Pricing options on assets with predictable white noise returns

We study the effect of predictability of an asset's return on the prices of options on that asset, for models in which returns are serially uncorrelated, yet predictable on the basis of a larger information set. We show that return predictability may matter in a discrete time world, especially for longer maturity options. However, discrepancies between the frequency of trading and observation become relevant in estimating the model parameters. When trading is continuous, Black-Scholes is valid, and the sample variance of holding returns over finite periods is an appropriate estimator of the variance of instantaneous returns.