Valuing Convertible Bonds: A New Approach
A recent paper by Finnerty expresses the value of a convertible bond as the value of the straight bond component plus the value of the option to exchange the bond component for a specified number of conversion shares and develops a closed-form convertible bond valuation model. This article illustrates how to apply the model to value nonredeemable convertible bonds and callable convertible bonds. The article also compares 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 postcrisis sample period.
Choosing the forced conversion date T̂2. The figure illustrates an iterative procedure for finding T̂2 and 
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The value of a convertible bond and the firm's option to force conversion. The voluntary conversion date that maximizes the value of the convertible bond is T2*, assuming the firm cannot force conversion prior to that date. Convertible security holders are forced to convert at T̂2, which results in a loss of value equal to the difference between the convertible security's value assuming optimal voluntary conversion and its value with forced early conversion. The value of the firm's option to force conversion, which is measured by the investors' loss of value resulting from forced conversion, declines as the exchange option seasons and reaches zero at T2*.
Components of the value of the nonredeemable EMC Corp. 1.75% convertible senior notes due December 1, 2011. This figure plots the clean market price and the clean model price and plots the value of the straight bond component and the value of the exchange option at monthly intervals between July 2009 and November 2011.
Value of bondholders' exchange option as a function of the implied volatility and the time to expiration of the option. The nonredeemable EMC Corp. 1.75% convertible senior notes due December 1, 2011, are valued and the sensitivities are calculated as of July 31, 2009.
Model price versus market price of the callable and nonputable Maxtor Corp. 2.375% convertible senior notes due August 15, 2012. The figure plots the clean model price and the clean market price at monthly intervals between July 2009 and August 2010. The expected time to forced conversion is determined using the stopping time model. The figure also plots the clean model price of the convertible note assuming no forced conversion.