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A Square-Root Interest Rate Model Fitting Discrete Initial Term Structure Data

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Abstract

This paper presents the one- and the multifactor versions of a term structure model in which the factor dynamics are given by Cox/Ingersoll/Ross (CIR) type "square root" diffusions with piecewise constant parameters. This 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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  • Erik Schlögl & Lutz Schlögl, 1999. "A Square-Root Interest Rate Model Fitting Discrete Initial Term Structure Data," Research Paper Series 24, Quantitative Finance Research Centre, University of Technology, Sydney.
  • Handle: RePEc:uts:rpaper:24
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    1. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters,in: Theory Of Valuation, chapter 5, pages 129-164 World Scientific Publishing Co. Pte. Ltd..
    2. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109.
    3. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    5. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    6. 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 637-654, May-June.
    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. F. Jamshidian, 1995. "A simple class of square-root interest-rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 61-72.
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    Cited by:

    1. Areski Cousin & Ibrahima Niang, 2014. "On the Range of Admissible Term-Structures," Working Papers hal-00968943, HAL.
    2. Yang Chang & Erik Schlogl, 2014. "A Consistent Framework for Modelling Basis Spreads in Tenor Swaps," Research Paper Series 348, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Samson Assefa, 2007. "Pricing Swaptions and Credit Default Swaptions in the Quadratic Gaussian Factor Model," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 31.
    4. Hans-Peter Bermin, 2012. "Bonds and Options in Exponentially Affine Bond Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(6), pages 513-534, December.
    5. Yang Chang, 2014. "A Consistent Approach to Modelling the Interest Rate Market Anomalies Post the Global Financial Crisis," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 18, November.
    6. Gabriel G. Drimus, 2012. "Options on realized variance by transform methods: a non-affine stochastic volatility model," Quantitative Finance, Taylor & Francis Journals, vol. 12(11), pages 1679-1694, November.

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