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Stochastic Volatility and Option Valuation: A Pricing-Density Approach

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  • Longstaff, Francis A.

Abstract

We develop a simple closed 0form valuation model for options when the volatility of the underlying asset is stochastic. Out approach differs from previous research in that we model the pricing density directly. We show that implied volatility estimates from the Black-Scholes model can be very misleading, even when at-the-money options are used in the estimation. We also illustrate that the smile effect in index option prices can be explained by allowing changes in volatility to be correlated with index returns.

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  • Longstaff, Francis A., 1995. "Stochastic Volatility and Option Valuation: A Pricing-Density Approach," University of California at Los Angeles, Anderson Graduate School of Management qt1wg89967, Anderson Graduate School of Management, UCLA.
    • Handle: RePEc:cdl:anderf:qt1wg89967
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    Cited by:

    1. Eberlein, Ernst & Keller, Ulrich & Prause, Karsten, 1998. "New Insights into Smile, Mispricing, and Value at Risk: The Hyperbolic Model," The Journal of Business, University of Chicago Press, vol. 71(3), pages 371-405, July.
    2. Scharfenaker, Ellis, 2020. "Implications of quantal response statistical equilibrium," Journal of Economic Dynamics and Control, Elsevier, vol. 119(C).

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