An efficient ETD method for pricing American options under stochastic volatility with nonsmooth payoffs

Based on Cox and Matthews Exponential Time Differencing (ETD) approach, a fourth–order strongly–stable method having real distinct poles is developed and applied to solve American options under stochastic volatility with nonsmooth payoffs. A computationally efficient version of the method is constructed using partial fraction splitting technique. This approach requires to solve several backward Euler‐type linear systems at each time step. Numerical experiments are presented to demonstrate the computational efficiency, accuracy, and reliability of the method. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013