Title page for etd-0622110-172307


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URN etd-0622110-172307
Author Chen-hui Hung
Author's Email Address No Public.
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Department Applied Mathematics
Year 2009
Semester 2
Degree Ph.D.
Type of Document
Language English
Title On a Fitted Finite Volume Method for the Valuation of Options on Assets with Stochastic Volatilities
Date of Defense 2010-06-10
Page Count 54
Keyword
  • stability and convergence
  • finite volume method
  • European option pricing
  • stochastic volatility
  • Black-Scholes equation
  • Abstract In this dissertation we first formulate the Black-Scholes equation with a tensor (or matrix) diffusion coefficient into a conservative form and present a convergence analysis for the two-dimensional Black-Scholes equation arising in the Hull-White model for pricing European options with stochastic volatility. We formulate a non-conforming Petrov-Galerkin finite element method with each basis function of the trial space being determined by a set of two-point boundary value problems defined on element edges. We show that the bilinear form of the finite element method is coercive and continuous and establish an upper bound of order O(h) on the discretization error of method, where h denotes the mesh parameter of the discretization. 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 presentd.
    Advisory Committee
  • Tzon-Tzer Lu - chair
  • Zi-Cai Li - co-chair
  • Weichung Wang - co-chair
  • Tsu-Fen CHEN - co-chair
  • Chien-Sen Huang - advisor
  • Files
  • etd-0622110-172307.pdf
  • indicate access worldwide
    Date of Submission 2010-06-22

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