Optimal hedging in discrete time

TL;DR

This paper derives explicit formulas for optimal mean square hedging in discrete time for multidimensional assets, including regime-switching and GARCH models, and compares these with delta hedging through simulations.

Contribution

It extends previous work by providing explicit formulas for optimal hedging in complex models like regime-switching and GARCH, with empirical comparisons.

Findings

Optimal hedging formulas reduce mean square error.

Monte Carlo simulations show advantages over delta hedging.

Explicit solutions facilitate practical implementation.

Abstract

Building on the work of Schweizer (1995) and Cern and Kallseny (2007), we present discrete time formulas minimizing the mean square hedging error for multidimensional assets. In particular, we give explicit formulas when a regime-switching random walk or a GARCH-type process is utilized to model the returns. Monte Carlo simulations are used to compare the optimal and delta hedging methods.