Implementing Option Pricing Models When Asset Returns are Predictable

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 a. 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.