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.