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Lookback option pricing for regime-switching jump diffusion models. (English) Zbl 1347.91234
Summary: In this paper, we will introduce a numerical method to price the European lookback floating strike put options, where the underlying asset price is modeled by a generalized regime-switching jump-diffusion process. In the Markov regime-switching model, the option value is a solution of a coupled system of nonlinear integro-differential partial differential equations. Due to the complexity of the regime-switching model, the involved jump process, and the nonlinearity, closed-form solutions are virtually impossible to obtain. We use Markov chain approximation techniques to construct a discrete-time Markov chain to approximate the option value. Convergence of the approximation algorithms is proved. Examples are presented to demonstrate the applicability of the numerical methods.
MSC:
91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods
65C40 Numerical analysis or methods applied to Markov chains
60J75 Jump processes (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
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