Valuing convertible bonds and the option to exchange bonds for stock

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. (C) 2015 Elsevier B.V. All rights reserved.