This paper uses Lie symmetry group methods to obtain transition probability densities for scalar diffusions, where the diffusion coefficient is given by a power law. We will show that if the drift of the diffusion satisfies a certain family of Riccati equations, then it is possible to compute a...

We investigate PDEs of the form u_t = 1/2 σ^2 (t, x)u_{xx} − g(x)u which are associated with the calculation of expectations for a large class of local volatility models. We find nontrivial symmetry groups that can be used to obtain standard integral transforms of fundamental solutions of the...