Option pricing under regime switching: Integration over simplexes method

This paper aims to develop an alternative method for pricing European options under regime-switching market conditions by representing their values as a sum of integrations over simplexes. We calculate the integrations by using the method of Grundmann and Möller (1978). The method is applicable to the valuation of European-type options written on underlying assets whose prices follow a regime-switching mean-reverting process as well as a conventional regime-switching geometric Brownian motion. Numerical examples provide evidence that this method can be a powerful tool for practitioners in option pricing.