A study on pricing American options under regime-switching model

Regime-switching models gained popularity over the past decade because of their distinctive advantage of modeling 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 it enables a larger parameter space for models to be calibrated for a specific market dynamics and thus allows a better quantitative risk management in terms of utilizing financial derivatives. However, due to the increased model complexity, the associated computational effort usually increases as well. Therefore, there is a demand for developing approximate option pricing approaches, which can be heavily used in algorithmic trading with their super computational efficiency.

This thesis contributes to the problem of pricing American options under regime-switching model. In Chapter 3, a novel computational approach is presented, which can enhance the computation efficiency when the price of an American option under a two-state regime-switching model needs to be numerically computed. Later in Chapters 4-5, a generalized regime-switching model is considered. Several highly efficient formulations based on different integral equation methods are presented, particularly when the number of regimes is large. In Chapter 6, analytical approximations of the American option prices and optimal exercise prices have been investigated, perturbed around a solution to a special case of either identical volatilities for all regimes (equivalently Black-Scholes model) or a short tenor. For both scenarios, an error bond is established for the proposed approximate solution in terms of accuracy. Finally, an illustration is provided in Chapter 7, to explain how the computational results obtained from a regime-switching model are implemented in the pricing of American options in financial practice.