Derivative pricing as a transport problem: MPDATA solutions to Black-Scholes-type equations

31 Dec 2018 Arabas Sylwester Farhat Ahmad

We discuss in this note applications of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA) to numerical solutions of partial differential equations arising from stochastic models in quantitative finance. In particular, we develop a framework for solving Black-Scholes-type equations by first transforming them into advection-diffusion problems, and numerically integrating using an iterative explicit finite-difference approach, in which the Fickian term is represented as an additional advective term... (read more)

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