A tree approach to options pricing under regime-switching jump diffusion models

Abstract

A simple, efficient tree is developed to price options in a very general regime switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime switching tree, we approximate Heston's stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.

Primal‐dual active set algorithm for valuating American options under regime switching

“…Combining a fitted finite volume method and an implicit time-stepping scheme, Zhang et al [31] presented an efficient solving approach. A tree method was used to solve this problem by Liu and Nguyen [21]. Egorova et al [8] applied a multi-variable front-fixing technique to develop an explicit finite difference method and prove its conditional stability.…”

Convergence rate of regime-switching trees

“…Costabile et al [3] present a binomial approach for pricing contingent claims when the parameters governing the underlying asset process follow a regimeswitching model. A tree approach to options pricing under a regime-switching jump di¤usion model is exhibited in Liu and Nguyen [15].…”