Multi-Factor Financial Derivatives on Finite Domains

Abstract

In this paper, we introduce reversion conditions for stochastic models. Also we prove that if the models satisfy reversion conditions and the market prices of risks are bounded, then the final-value problem of general two-factor financial derivative equations on rectangular domains has a unique solution. For such problems we can obtain their numerical solutions without using any artificial conditions. Examples show that if the singularity-seperating method and extrapolation techniques are used, then very good solutions can be obtained even on very coarse meshes.