Option Pricing with Regime Switching Correlation: a Numerical Pde Approach

Modelling correlation between financial quantities is important in the accurate pricing of financial derivatives. In this paper, we introduce some stochasticity in correlation, by considering a regime-switching correlation model, in which the transition rates between regimes are given. We present a derivation of the associated Partial Differential Equation (PDE) problem. The problem involves a system of l PDEs, where l is the number of regimes. We formulate a finite difference method for the solution of the PDE system, and numerically demonstrate that it converges with second order. We study the effect of certain model parameters on the computed prices. We compare prices from this model, associated PDE and method with those from a stochastic correlation model, associated PDE and method in van Emmerich, 2006, Leung, 2017, Leung et al., 2016 and discuss advantages and disadvantages. AMS subject classification: 65M06, 91G60.