and-its-impact-on-stock-prices/

Sure will check the link. Thank you 🙂

Welcome!

How can I calculate option pricing for strike price of 350 in option chain image of ICICIBANK above since IV is not given?

Check this – https://zerodha.com/tools/black-scholes/ along with this – https://zerodha.com/z-connect/queries/stock-and-fo-queries/option-greeks/how-to-use-the-option-calculator

The call and put delta calculated for ICICIBank ATM 280 strikes in the picture is 0.127 and -0.873 respectively. Aren’t these values for Deep OTM CE and Deep ITM PE.

Also I notice that: Delta (CE) + Delta (PE) = 1 in this case. Does this mathematically hold true everytime?

PS: Thank You for the modules. This has indeed helped me and others to gain a much deeper understanding of the Financial Markets.

Yes, by virtue of delta it is deep OTM and ITM.

Yes, for ATM strike

Cheers! Happy learning 🙂

Does this mean, an option can be classified to have a different moneyness than its actual based on the greeks. And at same time, it can be classified as different moneyness by different greeks at the same moment in time (because the interactions is hanging everything dynamically every second)?

If yes, then what should we consider for a strategy (I haven’t read the option strategies module yet, maybe that will shed some light on this). For a delta neutral strategy, I guess we would consider just the deltas. But this is a wide variation if an ATM option is classified as Deep ITM/OTM. And it may soon change its delta. But say I want to build a strategy myself, what should matter most for a classification?

Sujeet, the moneyness comes for the difference between the strike and spot. The greeks do not really have a play on moneyness. However, the changes in the greeks itself can alter the moneyness 🙂

I’d suggest you take a look at the strategies module 🙂

WHICH SHOULD BE TAKEN AS SPOT VALUE in calculator for bank nifty.Underlying or future value?

Underlying.

It seems there is a difference between the values(from option calculator and actual market value?)…why sir?

The difference is expected. This can be attributable to the market inefficiencies. If you feel the difference is too high then you could sell the option, otherwise, buy….in both case hoping it would align to fair value.

Hey! About the dividend, if it’s within the period, then we write the value (in percentage terms I believe?), if not, we leave it as zero?

Yup.

hi,

from where can i get dividend rate in case of nifty in order to get nifty future value for the current expiry

Check here – https://www.nseindia.com/products/content/equities/indices/historical_pepb.htm

Greetings Karthik

Today 24.11.17 Nifty Spot closed @ 10390

Nifty Dec 10400 Call @ 175 and Nifty Dec 10400 Put @ 123

As per Black & Scholes Option Pricing Formula with volatility 13.5 call should be @ 163 & put should be @ 173

Both call & put are ATM

my question is

1. Why so much difference in premium?

2. What would be the expected move for nifty in coming days in such situation?

3. How would you trade in this type of situation?

4. Is it wise to buy a ATM put as the premium is low?

1) Two things – (a) If markets price the options wrong, then the difference could occur. But I suspect this is the case. (B) Your assumption on Volatility could be wrong

2) Hard to say

3) Assuming my volatility input is correct and the markets are pricing the options wrongly, I’d buy both the options as they are cheaper compared to their respective fair price.

4) Yes, for reason stated above.

Greetings Karthik

Thanks for your quick reply

volatility 13.5 is as shown in the NSE India Vix Website

call option is trading according to B&S Formula but why not put too

as for my 2nd question i am sure there must have been similar instances in history and you must be knowing the aftermath of such situations

If your pricing is correct, then you can make profitable trades as the market price will eventually catch up with the fair price. Anyway, I’m not sure if Nifty ATM puts can trade with such a large discount to fair price.

Greetings

Thank for your quick reply karthik

I am also little surprised to see such huge difference between 10400 ATM CALL & Put

What could be the reason

Will the put price rise later on

Check today, I’m assuming the prices have corrected.

Can you explain a bit further on your 3rd point

Please don’t mind, me asking silly questions.

Just clarifying myself.

You will have to tell me which 3rd point 🙂

First of all thank you karthik sir. I learned alot with Zerodha varsity. I tried to calculate Option premium by using zerodha B&S option premium pricing formula for Nifty as on 08.12.2017 closing time. the details are as below.

Case:1

Nifty Spot: 10265.65

Strike price: 10500

Expiry: 28.12.2017 15:30Hrs

Volatility: 13.67% (India VIX)

Interest: 6.15% (91 day T-bill rate from RBI website)

Dividend: 0

The output from B&S calculator is as follows

CALL OPTION PREMIUM- 49.41

The actual LTP premium price is 37.20

Case:2

Nifty Spot: 10265.65

Strike price: 10500

Expiry: 28.12.2017 15:30Hrs

Volatility: 10.57% (IV from NSE website)

Interest: 6.15% (91 day T-bill rate from RBI website)

Dividend: 0

The output from B&S calculator is as follows

CALL OPTION PREMIUM- 27.61

The actual LTP premium price is 37.20

it seems to be there is vast difference between actual premium and the theoretical premium calculated. Kindly explain me where did i got wrong and correct me.

Can you try entering the dividend value? You can get the data from here – https://www.nseindia.com/products/content/equities/indices/historical_pepb.htm

The dividend for Nifty 50 is 1.11 from NSE website. B&S fromula in Zerodha website not taking decimals. i tried with 1, 2, 3 so on. whatever the value of dividend the premium is not changing.

CALL OPTION PREMIUM for 10400 Strike is – 49.41 but The actual LTP premium price is 37.20.

Well, in that case, I think there is mispricing. Market partici[ants will correct this sooner or later.

I have calculated call option premium for Nifty 10600 strike

Case1: with implied volatility 11.61 ( from option chain)

the calculated premium is 21.97 where as actual LTP premium is 27.60

Case2:with annualised volatility 12.62 ( from futures contract )

the calculated premium is 27.57 where as actual LTP premium is 27.60. this is matching perfectly.

i have calculated premium for reliance 960 strike using volatility from option chain and futures contract. in this case the IV selected from option chain is giving better result.

my understanding is that volatility of future contract for nifty is giving better result whereas for stock IV of option chain is giving better result.

Kindly clarify which volatility have to be chosen.

You need to considered the implied volatility of the option for calculating the option’s premium. However, you’ve made an interesting point of futures volatility. Let me check if this can be taken as a substitute.

I have made position for Nifty 10600CE on 14.12.2017 (Nifty Spot is 10252) during closing hours of market at a premium of 25.62 in anticipation of market opens gap-up on the back of positive gujrat exit polls which will be announced later in the evening. Later in the day all the Exit polls predicted BJP majority.

Market Today as expected opened gap-up 94 points but not made any follow through. The premium for my position opened at 35.6 and dropped to 27 after 30 minutes of market opening, but the underlying Nifty fell only 20 points.

My question is why premium fell suddenly when underlying not fell substantially.

This is because the volatility dropped the next day and with that the premiums also did.

Hi Team,

It could be really better if we can view the Greeks in the ‘Positions Table’ in Kite..! Hope you will work on this..!

Thanks!

Noted. Will pass the feedback, Rajesh.

Hello Sir,

1.B&S options calculator is used to know the Greeks values for that strike as per the spot how the premium calculated based on the volatility?

Correct me if I am wrong.

2.If the first point is correct

Now I want to modify the volatility increase/decrease, I can get the theoretical option price as per the B&S options calculator

Is B&S options calculator used for test cases?

3.Ideally this B&S options calculator value should match with the current option price in the market

How can figure out if options are over or under-valued and if volatility itself is under or over-estimated.

Please clarify.

Thanks & Regards,

Siva.

1) Not too clear with this – can you please rephrase it?

2) Yes, you can use B&S to calculate premium prices by altering the implied volatility. So essentially you can test for different scenarios

3) Not necessarily, the market can misprice the option leading to the difference in price.

Hello Sir,

Thank you for clarifying.

Thanks & Regards,

Siva.

Good luck!

Hello sir,

Whenever I use option calculator this gives me the theoretical value of option premium and then I compare this value to the actual value of premiums most of the time I found that the option calculator is providing a value for premium which is less than the actual market price of the premium it means that premiums are expensive to trade from the buyer’s perspective right sir

So I should not buy the options??? Because they are expensive.

Thanks sir….

Ankit, the value obtained from the calculator is a theoretical value, whereas the value seen in the market is reflective of the sentiment prevailing in the market. If the difference is beyond an acceptable value then it does not make sense to buy…rather you can opt to sell them and collect the premium.

Yes exactly this is the dilemma that what should be the acceptable difference of theoretical value of premium and actual value of premium for buying purpose

Actually sir I have an open position in currency

Where I bought February expiry 63.75PE @0.3675 ITM and position is working for me but after buying this I realise that I paid much more than should I need to pay to buy this option

When I divided this premium into intrinsic value and time value I found that the intrinsic value something near 0.2625

I want to tell you that I got this intrinsic value from the following strike rate -RBI reference rate yesterday which was set by RBI @approx 64.54 like and after buying this the premium value actually dropped to that 0.2625 and came back after touching that level with my experience I observed that time value in ITM option THE TIME VALUE SHOULD NOT BE LIKE ABOVE

So to avoid this silly mistakes in future I have some question

1. is I bought an expensive option

2. How to calculate intrinsic value means what should be the formula

Is it strike -RBI reference rate OR strike – future rate or something else

By the way I was slightly bullish on Rupee but not sure about the future direction actually in coming future so I played safe and bout IDM option I expected some 40 to 50% value gain in 4 to 5 days

Thanks for help sir

Ankit, if the RBI Reference rate is 64.54, then the intrinsic value of 63.75PE is 0. So the entire premium of 0.3675 is attributable to the time value. Such high time value is justified since you’ve bought the Feb contract, which will expire only next month. Intrinsic value is a non-negative number or 0. It is Strike – RBI Ref, but if it is -ve number, then the IV is considered 0, hence the rest becomes attributable to the time value.

Thanks but I am sorry RBI reference rate was 63.54 not 64.54.

I mistakenly wrote that 64.54

But now I got the point clearly that

INTRINSIC VALUE(PE)= STRIKE PRICE – RBI REFERENCE RATE

Right sir,

Thank you so much sir

Yes, that makes sense now. Good luck with the trade and remember, the intrinsic value of an option is always a non-negative number or 0.

Karthik, i see for some of the strike priices the IV is 0 then, i am getting the call premium as 0. pls advice.

This is because the option has no trading volume, no liquidity.

By seeing chart without indicator people calculate target SL etc. in stocks.

How about option trading without Greeks, expert people calculate the approximate premium ? or Greeks is required only or with experience it will come ?

Delta, helps you identify the premium to some extent but that apart, you can gauge this in the backdrop of your experience.

Demand and supply role ?

in option premium say ATM option people are doing more trading that means more demand so price will increase, how it differ from voltality ?

Volatility dictates the extent by which the premium varies, demand supply does not.

Dear Kartik,

Seems in the BS calculator AV

Ok.

Dear Kartik,

Seems in the BS calculator AV input of over 100 is not seen captured in the provided model.Could you pls check?

Let me check this, I’m dont think this is hard coded. Anyway, well see. Thanks.

Karthik,

Testing checked for R com 50 CE current month expiry for an IV of 107.34.No output available.Till a volatility of 100 it is ok.

Ok. Looking into this. Btw, IV of over 100 is an extreme case 🙂

An applied DV of 5.25 can take AV to over 100 and it is not that extreme Karthik.Its only that its not visible because of lack of liquidity in options and traded price is looked into rather than the settlement price.In a sort Black swans are happening in individual scrips during random walks at many instances on a daily basis.May seem gibberish in economic thoughts but when I tested it seems a fact.

Very interesting. I do get your point on lack of liquidity and the isolated black swan events.

Hello Sir,

I’m just curious to know, we calculate our profits based on an assumed Delta value for a given option premium based on whether the strike price of the chosen option is either Deep ITM (Delta – 0.75 to 1), ITM (Delta – 0.5 to 0.75), ATM (Delta – 0.5), OTM (Delta 0.3 to 0.5) or Deep OTM (Delta 0 to 0.3). Obviously the spot price keeps changing during the open market and I’m assuming that the Delta of any given option MUST also change based on which category (Deep ITM, ITM, ATM, OTM and Deep OTM) it falls under, as the spot price fluctuates. Is my assumption true? If Yes, how often is the Delta for any given option recalculated. If Not, are the Delta’s of every option fixed throughout the day and decided at the opening price of the contract value? I would really appreciate your answer to this question.

You are right, Clifford. Delta changes with the change in the spot. The rate of change of Delta depends on the Gamma. I’d suggest you read this chapter on Gamma – https://zerodha.com/varsity/chapter/gamma-part-1/

Dear Karthik,

Seems NSE uses overnight MIBOR rates for risk-free interest calculation .Cant understand the logic why NSE uses 10 percent for IV calculations as showed in the note below option chain.

Not sure, Najeeb. By the way, do you have a link which says NSE uses MIBOR? Can you please share? Thanks.

Karthik,

Dont remember the exact para in Nse website . Posting here what I copied earlier from Nse notes. .. F = S * e rt where : F = theoretical futures price S = value of the underlying index r = rate of interest ( MIBOR) t = time to expiration. …

https://www.nseindia.com/gsa/NSE_Search.jsp?q=mibor%20rate

you may try this one too.

Sure, thanks, Najeeb.

Hi Karthik

I understand that prices are governed by market dynamics but, today I saw 10800 Option closing at Rs2.5 but, BS calculator shows this value as 0.32 (Interest rate 10% + IV 12.85) which is almost 10 times less than the theoretical value – this seems bit too much of a deviation – in your experience is this normal?

Are you sure you’ve used the right volatility input? Wrong IV inputs can lead to big changes in the premium.

Thanks Karthik. I think I used the correct IV but, will double check next time. Few more questions

1) BS is used for getting both Call & Put option premium but, in Nifty option chain the IVs for put and call (for same strike) are different – Different IVs I do understand the rationality but, then shouldn’t the BS have different inputs of Volatility for calculating premium / Greeks of Put and Call option in this case?

2) Does is make sense to use dividend yield per the data provided on NSE website when using BS claculator

3) At what time on the expiry day Options stops trading. I am asking this because today (31/05) as you must be aware Nifty went to 10763 around 3:08PM and I had shorted 10750 CE but still the option price was 1.05. Shouldn’t it have shot up to somewhere around 13Rs? Had the market closed more than 10750 making 10750 CE ITM would the difference have been deducted from my account when the contract was being finalized? – Also, Noted that around the closing 3:25PM the market went beyond 10750 for sometime – in this case should we square off the position or just let it expire because premium price was stuck at 0.05 at this time.

Hope my questions makes sense.

1) Technically speaking, the IV of both CE & PE should be the same for a given strike. But you won’t see this in the market as each strike has its own demand-supply situation, impacting the IVs. The procedure for calculating the greeks and premium for CE and PE is the same, which is what the B&S calculator does. You need to enter the relevant IVs to get the appropriate figures.

2) YOu can if you are dealing with Nifty

3) It trades till 3:30 PM. Maybe there was no liquidity in the contract?

Thanks a lot sir

Yes there was no liquidity in contract as, there was no one bidding. It was an eye opener for me as even 2SD can sometime not be safe 🙂

Also, say market had closed at 10760 then I would have suffered a loss of 10 Rs (as I wrote 10750 CE) and money would have been deducted from my account – Is my understanding correct?

Yes, this is right, you’d have a loss of 10 bucks.

Hi Karthik

I’ve heard of IV Rank and IV Percentile. Can you please explain them with examples? How to use them while trading options?

The concept is similar to Vol skew, will try and make a post on this soon. Thanks.

Dear Karthik

suppose canara Bnk in running at 255 today and i want to test the 280 CE rate with the help of B&S calculator. at this position which IV have to input , ATM Strike price input or my selected Strike (i.e – 280 CE) IV input? please clear the doubt.

Yes, Khurshid, you can actually input the ATM strike IV.

Hi,

I am not able to interpret the premium on the BS calculator. I input 26700 strike and spot as current close 26503 (Thursday close) volatility of 10.22(IV of 26700 strike) and interest rate of 6.48(RBI) and expiring coming Thursday (12th July)

The result is 70.66 Call option premium on BS.

Currently the 26700 closed at 88.5

Question-

How to interpret this? Intrinsic value is 70.6 and traded at 88.5? Ok so what now?

This means the market is valuing the option more than its theoretical value.

Hello Sir,

I would like to know suppose if call option is 34 and theta is -4 at the starting of the day at around 9.30 am…If all the Greeks and price remain the same at market closing at around 3.30 pm option premium will be reduced by theta value of -4 and premium will become 30 or on next day opening it will reduce by -4…theta is calculated on hourly basis or daily basis?

Theta is on a daily basis, so all else equal, the next day morning the option will open at 30.

does theta decay value shown in b&s calculator also considers non trading days that is saturday and sunday while giving its input.

for example at friday the theta of option is 0.5 and its preimium is 5 .Then all else equal will it open by monday at 3.5 or at 4.5.

It does, Omi.

Hi Karthik,

Thanks for varasity very helpful

I tried zerodha B&S calculator model for maruti 10000CE aug expiry it shows option price18.68 but as of now it is trading at price 24.55 can you tell me why the difference.

I have taken following inputs.

Spot price 9188.35 as on 3 aug

strike:10000

EXPIRY:30/08/2018

VOLATILITY:21.41

INTEREST:6.73

dividend:0

I think the volatility is much higher. Also, if the difference can be attributable to the difference in demand and supply.

Hi Karthik,

The current page https://zerodha.com/tools/black-scholes/ gives us a way to calculate the premium as seen currently. Is there a tool by zerodha to know the premium with time as future datetime as additional input along with spot price, volatility?

i.e., For example, i want to know what the premium of a certain option will be at Nov 20 or 22nd right now itself? (Assuming spot price, volatility i will input)

If not zerodha tool, can we do the same in excel?

I’m not sure if this is possible. But however, one way to do this is to reduce the time to expiry to your target date.

Oh right! Thanks for the hack., just didn’t think of it.

So as per the example i gave, when i want to know the expected premium of option on Nov 20, all i should do is calculate the number of trading sessions from Nov 20 to expiry date, let’s say N days.

And input the expiry date is calculator as (Todays date+N trading sessions), which should give me the premium. Am i right?

Just one last help the above calculator. It doesn’t work when the IV is beyond 100 (works for 100 though). I wanted to calculate the premium of option PCJEWELLER18NOV75, where it’s IV is 101.43 as of now, it doesn’t give any output.

Thats right, Vishal. Reduce the number of trading days and you will know what the fair price of the option on that day. I think IV has an upper limit at 100…will double check. Thanks.

Hi Karthik,

Looking at Greek values, Can we build any strategy for Option buying and selling, any inputs what delta/gamma/theta/vega should be to buy or sell Options.

Do we need to use RBI interest rate for other stocks as well like Infosys, TCS, Tata Motors etc or it is only for banking stocks.

Thanks

Abdul

Yes, you certainly can. Especially things like the straddle and strangle. All of that and more here – https://zerodha.com/varsity/module/option-strategies/

Hi Karthik,

Should I use interest rate from RBI for non banking stock as well like Infosys, TCS etc.

Thanks

Abdul

Yes, that works.