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

Rakhymzhan Kazbek (), Yogi Erlangga, Yerlan Amanbek and Dongming Wei
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Rakhymzhan Kazbek: Nazarbayev University
Yogi Erlangga: Zayed University
Yerlan Amanbek: Nazarbayev University
Dongming Wei: Nazarbayev University

Computational Economics, 2025, vol. 65, issue 4, No 7, 1998 pages

Abstract: 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.

Keywords: TF model; Pricing convertible bonds; Finite element method; Penalty method; Financial derivatives; Greeks (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10614-024-10625-1

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