Implementing Option Pricing Models When Asset Returns Are Predictable

Authors

  • ANDREW W. LO,

  • JIANG WANG

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    • Both authors are from the Sloan School of Management, Massachusetts Institute of Technology. We thank Petr Adamek, Lars Hansen, John Heaton, Chi-fu Huang, Ravi Jagannathan, Barbara Jansen, René Stulz, and especially Bruce Grundy and the referee for helpful suggestions, and seminar participants at Boston University, Northwestern University, the Research Triangle Econometrics Workshop, the University of Texas at Austin, the University of Chicago, Washington University, the University of California at Los Angeles, the Wharton School, and Yale University for their comments. Financial support from the Laboratory for Financial Engineering is gratefully acknowledged. A portion of this research was conducted during the first author's tenure as an Alfred P. Sloan Research Fellow.

ABSTRACT

The predictability of an asset's returns will affect the prices of options on that asset, even though predictability is typically induced by the drift, which does not enter the option pricing formula. For discretely-sampled data, predictability is linked to the parameters that do enter the option pricing formula. We construct an adjustment for predictability to the Black-Scholes formula and show that this adjustment can be important even for small levels of predictability, especially for longer maturity options. We propose several continuous-time linear diffusion processes that can capture broader forms of predictability, and provide numerical examples that illustrate their importance for pricing options.

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