A generalized approach for pricing american options under a regime-switching model

Regime-switching models gained their popularity over the past decade because of their distinctive advantage of modelling different financial market statuses in a discrete manner rather than a continuous manner as in stochastic volatility models. When they are used in option pricing, the clear advantage is that they enable a larger parameter space for models to be calibrated for a specific market dynamics and thus allow a better quantitative risk management in terms of utilizing financial derivatives. However, when they are used to price American-style financial derivatives, a large number of economic statuses result in a demand for improved computational efficiency. This paper provides a new algorithm of high computational efficiency supplemented with a theorem that pre-analyzes the associated matrices and their eigenvalues, without concern about the possibility of duplicated roots being mistakenly identified as simple roots due to rounding errors or the presence of two extremely closely positioned simple roots within the original system.