Quantum Finance and Path Integrals

Abstract

Stimulated by the resemblance of the Black-Scholes equation and the Schrodinger equation, this chapter uses quantum-mechanical methods to determine the pricing kernel, which turns out to be equivalent to the Green’s function found in earlier chapters. Using the quantum-mechanical methods the down-and-out barrier option is treated in some detail. After covering Feynman’s description of quantum mechanics in terms of path integrals, they are used to re-derive the pricing kernel, found earlier. Since path integrals are very amenable to numerical evaluations, we introduce Monte-Carlo methods, including the Metropolis-Hasting algorithm, to evaluate the multi-dimensional integrals.