Valuation and Sensitives of Callable Debt

Project: Research

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Callable bonds are bonds attached with call provisions, which give the bond issuing firms the option to call the bonds back during a predetermined period at a predetermined price. Bond call provisions are commonly used by U.S. corporations when they issue bonds in the public debt market. Based on the bonds recorded in Fixed Investment Securities Database (FISD), more than 60% of U.S. corporate bonds with fixed-rate are callable bonds.Although there are several papers studied why firms issue callable bonds (e.g., Pye, 1966; King and Mauer, 2000, etc.), there are few papers examined the valuation and sensitivities of the callable bond. This proposed research try to close this gap by first deriving a structural model for callable bond pricing, and then studying the sensitivities/concavity/convexity of the callable bond pricing to the factors, such as stock price, short interest rate and their volatility.Since a higher stock price corresponds to greater firm asset value, an increase in the stock price reduces the risk of default and increase the value of callable bonds. In the structural model framework, the fair value of debt equals firm asset value less equity. Equity has a positive convexity to the firm asset value; consequently, we expect the second derivative of callable bond values to be negative to the stock volatility.There are several bond pricing theories suggesting that short interest rate and its volatility should affect the corporate bond pricing. Surprisingly, few empirical works tested the impact of short interest rate and its volatility on callable bond pricing. Bonds experience increases in value when the interest rates decrease; this effect is due to the discounting of future cash flows. While the sensitivity to the interest rate to be less pronounced for callable bonds due the price compression effect of the embedded call option, which caps the potential gains from lower short interest rate. Since the volatility of short interest rate may increase both the firm's default probability and call option values, the impact of short interest rate volatility on callable bond pricing is complicated.Our findings will have significant implications. First, we are the first to comprehensively investigate the callable bonds pricing and sensitivities/convexity to different factors. Second, our proposed research will be useful for market participants in building up portfolios and trading strategies. With a better understanding of the bonds pricing and its sensitivity to the factors, the portfolio managers can better adjust their portfolio among different kinds of assets to enhance their return and improve hedging performance.


Project number9042839
Grant typeGRF
Effective start/end date1/01/205/12/23