The Mathematical Institute, University of Oxford, Eprints Archive

Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance

Reisinger, Christoph and Giles, M. B. (2011) Stochastic finite differences and multilevel Monte Carlo for a class of SPDEs in finance. Working Paper. N/A. (Submitted)

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Abstract

In this article, we propose a Milstein finite difference scheme for a stochastic partial differential equation (SPDE) describing a large particle system. We show, by means of Fourier analysis, that the discretisation on an unbounded domain is convergent of first order in time and second order in the spatial grid size, and that the discretisation is stable with respect to boundary data. Numerical experiments clearly indicate that the same convergence order also holds for boundary-value problems. Multilevel path simulation, previously used for SDEs, is shown to give substantial complexity gains compared to a standard discretisation of the SPDE or direct simulation of the particle system. We derive complexity bounds and illustrate the results by an application to basket credit derivatives.

Item Type:Technical Report (Working Paper)
Subjects:D - G > Game theory, mathematical finance, economics, social and behavioral sciences
H - N > Numerical analysis
Research Groups:Mathematical and Computational Finance Group
ID Code:1349
Deposited By:Christoph Reisinger
Deposited On:22 Jul 2011 08:42
Last Modified:01 Mar 2013 13:30

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