Anderson (1976) was the first to give a non-standard construction of a Brownian motion. His approach was to use the binomial model in a discrete time with infinitesimal time steps. Pricing an option in a model similar to the Black-Scholes model with the nonstandard Brownian motion can be done by...

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis...