Valuing convertible bonds and the option to exchange bonds for stock

- Values a convertible bond as a straight bond plus an exchange option
- Models the firm's decision to force early conversion as a stopping time problem
- Empirically validates the model using a sample of 148 convertibles
- Achieves average median and mean pricing errors of − 0.18% and 0.21%
- Quantifies the impact of the financial crisis period's short selling restrictions

The value of a conventional convertible bond is the value of a straight bond plus the value of the option to exchange it for a specified number of shares of common stock. First, I develop a closed-form contingent-claims convertible bond valuation model that quantifies the value of the exchange option when the short-term riskless rate, the firm's credit spread, and its share price are stochastic. I model the firm's decision to force early conversion as a stopping time problem in which the firm forces conversion as soon as the conversion value reaches the forced conversion barrier. I empirically validate the model by comparing model and market prices for a sample of 148 corporate convertible bonds issued between 2006 and 2010. The average median and mean pricing errors are − 0.18% and 0.21%, respectively, which are within the average bid-ask spread for convertible bonds during the sample period. I use the model to quantify the disruptive impact that the prohibition on short selling during the recent financial crisis had on convertible bond prices.