Articlegreen2001

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

Andrea Buraschi · Jens Carsten Jackwerth

219 citations0/0 files storedReview of Financial Studies

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Stochastic processes and financial applications Financial Markets and Investment Strategies Financial Risk and Volatility Modeling

Abstract

The volatility smile changed drastically around the crash of 1987, and newoption pricing models have been proposed to accommodate that change. Deterministic volatility models allowfor 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&P 500 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 inconsistent with deterministic volatility models but are consistent with stochastic models that incorporate additional priced risk factors, such as stochastic volatility, interest rates, or jumps.

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References

1973The Pricing of Options and Corporate Liabilities 1993A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options 1973Theory of Rational Option Pricing 2005Theory of rational option pricing 1976Option pricing when underlying stock returns are discontinuous 1991Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation 1987The Pricing of Options on Assets with Stochastic Volatilities 1979Martingales and arbitrage in multiperiod securities markets

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