Pricing of Discretely Sampled Asian Options Under Levy Processes

We develop a new method for pricing options on discretely sampled arithmetic average in exponential L'evy models. The main idea is the reduction to a backward induction procedure for the difference W_n between the Asian option with averaging over n sampling periods and the price of the European option with maturity one period. This allows for an efficient truncation of the state space. At each step of backward induction, W_n is calculated accurately and fast using a piece-wise interpolation or splines, fast convolution and either iFFT or the parabolic inverse Fourier transform. Numerical results demonstrate the advantages of the method.