We develop the complete 6-dimensional classical symmetry group of the partial differential equation (PDE) that governs the fair price of a simple Asian option within a simple market model. The symmetries we expose include the 5-dimensional symmetry group partially noted by Rogers and Shi, and...

Heat kernel perturbation theory is a tool for constructing explicit approximation formulas for the solutions of linear parabolic equations. We review the crux of this perturbative formalism and then apply it to differential equations which govern the transition densities of several local...