Optimal static quadratic hedging

Tim Leung and Matthew Lorig

Quantitative Finance, 2016, vol. 16, issue 9, 1341-1355

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.

Date: 2016
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Working Paper: Optimal Static Quadratic Hedging (2015)
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DOI: 10.1080/14697688.2016.1161229

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