Fast Option Pricing using Nonlinear Stencils

We study the binomial option pricing model and the Black-Scholes-Merton pricing model. In the binomial option pricing model, we concentrate on two widely-used call options: (1) European and (2) American. Under the Black-Scholes-Merton model, we investigate pricing American put options. Our contributions are two-fold: First, we transform the option pricing problems into nonlinear stencil computation problems and present efficient algorithms to solve them. Second, using our new FFT-based nonlinear stencil algorithms, we improve the work and span asymptotically for the option pricing problems we consider. In particular, we perform $O(T\log^2 T)$ work for both American call and put option pricing, where $T$ is the number of time steps.