### 9.1 – Theta of an Option

All options – both Calls and Puts lose value as the expiration approaches. The Theta or **time decay factor** is the rate at which an option loses value as time passes. Theta is expressed in points lost per day when all other conditions remain the same. We will learn more in this video.

We recommend reading this chapter on Varsity to learn more and understand the concepts in-depth.

**Key takeaways from this chapter**

- Option sellers are always compensated for the time risk
- Premium = Intrinsic Value + Time Value
- All else equal, options lose money on a daily basis owing to Theta
- Time moves in a single direction hence Theta is a positive number
- Theta is a friendly Greek to option sellers
- When you short naked options at the start of the series you can pocket a large time value but the fall in premium owing to time is low
- When you short option close to expiry the premium is low (thanks to time value) but the fall in premium is rapid

Sir, will there be a video series on options strategies?

No plans for now, Poornesh.

could u explain why theta is friendly to option seller

With passage of time, theta increases and premium loses more value, which is good for sellers.

Basic logic behind selling —> Sell High Buy low

As all options – both Calls and Puts lose value as the expiration approaches.

Theta is friendly to option seller

RIGHT

Thank you Karthik Ji and team.

I would like to call you ‘PANDIT ’, coz person who is able to give us a deep insight into a subject is called Pandit

I am new to stock market world, whatever I know about stock market world, it’s because of you & Zerodha Varsity team. Thank you so much.

I have been reading modules available on this platform. I have few doubts in Option Theory, instead of annoying you about repeated question, I spent almost 10-12 hours reading all the 1914 comments, I found only 3-4 traders raised doubt regarding my Query No.1 (as follows) and you responded that you will look into this and reply. But I think still this query is unanswered. So I decided to put into the comments. I know you might be busy, but I request you to please find some time and solve this query.

Query 1:

a) In section 15.3 you have calculated Nifty & TCS lower range and upper range by directly subtracting and adding S.D. from their respective spot prices respectively (without adding/subtracting volatility to average value and doing rest of the calculations) {Eg. from section 15.3 is as: 8547-(16.5%*8547)=7136 & 8547+(16.5%*8547)=9957}

b) In section 17.4, you have calculated Nifty’s range for next 1 year with 68% & 95% confidence. Here you have added and subtracted 1SD or 2SD to Nifty’s average value and then you have taken exponential of these two (as we have calculated S.D. with Log to the base ‘e’) and multiplied to the spot price to get Nifty’s range for next 1 year. {Eg. from section 17.4 is as: 8337*exp (1.15%+5.73%)= 8930 & 8337*exp(1.15%-5.73%)=7963}

c) In section 18.1, you have calculated Nifty’s range till expiry (for 16 days) with 68% confidence. Here you have added and subtracted 1SD to Nifty’s average value and then without taking exponential of these two %, you have directly added & subtracted these % to Nifty’s spot price. {Eg. from section 18.1 is as: 8462 [1+(0.65%+3.567%)]=8818 & 8462 [1+(0.65%-3.567%)]= 8214}

Here are some observations:

Point 1: In a) & b) you have directly added/subtracted % to spot price to get the range, but there is slight difference between these two. In a) you haven’t added/subtracted S.D. to average value & calculated range and In b) you have added/subtracted S.D. to average value & calculated range. {e.g. from Section 17.4 : 1.15% +5.73%= 6.88% & 1.15%-5.73%=-4.58%}

Point 2: In b) & c) you have added/subtracted S.D. to average to calculate range, but difference between these two is as: In b) you have taken exponential of % and calculated the range of Nifty {e.g. from Sect 17.4 : 8337*exp (1.15%+5.73%)= 8930 } in c) you haven’t taken exponential of % to calculate range of Nifty. (eg. from section 18.1 : 8462 [1+(0.65%+3.567%)]=8818}

Point 3: average % is not taken with function of ‘Log’ to the base ‘e’, while calculating S.D. %, it is taken with function of ‘Log’ to the base ‘e’ (section 16.1). So how can we add these two % (average & S.D.) directly?

So kindly clarify which method to use.

Whether we should add/subtract S.D. to average OR not???? And accordingly which calculation method to use, with spot price multiplied by Exponential of % OR spot price should directly be multiplied by % to get range. (spot price shouldn’t be multiplied by exponential of %)

Query 2:

In section 18.2, you expect airtel trade to materialize over next 5 trading session. I have heard this from many persons that they expect particular stock XYZ to hit the target with certain ‘T’ (suppose) time period/trading sessions. So I want to know how one can predict or expect particular stock to materialize with certain trading sessions.??? Your guidance on this please.

Please please please solve query no. 1 & your guidance on query no. 2 (as usual). Thank you in advance.

Have replied to your query in ‘Volatility Basics’, chapter as well. I need sometime to respond to your query. I will get back.

Here are the exact steps to calculate the price range –

1) Calculate the daily log returns

2) Calculate the mean and SD

3) 68% confidence interval is – Current Price * Exp (mean*time +/- SD *Sqrt (time))

4) 95% confidence interval is – Current Price * Exp (mean*time +/- 2*SD *Sqrt (time))

The process in computationally intensive as it involves the calculation of mean, log returns, exponential etc. You can approximate it with simpler calculations –

1) For short time period (say for 1 year data), the (Mean*time) is so small that it hardly makes any difference to the final value i.e. Mean * time << SD * Sqrt (time) 2) When daily % movements <10%, % returns and log returns are nearly same. So use % returns instead of logs Faster approximation : 1) Calculate % return 2) Calculate SD and Mean 3) 68% confidence interval = Current price * (1 +/-SD*Sqrt(time)) 4) 95% confidence interval = Current price * (1 +/-2*SD*Sqrt(time)) I may have switched techniques between accurate and faster methods between chapters, hence all the confusion. If you are developing a system, go for a simpler method. If the price range is >20%, then calculate using the accurate method.