A Closed-Form Solution for the Global Quadratic Hedging of Options Under Geometric Gaussian Random Walks

Abstract

A closed-form solution is obtained for the discrete-time global quadratic hedging problem of Schweizer (1995) applied to vanilla European options under the geometric Gaussian random walk model for the underlying asset. The computation of coefficients embedded in the closed-form expression can be computed either directly or through a recursive algorithm.

Keywords: Variance-Optimal Hedging, Risk Management, Closed-Form Solution, Gaussian Random Walks

JEL Classification: G32, C61