# Option Maths and Markets¶

## What model are you using to price options and calculate IVs?¶

We use an improvised Black 76 model instead of the conventional Black Scholes model, which suits Indian markets better. Most professional traders across the country use the same.

In this model, we use the futures price instead of the stock price and ignore interest rate, dividends, etc as these are implied in the futures price. Also, when futures are in discount, a positive interest rate will result in big errors in the Black Scholes model.

## How do you calculate IVs?¶

We use the price and derive the IV by reverse calculation using the Black 76 model

## Why is the IV on NSE website different from Sensibull’s IV?¶

NSE uses Black-Scholes model with a constant interest rate assumption of 10%. The observed interest rate in the market is not 10% but it varies from time to time with changes in Reserve Bank’s repo rate and interbank lending rates.

This fault can be very clearly inferred by the fact that IV of the ATM put and call are two significantly different values in NSE option chain whereas they should both have the same IV.NSE shows separate IVs for calls and puts.

The problem with here is deep ITM options. Deep ITM options prices are corrupted by illiquidity and STT. So to find the IV at a strike, the better thing to do is to derive OTM IV of a strike, and apply the same to both call and put. Basically one IV for a strike, instead of a separate call and put. Also reduces mental clutter We use a Black 76 model, which corrects for the anomaly of interest rates, by using futures prices directly. This helps us capture the futures premium and discount, as well as any dividends etc more accurately than NSE's model

## Is the IV mentioned in the calculator for the Call or Put?¶

We always calculate IV for a strike from the OTM option of a Strike. ITM IVs are wrong because of low liquidity, and STT.

Example: Market is at 10400.If you ask us 10800 IV we will tell you the 10800 call IV. If you ask us 10000 IV we will tell you the 10000 Put IV

## Why is the IV on the call and put the same in your option chain? Why don't you have two separate IVs?¶

In academic theory, as well as in an efficient market, the call and put IV should be the same for the same strike. Examples include US / EU markets and OTC currency.

But before we go to the why, to be clear, let us repeat the what:

1. Call and puts of the same strike should have the same IV, theoretically

2. Calls and puts of different strikes will have different IVs, theoretically

In Indian equities you could see that this is not always the same. This is because:

1.STT affects ITM option prices and brings down volatility.

2.Wide bid-offer spreads, and off prices in illiquid ITM options will get you an off IV value

3.Also, we noticed that other platforms in India including NSE assume a constant interest rate `r = 10` and calculate Put and call options IVs using spot. This assumption is wrong because `r` does not remain constant. This is clear from the fact that sometimes stocks go in discount which violates the implied value of a positive `r`. We use the future price so that the `r` is implied and captured correctly. This `r` assumption gets some calculators to give different call and put vol. Theoretically, if Put and Call options have different volatilities at the same strike, there will be an arbitrage opportunity. You can try it yourself using the following calculation:

Put Call Parity says that Call Price - Put Price = Future Price - Spot Price. If you try this equation with different values of IV, the numbers won't add up. To rectify this, we use the IV of the OTM option for a strike, and put the same number for both calls and puts of the same strike.

For example, when NIFTY is at 11500 and we have to calculate the 11000 IV, we only look at the OTM option, which is the 11000 Put. We find the IV of that put and show the same IV for the 11000 Call.

## Why are IVs different across different strikes?¶

This is because of IV skew. Usually, in equities IV is higher for lower strikes, and higher for lower strikes.

## How do I interpret Theta?¶

Theta is not always positive. Theta is positive or negative depending on whether you have net earning time value decay or losing time value decay.

Theta positive, that is you are earning time value decay, normally means net you have sold options. Theta negative, you are losing time value every day, usually means net you have bought options.

## How do you handle things like dividends in your model?¶

We use the futures price instead of the underlying stock price. Future prices capture the expected dividend correctly and cleanly. This is all the more a reason why to use our calculator instead of the conventional Black Scholes calculators.

## How is STT Calculated? How do you deal with it?¶

STT, or securities transaction tax is paid whenever you buy or sell options. The STT you pay on selling options is small, so we can ignore it here. But STT on options you buy is BIG when they expire in the money. That is, you have to pay a big STT when you bought an option and it expires in-the-money (Stock Price>Strike for Calls, and Stock Price<Strike for Puts).

Say NIFTY is at 10000. The STT amount is .00125% of the underlying, which comes to 10000 .00125%75 = ~950 per lot of NIFTY.

You have to pay STT only on expires, which means you can avoid STT if you square off the in-the-money option anytime before expiry. However, the market knows that there is some STT on the option, and the price you realize will factor is some STT, which is typically half of the STT. We calculate option prices adjusted for this half STT.

## How do you compute PCR?¶

We do not calculate the PCR off one expiry only, we calculate it off the next three expiries. The reason for this is:

Sometimes there is significant OI in the next expiries, which cannot be neglected. A typical example is, there have been cases, even last year, there was action in Feb series of NIFTY in December. People were betting on the budget IV. In the last week of expiry, OI build up starts for the next month. That has to be accounted for

## Why is selling options better than buying options?¶

When you sell options, you gain time decay every day. When you buy options, you lose time value every day. Assuming all other things as constant - in buying options time works against you and in selling options time works for you.

You would want time to work in your favour, right?

## What is this Bank NIFTY implied weekly future?¶

Options are priced off the underlying futures. NIFTY options are priced off the NIFTY Jan Future.

However, for BANK NIFTY weekly options, there is no such thing as weekly futures. So we derive the theoretical weekly future price from the weekly call option and put option using Put call parity.

In other words, this is the price of the Weekly future, had it existed.

## Why do you not have Bank Nifty weekly IVP?¶

Bank Nifty weekly IVPs are misleading. This is because any movement on a Tuesday or Wednesday will spike the IVs due to lower Vega. And Fridays will have a lower IV majorly due to weekend effect and higher Vega.

So the IVPs will stay at high 80s and 90s percentile for almost every Tuesday and Wednesday, and will stay low on Fridays. Since this has nothing to do with IVs, or volatility, we decided to pull this number down.

The general idea is that any percentile system which compares will work well only in homogenous and somewhat uniform samples. We are trying to implement a more realistic metric for IV of bank nifty after normalilsing for these anomalies

## Special Expiry Warning¶

Note that today 17-Oct-18 is Banknifty weekly expiry for contract ending this week NOT tomorrow. NSE will be closed tomorrow for Dussehra.

So please close your weekly option trades ending 17-Oct-18. Do not let In The Money Options expire without closing. Please note that STT (Securities Transaction Tax) on BUY option positions that get exercised - means are in the money when the expiry day trading is closed- is 0.125% of the entire CONTRACT VALUE. Which is around 1200 Rs on every lot of Bank Nifty.

If you do not close in the money options you will unnecessary pay extra STT. Please avoid that and close latest by 3.15 pm to be safe.