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

C-S. Huang, C-H. Hung, Song Wang

    Research output: Contribution to journalArticle

    27 Citations (Scopus)

    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.
    Original languageEnglish
    Pages (from-to)297-320
    JournalComputing
    Volume77
    Issue number3
    DOIs
    Publication statusPublished - 2006

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