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On the distribution of extended CIR model

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  • Peng, Qidi
  • Schellhorn, Henry

Abstract

We study the probability distribution of the interest rate in the extended Cox–Ingersoll–Ross model, where all the parameters are time-varying. We show that the distribution can be represented as that of a convergent series of weighted independent central and noncentral chi-square random variables. Simulation algorithms and their applications to finance have been discussed.

Suggested Citation

  • Peng, Qidi & Schellhorn, Henry, 2018. "On the distribution of extended CIR model," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 23-29.
    • Handle: RePEc:eee:stapro:v:142:y:2018:i:c:p:23-29
    DOI: 10.1016/j.spl.2018.06.011
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    References listed on IDEAS

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    1. Duchesne, Pierre & Lafaye De Micheaux, Pierre, 2010. "Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 858-862, April.
    2. 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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    3. Yoosef Maghsoodi, 1996. "Solution Of The Extended Cir Term Structure And Bond Option Valuation," Mathematical Finance, Wiley Blackwell, vol. 6(1), pages 89-109, January.
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    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. Martin Keller-Ressel & Thomas Steiner, 2008. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 12(2), pages 149-172, April.
    7. Robert B. Davies, 1980. "The Distribution of a Linear Combination of χ2 Random Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 323-333, November.
    8. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    9. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    10. 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. Wulan Anggraeni & Sudradjat Supian & Sukono & Nurfadhlina Binti Abdul Halim, 2022. "Earthquake Catastrophe Bond Pricing Using Extreme Value Theory: A Mini-Review Approach," Mathematics, MDPI, vol. 10(22), pages 1-22, November.
    2. Sanae Rujivan & Athinan Sutchada & Kittisak Chumpong & Napat Rujeerapaiboon, 2023. "Analytically Computing the Moments of a Conic Combination of Independent Noncentral Chi-Square Random Variables and Its Application for the Extended Cox–Ingersoll–Ross Process with Time-Varying Dimens," Mathematics, MDPI, vol. 11(5), pages 1-29, March.
    3. Virginia Giorno & Amelia G. Nobile, 2021. "On the First-Passage Time Problem for a Feller-Type Diffusion Process," Mathematics, MDPI, vol. 9(19), pages 1-27, October.
    4. Virginia Giorno & Amelia G. Nobile, 2021. "Time-Inhomogeneous Feller-Type Diffusion Process in Population Dynamics," Mathematics, MDPI, vol. 9(16), pages 1-29, August.

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