Petrov-Galerkin Analysis for a Degenerate Parabolic Equation in Zero-Coupon Bond Pricing

  • R. L. Valkov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7116)


A degenerate parabolic equation in the zero-coupon bond pricing (ZCBP) is studied. First, we analyze the time discretization of the equation. Involving weighted Sobolev spaces, we develop a variational analysis to describe qualitative properties of the solution. On each time-level we formulate a Petrov-Galerkin FEM, in which each of the basis functions of the trial space is determined by the finite volume difference scheme in [2, 3]. Using this formulation, we establish the stability of the method with respect to a discrete energy norm and show that the error of the numerical solution in the energy norm is O(h), where h denotes the mesh parameter.


Stochastic Volatility Bond Price Stochastic Volatility Model Weighted Sobolev Space Degenerate Parabolic Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • R. L. Valkov
    • 1
  1. 1.Faculty of Mathematics and InformaticsUniversity of SofiaSofiaBulgaria

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