Valuing American floating strike lookback option and Neumann problem for inhomogeneous Black-Scholes equation

This paper presents our study of American floating strike lookback options written on dividend-paying assets. The valuation of these options can be mathematically formulated as a free boundary inhomogeneous Black-Scholes PDE with a Neumann boundary condition, which we, by using a Mellin transform, convert into a relatively simple ordinary differential equation with Dirichlet boundary conditions. We then use these results to derive an integral equation that can be used to calculate the price of American floating strike lookback options. In addition, we also used Mellin transforms to derive the closed-form of the perpetual case.