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 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.