Pricing convertible bonds based on a multi-stage compound option model

In this paper, we introduce the concept of multi-stage compound options to the valuation of convertible bonds. Rather than evaluating a nested high-dimensional integral that has arisen from the valuation of multi-stage compound options, we found that adopting the Finite Difference Method (FDM) to solve the Black-Scholes equation for each stage actually resulted in a better numerical efficiency. By comparing our results with those obtained by solving the Black-Scholes equation directly, we can show that the new approach does provide an approximation approach for the valuation of convertible bonds and demonstrate that it offers a great potential for a further extension to CBs with more complex structures such as those with call and/or put provisions.