The Random Yield Curve and Interest Rate Options

Meifang Chu
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Meifang Chu: CQF - Imperial College - London

Finance from University Library of Munich, Germany

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.

Keywords: Kolmogorov Field Equation; Brownian Sheet; Arbitrage Pricing Theory; Self-Financing Strategy; Heath-Jarrow-Morton Framework (search for similar items in EconPapers)
JEL-codes: C0 C6 E4 G1 G12 G13 (search for similar items in EconPapers)
Pages: 23 pages
Date: 1997-10-22
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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