Option Pricing and Hedging for Regime-Switching Geometric Brownian Motion Models

26 Pages Posted: 27 Apr 2015 Last revised: 24 Dec 2016

See all articles by Bruno Remillard

Bruno Remillard

Department of Decision Sciences, HEC Montreal

Sylvain Rubenthaler

Université de Nice Sophia Antipolis

Date Written: December 23, 2016

Abstract

We find the variance-optimal equivalent martingale measure when multivariate assets are modeled by a regime-switching geometric Brownian motion, and the regimes are represented by a homogeneous continuous time Markov chain. Under this new measure, the Markov chain driving the regimes is no longer homogeneous, which differs from the equivalent martingale measures usually proposed in the literature.

We show the solution minimizes the mean-variance hedging error under the objective measure. As argued by Schweizer (1996), the variance-optimal equivalent measure naturally extends canonical option pricing results to the case of an incomplete market and the expectation under the proposed measure may be interpreted as an option price. Solutions for the option value and the optimal hedging strategy are easily obtained from Monte Carlo simulations. Two applications are considered.

Keywords: Hedging error, option pricing, regime-switching

JEL Classification: C15, C32, C61, G13

Suggested Citation

Remillard, Bruno and Rubenthaler, Sylvain, Option Pricing and Hedging for Regime-Switching Geometric Brownian Motion Models (December 23, 2016). Available at SSRN: https://ssrn.com/abstract=2599064 or http://dx.doi.org/10.2139/ssrn.2599064

Bruno Remillard (Contact Author)

Department of Decision Sciences, HEC Montreal ( email )

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

Sylvain Rubenthaler

Université de Nice Sophia Antipolis ( email )

Nice
France

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