A New Model for Interest Rates

D. Epstein and P. Wilmott
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D. Epstein: Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford, OX1 3LB, UK
P. Wilmott: Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford, OX1 3LB, UK;

International Journal of Theoretical and Applied Finance (IJTAF), 1998, vol. 01, issue 02, 195-226

Abstract: There are many theories and models underlying the valuation of fixed income security portfolios. This work addresses the problem from a new perspective: the objective is to find a lower bound for the value of a portfolio of cash flows. We set up conditions for the evolution of a short-term interest rate and value a liability using its present value. We formulate a first-order nonlinear hyperbolic partial differential equation for the value,V, of the portfolio. We explore the solution of this equation and then hedge our portfolio with market-traded zero-coupon bonds of known value. We include some salient examples — generating the Yield Envelope and valuing caps, floors and bond options.

Date: 1998
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DOI: 10.1142/S0219024998000114

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