Optimal Hedging of American Options in Discrete Time

27 Pages Posted: 23 Dec 2010 Last revised: 21 Sep 2011

See all articles by Bruno Remillard

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Hugues Langlois

HEC Paris - Finance Department

Alexandre Hocquard

Pavilion Advisory Group; HEC Montreal - Department of Finance

Nicolas A. Papageorgiou

HEC Montreal - Department of Finance

Date Written: December 21, 2010

Abstract

In this article we study the price of an American style option based on hedging the underlying assets at discrete time. Like its European style analog, the value of the option is not given in general by an expectation with respect to an equivalent martingale measure. We provide the optimal solution that minimizes the hedging error variance. When the assets dynamics are Markovian or a component of a Markov process, the solution can be approximated easily by numerical methods already proposed for pricing American options. We proceed to a Monte Carlo experiment in which the hedging performance of the solution is evaluated. For assets returns that are either Gaussian or Variance Gamma, it is shown that the proposed solution results in lower root mean square hedging error than with traditional delta hedging.

Keywords: Hedging, European Option, American Option, Risk

JEL Classification: G11, G13

Suggested Citation

Remillard, Bruno and Langlois, Hugues and Hocquard, Alexandre and Papageorgiou, Nicolas A., Optimal Hedging of American Options in Discrete Time (December 21, 2010). Available at SSRN: https://ssrn.com/abstract=1729421 or http://dx.doi.org/10.2139/ssrn.1729421

Bruno Remillard (Contact Author)

Department of Decision Sciences, HEC Montreal ( email )

3000 Côte-Sainte-Catherine Road
Montreal, QC H2S1L4
Canada
514-340-6794 (Phone)

Hugues Langlois

HEC Paris - Finance Department ( email )

France

Alexandre Hocquard

Pavilion Advisory Group

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

HOME PAGE: http://www.hec.ca

Nicolas A. Papageorgiou

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

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