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A square root interest rate model fitting discrete initial term structure data

  • Erik Schlogl
  • Lutz Schlogl

This paper presents one-factor and multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type 'square root' diffusions with piece wise constant parameters. The model is fitted to initial term structures given by a finite number of data points, interpolating endogenously. Closed form and near closed form solutions for a large class of fixed income derivatives are derived in terms of a compound noncentral chi-square distribution. An implementation of the model is discussed where the initial term structure of volatility is fitted via cap prices.

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Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 7 (2000)
Issue (Month): 3 ()
Pages: 183-209

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Handle: RePEc:taf:apmtfi:v:7:y:2000:i:3:p:183-209
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  1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  2. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
  3. F. Jamshidian, 1995. "A simple class of square-root interest-rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 61-72.
  4. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
  5. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
  6. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  7. Schloegl, Erik & Lutz Schloegl, 1997. "A Tractable Term Structure Model with Endogenous Interpolation and Positive Interest Rates," Discussion Paper Serie B 396, University of Bonn, Germany.
  8. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109.
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