A Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities

Authors:
C.-S. Huang;C.-H. Hung;S. Wang
Affiliations:
Department of Applied Mathematics, National Sun Yat-sen University, 811, Kaohsiung, Taiwan;Department of Applied Mathematics, National Sun Yat-sen University, 811, Kaohsiung, Taiwan;School of Mathematics and Statistics, The University of Western Australia, 6009, Crawley, Australia
Venue:
Computing
Year:
2006

Citing 0
Cited 6

A computational scheme for uncertain volatility model in option pricing

Applied Numerical Mathematics
Finite-volume difference scheme for the Black-Scholes equation in stochastic volatility models

NMA'10 Proceedings of the 7th international conference on Numerical methods and applications
Pricing American bond options using a penalty method

Automatica (Journal of IFAC)
Pricing American bond options using a penalty method

Automatica (Journal of IFAC)
Petrov-Galerkin analysis for a degenerate parabolic equation in zero-coupon bond pricing

LSSC'11 Proceedings of the 8th international conference on Large-Scale Scientific Computing
An inverse finance problem for estimation of the volatility

Computational Mathematics and Mathematical Physics

Quantified Score

Hi-index	0.00

Visualization

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.