A lattice-based approach to option and bond valuation under mean-reverting regime-switching diffusion processes

Abstract

Nowadays, the pricing of financial instruments under continuous-time Markov switching models have received a widespread attention from researchers and practitioners in the finance industry. Lattice-based approaches are amongst the most widely used approaches to solve the pricing problem in this context. Recently, Yuen and Yang (2010) have proposed a simple and fast recombining trinomial tree method to handle the case of regime-switching geometric Brownian motion processes. In this paper, we generalize their approach to the regime-switching (exponential) mean-reverting case with state-dependent switching rates and derive the necessary conditions for the positivity of conditional branching probabilities. We employ the Hull and White’s tree-building procedure to limit tree growth away from the long-run mean of the process. We use the proposed lattice framework to price contingent claims of European, American and barrier type, and demonstrate its applicability in pricing default-free zero-coupon bonds. In the proposed tree structure, the number of nodes is substantially decreased and the computational cost is effectively reduced compared to the usual approaches. Extensive numerical experiments illustrate the efficiency and flexibility of the proposed scheme.