The Yield Envelope: Price Ranges for Fixed Income Products

D. Epstein and P. Wilmott

Abstract

There is an extensive literature on the valuation of a fixed income contracts. The present work addresses the problem from a new outlook: we find upper and lower bounds for the value of a contract. Constraints are imposed on the evolution of a short-term interest rate and a liability is valued using its present value. A first-order non-linear hyperbolic partial differential equation is formulated for the value, V, of the contract. The numerical solution of this equation is then explored. To optimise its value, our contract is hedged with market traded zero-coupon bonds. We can then generate the 'Yield Envelope' (an alternative to the yield curve). At a maturity for which there are no traded instruments, a spread for the yield is obtained.

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