Numerical Ross Recovery for Diffusion Processes Using a PDE Approach

We develop and analyse a numerical method for solving the Ross recovery problem for a diffusion problem with unbounded support, with a transition independent pricing kernel. Asset prices are assumed to only be available on a bounded subinterval $$B = [- N,N]$$B=[−N,N]. Theoretical error bounds on the recovered pricing kernel are derived, relating the convergence rate as a function of $$N$$N to the rate of mean reversion of the diffusion process. Our suggested numerical method for finding the pricing kernel employs finite differences, and we apply Sturm–Liouville theory to make use of inverse iteration on the resulting discretized eigenvalue problem. We numerically verify the derived error bounds on a test bench of three model problems.