Black-Equivalent Volatility

Can Someone Explain to me what this term means, and how it's used?

Answer

Quite a lot of options on asset $S(t) > 0$ have a payoff at tinme $T$ equal (at least approximately -- it's a bit more complicated in the case of e.g. credit index options)

$ (S(T) - K)^+ $

You can always find a number $\sigma$ such that, when plugged into Black formula together with strike $K$, spot price $S(t)$, interest rate $r$ and time to expiry $T-t$, you will recover the market price of the option $V(t)$. This number is called the Black implied volatility of the option. Basically, it's a quoting convention for the option prices. Traders use it because:

• it makes it easier for them to compare prices of options on different days, with different strikes


• Black vols tend to be similar across strikes and expiries (not always!)


• it is better (in the sense: you're less likely to suffer lots of arbitrage) to interpolate market prices in the $\sigma$ space then directly; that is, if prices for strikes $K_1$ and $K_2$ are quoted, it's better to use some interpolation method on their Black vols $\sigma_1$ and $\sigma_2$ than on their prices $V_1$ and $V_2$


• it fits their intution better (a paramount argument)