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

The 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.