Financial derivatives and Lie symmetries

Derivatives in finance have become pervasive in recent decades. Tremendous impetus was given to this aspect of finance by the pioneering papers of Black and Scholes (1973) and Merton (1973) and has attracted considerable interest since. In general the evolution partial differential equations were solved by means of the traditional methods of partial differential equations and by ansatz previously useful in similar contexts. Here we illustrate the benefits of an algorithmic approach using the method of symmetry analysis introduced by Sophus Lie in the nineteenth century. We demonstrate the utility of this analytic approach with several examples chosen from the field of financial mathematics.