  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.
