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Implementation and performance of various stochastic models for interest rate derivatives

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  • Francesco Rapisarda
  • Roberto Silvotti

Abstract

The arbitrage free market framework of Heath, Jarrow and Morton provides a mathematical scheme according to which the valuation of all interest rate derivatives depend on two kinds of basic parameters: the discount function and the (generally stochastic) volatilities of zero coupon bonds of all maturities. Among the models in this class, Flesaker‐Hughston's rational lognormal model stands out for naturality and simplicity while incorporating positivity of interest rates: all fundamental processes (short rate, discount and zero‐coupon bonds) are parametrized as rational functions of an exponential martingale. Its practical implementation presents, however, a few subtle aspects. We discuss its numerical implementation with special attention to issues of fitting and calibration, and pricing of exotic options. A comparison with other standard models such as Hull‐White and Black‐Karasinki will be presented in test cases. Copyright © 2001 John Wiley & Sons, Ltd.

Suggested Citation

  • Francesco Rapisarda & Roberto Silvotti, 2001. "Implementation and performance of various stochastic models for interest rate derivatives," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 17(1), pages 109-120, January.
    • Handle: RePEc:wly:apsmbi:v:17:y:2001:i:1:p:109-120
    DOI: 10.1002/asmb.432
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    Cited by:

    1. Matheus R Grasselli & Tsunehiro Tsujimoto, 2011. "Calibration of Chaotic Models for Interest Rates," Papers 1106.2478, arXiv.org.

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