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Coupon Bond Valuation with a Non-Affine Discount Yield Model

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  • Peter D Spencer

Abstract

I report a closed form for the Laplace transform of the Ahn Gao (RFS, 1999) discount function and show how this can be used for pricing non-zero coupon bond prices, including hybrid fixed/variable rate instruments. In contrast, numerical techniques have to be used to analyse these prices for the standard affine yield specifications. I find that many of the characteristics of the Cox Ingersoll and Ross (JF, 1980) solutions extend to this more general non-affine specification. The allowance for mean reversion in the Ahn-Gao specification means that the solutions are hypergeometric rather than power functions, but the properties of these functions are nicely established, facilitating qualitative analysis. The prices of interest rate options can be backed out of these formulae by Laplace inversion, overcoming a major problem with the original Ahn and Gao (1999) valuation approach.

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Paper provided by Department of Economics, University of York in its series Discussion Papers with number 03/16.

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Handle: RePEc:yor:yorken:03/16

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Keywords: Non-affine yield curve; Bond valuation; Laplace transform;

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  1. Fries, Steven & Mella-Barral, Pierre & Perraudin, William, 1997. "Optimal bank reorganization and the fair pricing of deposit guarantees," Journal of Banking & Finance, Elsevier, vol. 21(4), pages 441-468, April.
  2. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  3. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(05), pages 615-645, October.
  4. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
  5. Buttler, Hans-Jurg, 1995. "Evaluation of Callable Bonds: Finite Difference Methods, Stability and Accuracy," Economic Journal, Royal Economic Society, vol. 105(429), pages 374-84, March.
  6. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
  7. Dothan, L. Uri, 1978. "On the term structure of interest rates," Journal of Financial Economics, Elsevier, vol. 6(1), pages 59-69, March.
  8. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-77.
  9. 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.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. " An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May.
  11. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
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Cited by:
  1. Leunglung Chan & Eckhard Platen, 2010. "Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model," Papers 1007.2968, arXiv.org, revised Jan 2011.
  2. Peter Carr & Jian Sun, 2007. "A new approach for option pricing under stochastic volatility," Review of Derivatives Research, Springer, vol. 10(2), pages 87-150, May.

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