The Random Yield Curve and Interest Rate Options

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 eld 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 innnite-factor Gaus-sian 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. Rebonato for their encouragement and stimulating discussions. She would also like to thank the directors of the Centre for Quantitative Finance, Nicos Christoodes and Gerry Salkin, for their support of this work.