Before revision: We study the price of Asian options with floating-strike when the underlying asset price follows a Markov-modulated (or regime-switching ) geometric Brownian motion and both the interest rate and diffusion coefficient depend on an independent continuous-time finite-state Markov chain.
After revision: We study the price of an Asian option, a financial contract, as a fixed-point of a non-linear operator. In recent years, there has been interest in incorporating changes of regime into the parameters describing the evolution of the underlying asset price, namely the interest rate and the volatility, to model sudden exogenous events in the economy. Asian options are particularly interesting because the payoff depends on the integrated asset price. We study the case of both floating- and fixed-strike Asian call options with arithmetic averaging when the asset follows a regime-switching ) geometric Brownian motion and both the interest rate and diffusion coefficient depend on an independent continuous-time finite-state Markov chain.