European Call and Put Option Pricing in a Three-State Regime-Switching Economy

Abstract

In recent decades, regime-switching models have gained popularity in mathematical finance as a way of overcoming the limitations of the Black-Scholes formula for European Options pricing. Rather than treat volatility as constant, regime-switching models employ Markov chains which assign unique volatility to each state. As a result, a given economy may now be modelled by “good”, “bad”, or “neutral” states with volatility of the underlying asset depending on the current state of the economy. By utilizing both the Black-Scholes formula as well as recent advances in the theory of stochastic processes, we provide a closed form representation of the European Call and Put Options prices in Three-State regime-switching economy driven by discrete time Markov chains, and an infinite series representation for continuous time Markov chains. We establish option price formulas that were previously known only in the case of Two-State regime-switching economy. Illustrative examples show excellent agreement of Monte Carlo simulation with exact option values.