Petrov-Galerkin Analysis for a Degenerate Parabolic Equation in Zero-Coupon Bond Pricing
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.
KeywordsStochastic Volatility Bond Price Stochastic Volatility Model Weighted Sobolev Space Degenerate Parabolic Equation
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