Lookback option pricing for regime-switching jump diffusion models

Zhuo Jin; Linyi Qian

doi:10.3934/mcrf.2015.5.237

Article Contents

2015, Volume 5, Issue 2: 237-258. Doi: 10.3934/mcrf.2015.5.237

This issue Previous Article Feedback optimal control for stochastic Volterra equations with completely monotone kernels Next Article Largest space for the stabilizability of the linearized compressible Navier-Stokes system in one dimension

Lookback option pricing for regime-switching jump diffusion models

Zhuo Jin^1, and
Linyi Qian^2,

1.
Centre for Actuarial Studies, Department of Economics, The University of Melbourne, VIC 3010
2.
School of Finance and Statistics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241

Received: May 31, 2014

Revised: July 31, 2014

Published: May 2015

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Abstract

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 regime-switching model, the jump process involved, 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.

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Mathematics Subject Classification: 60H35, 91G20, 91G80, 65C05.

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