Implementing Option Pricing Models When Asset Returns are Predictable

55 Pages Posted: 1 Sep 2000

See all articles by Andrew W. Lo

Andrew W. Lo

Massachusetts Institute of Technology (MIT) - Sloan School of Management; National Bureau of Economic Research (NBER); Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

Jiang Wang

Massachusetts Institute of Technology (MIT) - Sloan School of Management; China Academy of Financial Research (CAFR); National Bureau of Economic Research (NBER)

Multiple version iconThere are 2 versions of this paper

Date Written: April 1994

Abstract

Option pricing formulas obtained from continuous-time no- arbitrage arguments such as the Black-Scholes formula generally do not depend on the drift term of the underlying asset's diffusion equation. However, the drift is essential for properly implementing such formulas empirically, since the numerical values of the parameters that do appear in the option pricing formula can depend intimately on the drift. In particular, if the underlying asset's returns are predictable, this will influence the theoretical value and the empirical estimate of the diffusion coefficient å. We develop an adjustment to the Black-Scholes formula that accounts for predictability and show that this adjustment can be important even for small levels of predictability, especially for longer-maturity options. We propose a class of continuous-time linear diffusion processes for asset prices that can capture a wider variety of predictability, and provide several numerical examples that illustrate their importance for pricing options and other derivative assets.

Suggested Citation

Lo, Andrew W. and Wang, Jiang, Implementing Option Pricing Models When Asset Returns are Predictable (April 1994). NBER Working Paper No. w4720. Available at SSRN: https://ssrn.com/abstract=240793

Andrew W. Lo (Contact Author)

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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Massachusetts Institute of Technology (MIT) - Computer Science and Artificial Intelligence Laboratory (CSAIL)

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Jiang Wang

Massachusetts Institute of Technology (MIT) - Sloan School of Management ( email )

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United States
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China Academy of Financial Research (CAFR)

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China

National Bureau of Economic Research (NBER)

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