Exact solution of a generalized version of the Black-Scholes equation

Abstract

We analyze a generalized version of the Black-Scholes equation depending on a parameter $a\in (-\infty ,0)$. It satisfies the martingale condition and coincides with the Black-Scholes equation in the limit case $a\nearrow 0$. We show that the generalized equation is exactly solvable in terms of Hermite polynomials and numerically compare its solution with the solution of the Black-Scholes equation.

References in corpus (1)

• A finite-dimensional quantum model for the stock market