LO 15.7: Describe volatility term structures and volatility surfaces and how they may be used to price options.
The volatility term structure is a listing of implied volatilities as a function of time to expiration for at-the-money option contracts. When short-dated volatilities are low (from historical perspectives), volatility tends to be an increasing function of maturity. When short-dated volatilities are high, volatility tends to be an inverse function of maturity. This phenomenon is related to, but has a slightly different meaning from, the mean-reverting characteristic often exhibited by implied volatility.
A volatility surface is nothing other than a combination of a volatility term structure with volatility smiles (i.e., those implied volatilities away-from-the-money). The surface provides guidance in pricing options with any strike or maturity structure.
A traders primary objective is to maintain a pricing mechanism that generates option prices consistent with market pricing. Even if the implied volatility or model pricing errors change due to shifting from one pricing model to another (which could occur if traders use an alternative model to Black-Scholes-Merton), the objective is to have consistency in model-generated pricing. The volatility term structure and volatility surfaces can be used to confirm or disprove a models accuracy and consistency in pricing.
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