Wavelet Galerkin pricing of American options on Levy driven assets

The price of an American-style contract on assets driven by a class of Markov processes containing. in particular, Levy processes of pure jump type with infinite jump activity is expressed as the solution of a parabolic variational integro-diffierential inequality (PIDI). A Galerkin discretization in logarithmic price using a wavelet basis is presented. Log-linear complexity in each time-step is achieved by wavelet compression of the moment rnatrix of the price process jump measure and by wavelet preconditioning of the large matrix LCPs at each time-step. Efficiency is demonstrated by numerical experiments for pricing American put contracts on various jump-diffusion and pure jump models. Failure of the smooth pasting principle is observed for American Put Contracts for certain finite variation pure jump price processes.