Do Lead-Lag Effects Affect Derivative Pricing?

Abstract

A well-known feature of the Black-Scholes (BS) model and others in that framework is that the mean return on the underlying asset does not enter the option price, only the volatility. But, as Lo and Wang [1995] showed, the actual drift process must be taken into account correctly in order to estimate the volatility from observed returns. If the underlying follows a mean-reverting Ornstein-Uhlenbeck (O-U) process but the drift is treated as a fixed constant, the estimated volatility will overstate the true value. In this article, Korn and Uhrig-Homburg extend the analysis to the problem of estimating the correlation between two O-U processes when the drift for one may lead or lag the drift for the other. They demonstrate how this affects the estimation problem and develop formulae to correct the answers. They then illustrate their approach on three important types of problems: index-linked stock option plans, cross-currency derivatives, and mutual fund performance fees. Specific examples show that the estimation problems described in the article can be quite significant in the real world.