Pricing the Aunt Michaela Option with a Modified Black-Scholes Equation with a Maturity Condition of Gamma Type

Using Maple, we compute a new exact series solution of a modified Black-Scholes equation, recently proposed, for the case of the Aunt Michaela option with a maturity condition of gamma type. We show that the modified Black-Scholes equation with the Aunt Michaela option is exactly solvable in terms of associated Laguerre polynomials or equivalently, in terms of Whittaker M functions. Finally, we make some numerical experiments with the analytical solutions