IDEAS home Printed from https://ideas.repec.org/p/uts/rpaper/24.html
   My bibliography  Save this paper

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

Author

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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    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. 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..
    4. 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.
    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. 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. F. Jamshidian, 1995. "A simple class of square-root interest-rate models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(1), pages 61-72.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Areski Cousin & Ibrahima Niang, 2014. "On the Range of Admissible Term-Structures," Working Papers hal-00968943, HAL.
    2. 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, July-Dece.
    3. 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.
    4. Mesias Alfeus, 2019. "Stochastic Modelling of New Phenomena in Financial Markets," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2019, January-A.
    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, July-Dece.
    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.
    7. 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 2-2014, January-A.
    8. 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.
    9. 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 3-2007, January-A.
    10. Lin-Yee Hin & Nikolai Dokuchaev, 2016. "Short Rate Forecasting Based On The Inference From The Cir Model For Multiple Yield Curve Dynamics," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-33, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    2. repec:uts:finphd:40 is not listed on IDEAS
    3. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2007, January-A.
    4. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018, January-A.
    5. Shane Miller, 2007. "Pricing of Contingent Claims Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 25, July-Dece.
    6. Josheski Dushko & Apostolov Mico, 2021. "Equilibrium Short-Rate Models Vs No-Arbitrage Models: Literature Review and Computational Examples," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 25(3), pages 42-71, September.
    7. Egorov, Alexei V. & Li, Haitao & Xu, Yuewu, 2003. "Maximum likelihood estimation of time-inhomogeneous diffusions," Journal of Econometrics, Elsevier, vol. 114(1), pages 107-139, May.
    8. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    9. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    10. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2011, January-A.
    11. Benjamin Cheng & Christina Nikitopoulos-Sklibosios & Erik Schlogl, 2015. "Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates," Research Paper Series 366, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    13. Boero, G. & Torricelli, C., 1996. "A comparative evaluation of alternative models of the term structure of interest rates," European Journal of Operational Research, Elsevier, vol. 93(1), pages 205-223, August.
    14. repec:wyi:journl:002108 is not listed on IDEAS
    15. Alain Monfort & Fulvio Pegoraro, 2006. "Multi-Lag Term Structure Models with Stochastic Risk Premia," Working Papers 2006-29, Center for Research in Economics and Statistics.
    16. Qian Li & Li Wang, 2023. "Option pricing under jump diffusion model," Papers 2305.10678, arXiv.org.
    17. Carl Chiarella & Christina Nikitopoulos Sklibosios & Erik Schlogl, 2007. "A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 365-399.
    18. Cheng, Benjamin & Nikitopoulos, Christina Sklibosios & Schlögl, Erik, 2018. "Pricing of long-dated commodity derivatives: Do stochastic interest rates matter?," Journal of Banking & Finance, Elsevier, vol. 95(C), pages 148-166.
    19. Arismendi-Zambrano, Juan & Belitsky, Vladimir & Sobreiro, Vinicius Amorim & Kimura, Herbert, 2022. "The implications of dependence, tail dependence, and bounds’ measures for counterparty credit risk pricing," Journal of Financial Stability, Elsevier, vol. 58(C).
    20. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, September.
    21. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, March.
    22. Peng, Qidi & Schellhorn, Henry, 2018. "On the distribution of extended CIR model," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 23-29.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:uts:rpaper:24. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Duncan Ford (email available below). General contact details of provider: https://edirc.repec.org/data/qfutsau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.