A fast algorithm for computing integrals in function spaces: Financial applications

The paper describes a fast and general numerical algorithm for computing path integrals in function spaces. Efficiency is ensured by use of FFT-based procedures as the primary element of the algorithm. The total number of operations required by the algorithm can be shown to be proportional to the total number of discretization nodes. A number of financial applications of the algorithm are considered, including pricing European and American style interest rate options, path dependent options, and index amortization swaps.