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.