Discrete-Time, Minimum-Variance Hedging of European Contingent Claims

This paper addresses minimum-variance hedging of European contingent claims (ECC) in the case where trading dates are discrete and fixed. A simple derivation of the minimum-variance hedging strategy is first given in a general setting. The strategy is then applied to a general class of European contingent claims written on an underlying asset whose price process is a martingale modeled by a geometric Brownian motion. A Wiener space setting is used to show that the minimum-variance strategy requires the asset holding to equal the ratio of conditional expectations of the changes in the ECC payoff and the underlying asset price that occur when sample paths of the Wiener process are modified in a certain manner. In the case of specific claims, the minimum-variance hedging strategy can be further expressed in terms of pricing functions. Unlike previous work, the results of this paper apply equally well to simple as well as path-dependent claims.