Option Pricing and Hedging for Regime-Switching Geometric Brownian Motion Models
26 Pages Posted: 27 Apr 2015 Last revised: 24 Dec 2016
Date Written: December 23, 2016
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
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