New Analytical Solutions of a Modified Black-Scholes Equation with the European Put Option

Using Maple, we compute some analytical solutions of a modified Black-Scholes equation, recently proposed, in the case of the European put option. We show that the modified Black-Scholes equation with the European put option is exactly solvable in terms of associated Laguerre polynomials. We make some numerical experiments with the analytical solutions and we compare our results with the results derived from numerical experiments using the standard Black-Scholes equation.