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Pricing caps and floors with the extended CIR model

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  • Antonio Mannolini

    (Dipartimento di Economia Politica, Universit� di Siena, Italy)

  • Carlo Mari

    (Dipartimento di Metodi Quantitativi e Teoria Economica, Universit� di Chieti-Pescara, Italy)

  • Roberto Ren�

    (Dipartimento di Economia Politica, Universit� di Siena, Italy)

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    Abstract

    We use the extended CIR model to value interest rate caps and floors. The extension allows arbitrary initial term structure, in the spirit of Hull and White, a crucial feature since we show that the pricing of the considered contingent claims improves dramatically after taking into account the big stake of market information contained in the yield curve. We compute model prices of at the money caps using only yield curve data, and we compare prices with those obtained when other well-known short-rate models are used, including the extended Vasicek model. With respect to natural benchmarks, we find a significant decrease in the pricing error for longer maturity caps when our model is used. These results witness that when a better specification of the dynamics of spot rate is provided, a satisfactory pricing of caps and floors is possible using only the information available in the bond market. Copyright © 2008 John Wiley & Sons, Ltd.

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    File URL: http://hdl.handle.net/10.1002/ijfe.369
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    Bibliographic Info

    Article provided by John Wiley & Sons, Ltd. in its journal International Journal of Finance & Economics.

    Volume (Year): 13 (2008)
    Issue (Month): 4 ()
    Pages: 386-400

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    Handle: RePEc:ijf:ijfiec:v:13:y:2008:i:4:p:386-400

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    1. Ravi Jagannathan & Andrew Kaplin & Steve Guoqiang Sun, 2001. "An Evaluation of Multi-Factor CIR Models Using LIBOR, Swap Rates, and Cap and Swaption Prices," NBER Working Papers 8682, National Bureau of Economic Research, Inc.
    2. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
    3. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109.
    4. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-89, October.
    5. 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.
    6. Gupta, Anurag & Subrahmanyam, Marti G., 2005. "Pricing and hedging interest rate options: Evidence from cap-floor markets," Journal of Banking & Finance, Elsevier, vol. 29(3), pages 701-733, March.
    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. 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.
    9. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
    10. Driessen, Joost & Klaassen, Pieter & Melenberg, Bertrand, 2003. "The Performance of Multi-Factor Term Structure Models for Pricing and Hedging Caps and Swaptions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(03), pages 635-672, September.
    11. Pierre Collin-Dufresne & Robert S. Goldstein, 2002. "Do Bonds Span the Fixed Income Markets? Theory and Evidence for Unspanned Stochastic Volatility," Journal of Finance, American Finance Association, vol. 57(4), pages 1685-1730, 08.
    12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    13. Carlo Mari & Roberto Reno, 2006. "Arbitrary Initial Term Structure within the CIR Model: A Perturbative Solution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 143-153.
    14. Brown, Stephen J & Dybvig, Philip H, 1986. " The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 41(3), pages 617-30, July.
    15. Jeffrey, Andrew, 1995. "Single Factor Heath-Jarrow-Morton Term Structure Models Based on Markov Spot Interest Rate Dynamics," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(04), pages 619-642, December.
    16. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    17. Damiano Brigo & Fabio Mercurio, 2001. "A deterministic-shift extension of analytically-tractable and time-homogeneous short-rate models," Finance and Stochastics, Springer, vol. 5(3), pages 369-387.
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