FOURST: A code generator for FFT-based fast stencil computations

Fast Option Pricing using Nonlinear Stencils

“…𝑇 is the number of time steps. Inspired by the results in[2,3], which show that 𝑇 time steps of a linear stencil computation on a one-dimensional input grid of length Θ (𝑇 ) take O 𝑇 log 2 𝑇 time, we show how a class of nonlinear stencil computations can be performed in O 𝑇 log 2 𝑇 time as well. More specifically, we design an FFT-based algorithm to solve the stencil computation problem obtained by discretizing the Black-Scholes PDE for the American put option, which requires O 𝑇 log 2 𝑇 time and achieves O 1 𝑇 global error…”