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The Random Yield Curve and Interest Rate Options

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  • Meifang Chu

    (CQF - Imperial College - London)

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    Abstract

    This paper proposes a simple and unifying model to price the interest rate contingent claims in a complete market where trading can be made in continuous time. The underlying dynamics of the yield curve is modelled by a random string whose trajectory produces a random surface described by a Brownian sheet. Generalising Black-Scholes' PDE methodology, we derive the Kolmogorov field equation which describes the time-evolution of the contingent claims and obtain explicit pricing formulae for a large class of interest rate options including European calls, compound options, swaps, swaptions, caps and captions. This model can be thought of as an infinite-factor Gaussian model in the Heath-Jarrow-Morton framework and can be implemented without having to calibrate explicit parameters in the covariance function of the discount bond returns.

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    File URL: http://128.118.178.162/eps/fin/papers/9710/9710003.ps.gz
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    File URL: http://128.118.178.162/eps/fin/papers/9710/9710003.pdf
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    Bibliographic Info

    Paper provided by EconWPA in its series Finance with number 9710003.

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    Length: 23 pages
    Date of creation: 22 Oct 1997
    Date of revision:
    Handle: RePEc:wpa:wuwpfi:9710003

    Note: Type of Document - ps; prepared on UNIX Sparc TeX; to print on HP/PostScript; pages: 23; figures: none. This paper has been submitted for publication.
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    Web page: http://128.118.178.162

    Related research

    Keywords: Kolmogorov Field Equation; Brownian Sheet; Arbitrage Pricing Theory; Self-Financing Strategy; Heath-Jarrow-Morton Framework;

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    References

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    2. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    3. Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
    4. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258.
    5. 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.
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