Hedging options in a hidden Markov‐switching local‐volatility model via stochastic flows and a Monte‐Carlo method

Abstract

AbstractThe hedging of European contingent claims in a continuous‐time hidden Markov‐regime‐switching diffusion model is discussed using stochastic flows of diffeomorphisms and Monte‐Carlo simulations. Specifically, the price dynamics of an underlying risky asset are governed by a continuous‐time hidden Markov‐modulated local‐volatility model. Filtering theory is used to estimate the unobservable drift given observable price information and to define a filtered market with complete observations. The delta–hedge ratio of a European option is derived using a martingale representation and stochastic flows of diffeomorphisms. The numerical computation of the delta–hedge ratio is estimated via Monte‐Carlo simulations. Numerical results for illustrating the proposed method and the (relative) importance of the impacts of the information risk and the local‐volatility parametrizations on the delta–hedge ratio are provided for the case of European call options.