Two-Factor Convertible Bond Pricing with Pull-to-Par

We derive a two-dimensional partial differential equation to examine the pricing of convertible bonds and callable convertible bonds. We combine the well-known geometric Brownian motion process for the evolution of the stock price with a recently developed pull-to-par model for bond price evolution. To account for default risk, we price securities using a default-adjusted discount rate. As an illustration, we provide some solutions and sensitivity analysis using a finite difference approximation to the partial differential equation.