Discretization Schemes for Option Pricing Models with Jumps and State-dependent Volatility
Professor Claudio Albanese, Department of Mathematics, University of Toronto

Abstract:
I introduce a Poisson approximation scheme for jump processes with state-dependent local volatility and use it to construct arbitrage-free discretization schemes for the corresponding pricing PIDEs. The crucial property of these lattice models is their great stability, as one can set the time nodes at arbitrary dates without affecting the end-result for the price of European options. This is achieved by computing node-to-node transition probabilities analytically as expansions in hypergeometric polynomials. I outline applications of this technique to equity and credit derivatives.