Implied Volatility and Skew

Of all the inputs into the Black-Scholes option pricing model, the only one that’s not knowable is volatility. Interest rates might change slightly over the term of the option, but any change is likely to be fairly small and the effect of changes (the rho sensitivity we discussed in Chapter 4) in interest rates on option values is usually even smaller. While dividends might not be precisely knowable, particularly for longer-dated options, we can generally be very confident of the dividend stream, and even for those longer-dated options we can come really close to knowing the amount and timing of dividend payouts. These other inputs are absolutely certain and knowable: time to expiration, strike price, and call or put. Volatility, on the other hand, is anyone’s guess—and nearly everyone has a guess. In fact, nearly everyone has several guesses.

The volatility measure we’d like to know—the one that, if we had it would allow us to precisely calculate the correct value for an option—is the realized volatility of the underlying instrument from the time we initiate our option position to the time the option expires. This is the volatility we’ve discussed previously.

Even if we intend to exit our option trade prior to expiration there’s no way to be certain the market price of the option would reflect the correct volatility when we wanted to exit. The only way to make certain that we’ve got the right number is to take our position to expiration when ...

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