Adaptive Wavelet Method for Pricing Two-Asset Asian Options with Floating Strike

Asian options are path-dependent option contracts which payoff depends on the average value of the asset price over some period of time. We focus on pricing of Asian options on two assets. The model for pricing these options is represented by a parabolic equation with time variable and three state variables, but using substitution it can be reduced to the equation with only two state variables. For time discretization we use the theta-scheme. We propose a wavelet basis that is adapted to boundary conditions and use an adaptive scheme with this basis for discretization on the given time level. The main advantage of this scheme is small number of degrees of freedom. We present numerical experiments for the Asian put option with floating strike and compare the results for the proposed adaptive method and the Galerkin method.