Lookback option pricing for regime-switching jump diffusion models.

*(English)*Zbl 1347.91234Summary: 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.) |

##### Keywords:

lookback options; jump-diffusion models; floating strike; Markov chain approximation; integro-differential partial differential equations
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\textit{Z. Jin} and \textit{L. Qian}, Math. Control Relat. Fields 5, No. 2, 237--258 (2015; Zbl 1347.91234)

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