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

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.