Bond, futures and option evaluation in the quadratic interest rate model

Abstract

This paper develops the quadratic interest-rate model of Beaglehole and Tenney in detail. For the quadratic model as well as the multifactor Cox-Ingersoll-Ross square-root model, explicit pricing formulae in terms of one-dimensional integrals of elementary functions are given for bond options, bond exchange options, caps, options on bond futures and forward contracts, and futures delivery options. For the quadratic model, certain forward and transport equations are found that explicitly determine the dynamics of the term structure in terms of initial yield and volatility curves. These option-pricing formulae are thus determined in term of the initial curves. Some shortcomings of the model are identified. New formulae for some distributions and their truncated moments are also derived.

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