Application of Lie point symmetries to the resolution of certain problems in financial mathematics with a terminal condition

Abstract

We demonstrate the power of symmetry in the resolution of some evolution partial differential equations which arise in various aspects of finance. The essential theme is that which Lie promulgated approximately 140 years ago. What we emphasise here is that there are differential equations which arise in applications which are amenable to a method of solution which is both algorithmic and elegant. We consider the Vasicek short rate model, the inclusion of transaction costs into the Black-Scholes model and the Vasicek model with time-varying parameters. © 2013 Springer Science+Business Media Dordrecht.