In this paper we present a finite volume method for a two-dimensional Black-Scholes equation with stochastic volatility governing European option pricing. In this work, we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conversative form. We then present a finite volume method for the resulting equation, based on a fitting technique proposed for a one-dimensional Black-Scholes equation. We show that the method is monotone by proving that the system matrix of the discretized equation is an M-matrix. Numerical experiments, performed to demonstrate the usefulness of the method, will be presented.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0705104-120606 |
| Date | 05 July 2004 |
| Creators | Hung, Chen-Hui |
| Contributors | Mei-Hui Guo, Tzon-Tzer Lu, Zi-Cai Li, Chien-Sen Huang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0705104-120606 |
| Rights | unrestricted, Copyright information available at source archive |
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