The calculation of the VIX is based on the popular Black & Scholes model for option valuation. Before getting into the mathematics of Black & Sholes, let us understand the concept underlying the model. The mathematical formula for VIX is as under:

The above formula of Black and Scholes only allows you to find out the value of an option. How do you use that to calculated VIX? You slightly reverse the above formula. Instead of treating option value as unknown, you assume that the option price represents the option value. Therefore, the missing piece is volatility that is implied in the option valuation. Once the IV is calculated for a strike, it is repeated for a series of strikes of the Nifty and based on that the VIX is calculated.

Let us possibly now recap this whole idea of VIX. We tweak this formula a little bit. Instead of finding the fair value of option, we assume the option price is the fair value of the option. We then use the other inputs and then calculate the missing volatility figure. This is called implied volatility (IV) as it is the volatility that is implied in the option market price. When the IVs of a series of Nifty strikes of puts and calls are combined the outcome is the VIX index. Since the VIX captures the volatility assumption in various strikes, it becomes a good and reliable gauge of the extent of risk perception in the market.

Of course, there are simpler excel sheets available and your trading terminal itself allows you to calculate the Black & Scholes options value by merely imputing the input values. Let us look at what the Black & Scholes formula calculates and the key factors that determine the value

The calculation of the VIX is based on the popular Black & Scholes model for option valuation. Before getting into the mathematics of Black & Sholes, let us understand the concept underlying the model. The mathematical formula for VIX is as under:

The above formula of Black and Scholes only allows you to find out the value of an option. How do you use that to calculated VIX? You slightly reverse the above formula. Instead of treating option value as unknown, you assume that the option price represents the option value. Therefore, the missing piece is volatility that is implied in the option valuation. Once the IV is calculated for a strike, it is repeated for a series of strikes of the Nifty and based on that the VIX is calculated.

Let us possibly now recap this whole idea of VIX. We tweak this formula a little bit. Instead of finding the fair value of option, we assume the option price is the fair value of the option. We then use the other inputs and then calculate the missing volatility figure. This is called implied volatility (IV) as it is the volatility that is implied in the option market price. When the IVs of a series of Nifty strikes of puts and calls are combined the outcome is the VIX index. Since the VIX captures the volatility assumption in various strikes, it becomes a good and reliable gauge of the extent of risk perception in the market.