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

TL;DR

This paper derives an exact analytical solution for the Aunt Michaela option pricing model using a modified Black-Scholes equation, employing special functions and numerical experiments to validate the approach.

Contribution

It introduces a new exact series solution for a modified Black-Scholes equation with a gamma-type maturity condition, expanding analytical methods in option pricing.

Findings

Exact solution expressed via Laguerre polynomials and Whittaker functions

Numerical validation of the analytical solution

Enhanced understanding of options with gamma-type maturity conditions

Abstract

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