Non-structural Option Pricing

Abstract

The Black-Scholes-Merton option pricing model, described in Chapter 10, critically relies on the assumption that asset price follows a log-normal diffusion process. A direct consequence is that volatility deduced from the BSM formula should be constant across exercise prices and across maturities. In Section 11.1, we illustrate that the log-normal assumption does not hold in practice. Implied volatilities of options of different strike prices are not the same, and in addition the volatility smiles are different from one maturity to another. These two features contradict the log-normal diffusion assumption and suggest that option pricing models more general than the BSM model are required. We then explain in Section 11.2 that state prices may be inferred from option prices. In a continuous setting, prices of future states will be given by a state price density. This state price density is often referred to in the literature as a risk-neutral densitie (RND).