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- Title
A Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities.
- Authors
Huang, C.-S.; Hung, C.-H.; Wang, S.
- Abstract
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 conservative 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.
- Subjects
FINITE volume method; STOCHASTIC processes; MATRICES (Mathematics); PRICES; PRICING
- Publication
Computing, 2006, Vol 77, Issue 3, p297
- ISSN
0010-485X
- Publication type
Article
- DOI
10.1007/s00607-006-0164-4