## 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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