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 (CBs). 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 CBs 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.