Pricing multidimensional financial derivatives with stochastic volatilities using the dimensional-adaptive combination technique

Janos Benk and Dirk Pflüger

Journal of Computational Finance

Abstract: In this paper, we present a new and general approach to price derivatives based on the Black–Scholes partial differential equation (BS-PDE) in a multidimensional setting. The first ingredient in our approach is the dimensional-adaptive sparse grid combination technique, which, in the case of underlying models with stochastic volatilities, allows for inhomogeneous discretization levels of the dimensional axes. Thus, by applying the dimensional-adaptive combination technique to such problems, one may achieve higher numerical efficiency. We combine this approach with a stretched grid discretization that is derived from the underlying’s stochastic differential equation (SDE) in a general manner. This stretching enables us to employ efficient geometrical multigrid solvers, even for the strong anisotropic convection and diffusion coefficients that frequently occur in application. Our combination of the dimensional-adaptive sparse grid combination technique with SDE-based grid stretching and an efficient multigrid solver represents a new approach designed to enable derivative pricing by directly solving PDEs in higher dimensions than were possible before. The numerical results outlined in the paper demonstrate the efficacy of this new approach and of our implementation method, which entails pricing various derivatives with up to twelve dimensions in a general and simple manner.

References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.risk.net/journal-of-computational-fina ... ombination-technique (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:rsk:journ0:5363961

Access Statistics for this article

More articles in Journal of Computational Finance from Journal of Computational Finance
Bibliographic data for series maintained by Thomas Paine ().