Journal of Computational Finance

Numerical valuation of derivatives in high-dimensional settings via partial differential equation expansions

Christoph Reisinger and Rasmus Wissmann


We propose a new numerical approach to solving high-dimensional partial differential equations (PDEs) that arise in the valuation of exotic derivative securities. The proposed method is extended from the work of Reisinger andWittum and uses principal component analysis 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 decompositions and is expected to be accurate whenever the covariance matrix has one or few dominating eigenvalues. We give a careful analysis of the numerical accuracy and computational complexity compared with state-of-the-art Monte Carlo methods, using Bermudan swaptions and ratchet floors, which are considered difficult benchmark problems, as examples. We demonstrate that, for problems with medium to high dimensionality and moderate time horizons, the PDE method presented delivers results comparable in accuracy to the Monte Carlo methods considered here in a similar or (often significantly) faster run time.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here