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

Liviu-Adrian Cotfas, Camelia Delcea and Nicolae Cotfas

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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.

Date: 2014-11
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