Option valuation under a regime-switching constant elasticity of variance process

We investigate the pricing of both European and American-style options when the price dynamics of the underlying risky assets are governed by a Markov-modulated constant elasticity of variance process. Both probabilistic and partial differential equation approaches are considered in deriving the value of a European-style option. For the case of an American-style option, we consider a probabilistic approach and derive an integral representation for the early exercise premium.