Numerical PDE-Based Pricing of Convertible Bonds Under Two-Factor Models

Authors

  • Radha Krishn Coonjobeharry Department of Mathematics, University of Mauritius, Reduit, Mauritius
  • Dhiren Kumar Behera Mechanical Engineering Department, Indira Gandhi Institute of Technology, Sarang, Dhenkanal, India
  • Nawdha Thakoor Department of Mathematics, University of Mauritius, Reduit, Mauritius

DOI:

https://doi.org/10.37256/cm.5120243343

Keywords:

convertible bonds, two-factor models, Alternating-Direction-Implicit method, Craig-Sneyd scheme

Abstract

Convertible bonds are popular financial instruments by which firms raise capital. Owing to the various features of such bonds, especially the early-exercise call, put, and conversion provisions, they can be valued by numerical techniques only. The price of a convertible bond is driven by both the underlying stock price and the interest rate, and these two factors are correlated. Under the partial differential equation framework, a two-dimensional convection-diffusion-reaction equation containing a mixed derivative must be solved. In this work, we employ an Alternating-Direction-Implicit method, namely the Craig-Sneyd scheme to solve the two-factor pricing equation. Comparison against the commonly employed Crank-Nicolson method shows the merit of the scheme. Besides, we analyze how the different contractual features of a convertible bond affect its price.

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Published

2024-01-02

How to Cite

1.
Coonjobeharry RK, Behera DK, Thakoor N. Numerical PDE-Based Pricing of Convertible Bonds Under Two-Factor Models. Contemp. Math. [Internet]. 2024 Jan. 2 [cited 2024 Feb. 27];5(1):93-104. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3343