Implementing Option Pricing Models When Asset Returns are Predictable

The predictability of an asset's returns will affect option prices 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