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A New Model for Interest Rates

Author

Listed:
  • 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;
    Dept. of Mathematics, Imperial College, Exhibition Road, SWT 2AZ, London, UK)

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.

Suggested Citation

  • D. Epstein & P. Wilmott, 1998. "A New Model for Interest Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 1(02), pages 195-226.
    • Handle: RePEc:wsi:ijtafx:v:01:y:1998:i:02:n:s0219024998000114
    DOI: 10.1142/S0219024998000114
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