An efficient convergent lattice method for Asian option pricing with superlinear complexity

ABSTRACT Asian options have payoffs that depend strongly on the historical information of the;underlying asset price. Although approximated closed-form formulas are available;with various assumptions, most of them do not guarantee convergence. Binomial tree;and partial differential equation (PDE) methods are two popular numerical solutions;for pricing. However, both methods have a complexity of at least O(N ²), where N;is the number of time steps. We propose a convergent lattice method with a complexity of O;(N1.5), based on Curran's willow tree method. We also analyze the corresponding;convergence rate and error bounds and show that our proposed method can provide;the same accuracy as the PDE and binomial tree methods but requires much less;computational time. When a quick pricing is required, our method can give the price;to within one US cent in less than half a second. We give numerical results to support;our claims.