A numerical PDE approach for pricing callable bonds
Many debt issues contain an embedded call option that allows the issuer to redeem the bond at specified dates for a specified price. The issuer is typically required to provide advance notice of a decision to exercise this call option. The valuation of these contracts is an interesting numerical exercise because discontinuities may arise in the bond value or its derivative at call and/or notice dates. Recently, it has been suggested that finite difference methods cannot be used to price callable bonds requiring notice. Poor accuracy was attributed to discontinuities and difficulties in handling boundary conditions. As an alternative, a semi-analytical method using Green's functions for valuing callable bonds with notice was proposed. Unfortunately, the Green's function method is limited to special cases. Consequently, it is desirable to develop a more general approach. This is provided by using more advanced techniques such as flux limiters to obtain an accurate numerical partial differential equation method. Finally, in a typical pricing model an inappropriate financial condition is required in order to properly specify boundary conditions for the associated PDE. It is shown that a small perturbation of such a model is free from such artificial conditions.
Volume (Year): 8 (2001)
Issue (Month): 1 ()
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- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
- Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- Mauer, David C, 1993. "Optimal Bond Call Policies under Transactions Costs," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 16(1), pages 23-37, Spring.
- Ram Bhar & Carl Chiarella & Nadima El-Hassan & Xiaosu Zheng, 2000. "The Reduction of Forward Rate Dependent Volatility HJM Models to Markovian Form: Pricing European Bond Option," Research Paper Series 36, Quantitative Finance Research Centre, University of Technology, Sydney.
- Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
- Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
- Francis A. Longstaff & Bruce A. Tuckman, 1994. "Calling Nonconvertible Debt and the Problem of Related Wealth Transfer Effect," Financial Management, Financial Management Association, vol. 23(4), Winter.
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