Article2011

Methods for Pricing American Options under Regime Switching

79 citations0/0 files storedSIAM Journal on Scientific Computing

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Stochastic processes and financial applications Advanced Numerical Methods in Computational Mathematics Adaptive Dynamic Programming Control

Abstract

We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations. Numerical tests indicate that a fixed point policy iteration, coupled with a direct control formulation, is a reliable general purpose method. Finally, we remark that we formulate the American problem as an abstract optimal control problem; hence our results are applicable to more general problems as well.

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References

2005Applied Stochastic Control of Jump Diffusions 1977THE VALUATION OF AMERICAN PUT OPTIONS 1977The Valuation of American Put Options 2001A Regime-Switching Model of Long-Term Stock Returns 2002Quadratic Convergence for Valuing American Options Using a Penalty Method 1998Penalty methods for American options with stochastic volatility 2004Robust numerical methods for contingent claims under jump diffusion processes 2004A penalty method for American options with jump diffusion processes

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2012A radial basis collocation method for pricing American options under regime-switching jump-diffusion models 2014An optimal stochastic control framework for determining the cost of hedging of variable annuities 2014Financial options pricing with regime-switching jump-diffusions 2018COS method for option pricing under a regime-switching model with time-changed Lévy processes 2019An IMEX‐BDF2 compact scheme for pricing options under regime‐switching jump‐diffusion models

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