Pricing Options Embedded in Corporate Bonds Using the Binomial Method
Abstract
It is common for a corporate bond to include a call provision that gives the issuing company an option to call, or redeem, the bond at some prespecified set of call prices before the stated maturity date. Since the option is embedded in the bond, it is not traded publicly and thus its value is unknown to bondholders. This study is aimed to price these embedded options and their related bonds, both callable and noncallable, using the binomial method such that the method is set up to approximate the evolution of the short rate. Using reasonable values for the relevant factors and parameters, our results show that the prices of the options and the two types of bonds are noticeably affected by such factors and parameters as the maturity of the bonds, the coupon, the call price, the volatility of the short rate, and the initial short rate.
References
Aitchison, J. and Brown, J. A. C. (1957). The Lognormal Distribution. Cambridge University Press, Cambridge.
Bartter, B. J. and Rendleman, R. J. (1979). Fee-Based Pricing of Fixed Rate Bank Loan Commitments. Financial Management, Spring:13–20.
Black, F., Derman, E., and Toy, W. (1990). A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options. Financial Analysts Journal, 46:33–39.
Black, F. and Karasinski, P. (1991). Bond and Option Pricing When Short Rates Are Lognormal. Financial Analysts Journal, 47:52–59.
Black, F. and Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81:637–659.
Brennan, M. J. and Schwartz, E. S. (1977). Savings Bonds, Retractable Bonds and Callable Bonds. Journal of Financial Economics, 5:67–88.
Brennan, M. J. and Schwartz, E. S. (1980). Analyzing Convertible Bonds. Journal of Financial and Quantitative Analysis, 15:907–929.
Cox, J. C., Ingersoll, J. E., and Ross, S. A. (1985). A Theory of the Term Structure of Interest Rates. Econometrica, 53:385–407.
Fabozzi, F. J. (2015). Bond Markets, Analysis and Strategies. Pearson, Boston, 9 edition.
Hull, J. C. (2018). Options, Futures, and Other Derivatives. Prentice Hall, Upper Saddle River, 9 edition.
Johnson, R. S. (2010). Bond Valuation, Selection, and Management. John Wiley & Sons, Inc., New York, 2 edition.
Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science, 4:141–183.
Rendleman, R. and Bartter, B. (1980). The Pricing of Options on Debt Securities. Journal of Financial and Quantitative Analysis, 15:11–24.
Tuckman, B. and Serrat, A. (2011). Fixed Income Securities: Tools for Today’s Markets. John Wiley & Sons, Inc., New York.
Vasicek, O. (1977). An Equilibrium Characterization of the Term Structure. Journal of Financial Economics, 5:177–188.
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