SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Pricing Derivatives in High-Dimensional Settings via PDE Expansions

C. Reisinger and R. Wissmann

Abstract
We propose a new numerical approach to high-dimensional partial differential equations (PDEs) arising in the valuation of exotic derivatives on the LIBOR curve. The proposed method uses principal component analysis (PCA) of the underlying process in combination with a Taylor expansion of the value function into solutions to low-dimensional PDEs. The approximation is related to anchored analysis of variance (ANOVA) decompositions and is expected to be accurate whenever the covariance matrix has one or few dominating eigenvalues. On the example of Bermudan swaptions and Ratchet floors, which are considered difficult benchmark problems, we are able to demonstrate that for problems with medium to high dimensionality and moderate time horizons the presented PDE method delivers results comparable in accuracy to the MC methods considered here in similar or (often significantly) faster runtime.

Organized by         Universidad de Valladolid     IMUVA