Anmerkungen:
Nach Informationen von SSRN wurde die ursprüngliche Fassung des Dokuments November 2015 erstellt
Beschreibung:
One approach to price financial derivatives in an arbitrage free manner is to work directly with the probability density function. For many models, it is possible to find an expansion of the density that follows a Fokker-Planck partial differential equation. In order to keep the arbitrage-free property numerically, it is particularly important to use a positivity preserving finite difference scheme. With a discontinuous initial condition like a Dirac, many schemes will produce oscillations or negative densities. This paper analyzes the behavior of a few simple schemes related to backward Euler, namely BDF2, Lawson-Morris and Lawson-Swaybe on the specific problem of a diffusion with Dirac initial condition. The case of the arbitrage free SABR model for interest rate derivatives is then evaluated