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I further explain how to apply the model to value putable convertibles. I extend the model to callable convertibles by incorporating the firm's option to force early conversion within a stopping time framework. I extend Margrabe's (1978) model to obtain an explicit expression for the value of the option to exchange the straight bond for the conversion shares. The strike price is the market value of the straight bond component, which varies with interest rates and the bond's credit risk. ![]() I model the investors' option to exchange the straight bond component for the conversion shares and develop a closed-form convertible bond valuation model. The credit spread process incorporates default risk within a reduced-form model. ![]() I model the evolution of the riskless rate and the credit spread as correlated mean-reverting diffusion processes. Fourth, I use the model to quantify the disruptive impact that the SEC's short selling restrictions had on convertible bond prices during the recent financial crisis.Ī corporate bond is both an interest-rate derivative and a credit derivative. I find that the overall average median and mean pricing errors are − 0.18% and 0.21%, respectively, which are within the average bid–ask spread for the convertible bond sample. ![]() Third, I empirically test the model on a sample of 148 convertible bonds issued between Januand Decembased on TRACE prices for the Januthrough Janutime period. Second, I develop a procedure for estimating the expected forced conversion date of a callable convertible bond by treating 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 a forced conversion barrier. It builds on Ingersoll's (1977a) insight that a convertible bond can be viewed as a combination of a straight bond and an option to exchange it for the underlying common stock and draws on Margrabe's (1978) insight concerning the valuation of an option to exchange one asset for another. First, it demonstrates that modeling a conventional convertible bond as a straight bond coupled with an option to exchange the bond for a specified number of common shares can lead to a closed-form expression that provides an accurate approximation to the convertible bond's value. This paper makes four contributions to the corporate finance literature. However, an accurate approximation can be achieved if the exchange option and these option interactions can be modeled appropriately. The interaction of these options with the firm's default option requires a contingent claims valuation model to capture fully a convertible bond's complex optionality. Often, the firm has an American call option, which it can use to force conversion before the bondholders voluntarily convert, if the conversion option is in-the-money, and the bondholders may have one or more European put options, which they can use to force premature redemption. A convertible bond gives the holder an American option to convert the bond into common stock by exchanging it for a specified number of common shares at any time prior to the bond's redemption. ![]() 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.Ĭonvertible bond valuation is not amenable to an exact closed-form solution because of the security's complex optionality. 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 empirically validate the model by comparing model and market prices for a sample of 148 corporate convertible bonds issued between 20. 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. 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. 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.
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