We study the price of Asian options with floating-strike when the underlying asset price follows a  regime-switching  geometric Brownian motion  . We propose an iterative procedure to compute the option prices without recourse to solving a  PDE system. Our approach makes use of the scaling property of Brownian motion and the Fixed-Point Theorem.
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 , where both the drift and diffusion coefficients depend on an independent continuous-time finite-state Markov chain . We propose an iterative procedure that converges to the option prices without recourse to solving a coupled PDE system. Our approach makes use of path properties of Brownian motion and the Fixed-Point Theorem.
A
Markov-modulated (or
A
)
A
, where both the drift and diffusion coefficients depend on an independent continuous-time finite-state Markov chain
R
to compute
that converges to
A
coupled
R
the scaling property
path properties