Variance Minimizing Strategies for Stochastic Processes with Applications to Tracking Stock Indices

Abstract

This paper extends the notion of variance optimal hedging of contingent claims under the incomplete market setting to the hedging of entire processes, and applies the results to the problem of tracking stock indices. Sufficient conditions under which this is possible are given, along with the corresponding variance optimal strategy in feedback form as given in Schweizer (1996) and Pham, Rheinlander, and Schweizer (1998) for contingent claims. The performances of tracking error variance minimizing, locally risk minimizing, and variance minimizing strategies in tracking stock indices are investigated using both simulated and historical market data.