PDE option pricing with variable correlations
Correlation between financial quantities plays an important role in pricing financial derivatives. Existing popular models assume that correlation either is constant, or exhibits some deterministic behaviour. However, market observations suggest that correlation is a more complicated process.
We consider correlation structures that are guided by regime switching or by a stochastic process. We derive the related Partial Differential Equation (PDE) problems for pricing several types of financial derivatives, and solve them by accurate and efficient numerical methods. We also study the effect of model parameters to the prices. We present the PDE, the numerical solution, and comparison of the PDE results to Monte-Carlo simulations. We also discuss the relevant numerical challenges.
Joint work with Chun Ho (Nat) Leung