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- W3122513784 abstract "This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we implement an implicit approach by explicitly treating the nonlinear terms and/or the linear terms from other regimes, resulting in computationally efficient algorithms. We establish an upper bound condition for the time step size and prove that under the condition the implicit schemes satisfy a discrete version of the positivity constraint for American option values. We compare the implicit schemes with a tree model that generalizes the Cox-Ross-Rubinstein (CRR) binomial tree model, and with an analytical approximation solution for two-regime case due to Buffington and Elliott. Numerical examples demonstrate the accuracy and stability of the new implicit schemes." @default.
- W3122513784 created "2021-02-01" @default.
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- W3122513784 date "2008-05-05" @default.
- W3122513784 modified "2023-09-26" @default.
- W3122513784 title "New Numerical Scheme for Pricing American Option with Regime-Switching" @default.
- W3122513784 hasPublicationYear "2008" @default.
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