The Price of a Smile : Hedging and Spanning in Option Markets

The volatility smile changed drastically around the crash of 1987 and new option pricing models have been proposed in order to accommodate that change. Deterministic volatility models allow for more flexible volatility surfaces but refrain from introducing additional risk-factors. Thus, options are still redundant securities. Alternatively, stochastic models introduce additional risk-factors and options are then needed for spanning of the pricing kernel. We develop a statistical test based on this difference in spanning. Using daily S&P500 index options data from 1986-1995, our tests suggest that both in- and out-of-the-money options are needed for spanning. The findings are nconsistent with deterministic volatility models but are consistent with stochastic models which incorporate additional priced risk-factors such as stochastic volatility, interest rates, or jumps.