An Exact Closed-Form Solution for the Valuation of European Options in a Regime-Switching Economy
by
Alex Badran
University of Wollongong
Coauthors: Xiao-Ping Lu and Song-Ping Zhu

We derive a new exact closed-form solution for the price of a European option in a regime-switching economy. Two coupled partial differential equations (PDEs) are derived based on the assumption that the volatility process is driven by a two-state continuous-time Markov process. These equations are then solved by using the Fourier Transform method. The new closed-form formulae are in the form of a single integral, whereas the existing solutions contain double integrals. Consequently our formulae provide more computing efficiency and accuracy. Numerical examples are provided to illustrate the results.

Date received: December 19, 2009