MPDATA Meets Black-Scholes: Option Pricing as a Transport Problem. (arXiv:1607.01751v1 [q-fin.CP])

In this note, we discuss applications of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) to numerical solutions of option pricing equations arising in quantitative finance. To demonstrate, we present an application of an unmodified open-source MPDATA solver library, libmpdata++, developed recently in the geoscientific community. We use the library to numerically price a typical example of a financial instrument, an interest rate corridor, assuming the Black-Scholes model. The results obtained with different solver settings are compared with the analytical solution with the aim of depicting the accuracy of the numerical scheme. The goal of this study is to highlight the potential MPDATA has as an accurate finite-difference approach for solving a wide variety of option pricing problems, including problems of current interest.