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)

Abstract

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.

Keywords

Stochastic Volatility Bond Price Stochastic Volatility Model Weighted Sobolev Space Degenerate Parabolic Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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