Pricing Convertible Bonds with the Penalty TF Model Using Finite Element Method

Document Type

Article

Source of Publication

Computational Economics

Publication Date

1-1-2024

Abstract

In this paper, we discuss finite element methods (FEM) for solving numerically the so-called TF model, a PDE-based model for pricing convertible bonds. The model consists of two coupled Black-Scholes equations, whose solutions are constrained. The construction of the FEM is based on the P1 and P2 element, applied to the penalty-based reformulation of the TF model. The resultant nonlinear differential algebraic equations are solved using a modified Crank-Nicolson scheme, with non-linear part with non-smooth terms solved at each time step by Newton’s method. While P1-FEM demonstrates a comparable convergence rate to the standard finite difference method, a better convergence rate is achieved with P2-FEM. The fast convergence of P2-FEM leads to a significant reduction in CPU time, due to the reduction in the number of elements used to achieve the same accuracy as P1-FEM or FDM. As the Greeks are important numerical parameters in the bond pricing, we compute some Greeks using the computed solution and the corresponding FEM approximation functions.

ISSN

0927-7099

Publisher

Springer Science and Business Media LLC

Disciplines

Physical Sciences and Mathematics

Keywords

Financial derivatives, Finite element method, Greeks, Penalty method, Pricing convertible bonds, TF model

Scopus ID

85193245025

Indexed in Scopus

yes

Open Access

no

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