Friday, March 12, 2010

On the localization of PDE problems arising in financial option pricing

Fernando Gonçalves

Abstract: Cauchy problems for linear parabolic PDEs arise in financial option pricing. When their numerical approximation is pursued, there is the need to localize the problem on a bounded domain in order to obtain implementable numerical schemes. In our work, we develop a localization procedure for the case where the PDE is multidimensional, possibly degenerate, with growing time and space-dependent coefficients. Then, we deduce the stochastic representation of both the solutions of the Cauchy and the initial boundary-value problems, under milder conditions and capturing wider situations than it is usual. Finally, we obtain an estimate for the localization error. Applications to multi-asset models and to stochastic volatility models for financial options with fixed exercise are given. This is a joint work with M.R. Grossinho (ISEG-UTL/CEMAPRE) and D. Heath (Australian National University).

Friday, March 12, 2010
Time: 11h00
Room: Sala IAPMEI, Edificio Quelhas, ISEG