A Monte Carlo Method using PDE Expansions for a Diversifed Equity Index Model

David Heath and Eckhard Platen ()
Additional contact information
David Heath: Australian National University

No 350, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: This paper considers a new class of Monte Carlo methods that are combined with PDE expansions for the pricing and hedging of derivative securities for multidimensional diffusion models. The proposed method combines the advantages of both PDE and Monte Carlo methods and can be directly applied to models with more than two state variables. The pricing procedure is illustrated using a three-component index model that captures some of the key features of a diversified stock index over long time periods. The method is widely applicable and is demonstrated here in the general setting of the benchmark approach, where spatial boundary limiting conditions for the PDE need to be appropriately chosen and approximated. The PDE expansion is based on a Taylor series approximation for the underlying three-component PDE. A Monte Carlo method with variance reduction is then formulated to approximate the true solution. Almost exact simulation schemes are described for the given state variables in the model. Numerical results are presented that demonstrate the effectiveness and tractability of the proposed pricing and hedging methodology.

Keywords: Multi-factor diffusion; Monte Carlo methods; diversified equity index, pricing PDE; exact simulation; variance reduction; benchmark approach (search for similar items in EconPapers)
JEL-codes: G10 G13 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2014-08-01
New Economics Papers: this item is included in nep-cmp and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.uts.edu.au/sites/default/files/rp350.pdf (application/pdf)

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:uts:rpaper:350

Access Statistics for this paper

More papers in Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney PO Box 123, Broadway, NSW 2007, Australia. Contact information at EDIRC.
Bibliographic data for series maintained by Duncan Ford ().