Equity Options Vega and Implied Volatility

What is Implied Volatility?

Implied Volatility of an option is the market’s expectation of future realised volatility of the underlying equity up to a given maturity.

How do we use the Black-Scholes model to extract implied volatility from market option prices?

The Black-Scholes formula allows us to convert a fair option price, which is determined from the market by aggregating all buyers and sellers, into an annualised volatility which we call the implied volatility. We can 'imply' the volatility because the other inputs to the model are known and so the only unknown is the volatility which we can then solve for to arrive at our desired option fair value.

What is Vega & term structure of volatility?

Vega is the shift in option value caused by an increase in implied volatility of 1% or 1 vol point. You are Long Vega if you are long an option. As the implied volatility increases, the time value increases and the option gains in value.  If the implied volatility went down to zero, the option would lose all its time value and be only worth its intrinsic value (if it had any).

We can trade options of many different expiries. These different expiries or maturities do not have to be priced on the same implied volatility for any given asset. We can see that implied volatility has a term structure, similar to a yield curve in interest rates, when we plot vol on the y-axis and maturity on the X-axis. The shape of that term structure can vary depending on market conditions.

How do we calculate weighted vega?

Because of the way the variable of time appears in the BS model, we infer that the acceptable weighting factor to use is 1/sqrt(T), where T is maturity in years. It is also the market convention and accurately reflects how we observe volatility surface changes on a daily basis.

What is Forward Volatility?

It is the implied volatility for a specific period of time in the future between two points on the curve.