Optimal Static Quadratic Hedging

TL;DR

This paper introduces a model-free framework for static hedging of contingent claims using vanilla options and other instruments, minimizing expected squared error under cost constraints, with practical approximation methods and numerical examples.

Contribution

It provides a novel, model-free method for optimal static hedging that accounts for asset dependence and offers analytical approximation techniques in Markov diffusion markets.

Findings

Effective static hedging strategies for various options

Analytical approximation methods demonstrated in numerical examples

Versatile approach applicable to path-dependent and correlated options

Abstract

We propose a flexible framework for hedging a contingent claim by holding static positions in vanilla European calls, puts, bonds, and forwards. A model-free expression is derived for the optimal static hedging strategy that minimizes the expected squared hedging error subject to a cost constraint. The optimal hedge involves computing a number of expectations that reflect the dependence among the contingent claim and the hedging assets. We provide a general method for approximating these expectations analytically in a general Markov diffusion market. To illustrate the versatility of our approach, we present several numerical examples, including hedging path-dependent options and options written on a correlated asset.