IDEAS home Printed from https://ideas.repec.org/a/gam/jijfss/v10y2022i2p38-d820074.html
   My bibliography  Save this article

On the Deterministic-Shift Extended CIR Model in a Negative Interest Rate Framework

Author

Listed:
  • Marco Di Francesco

    (UnipolSai Assicurazioni, Via Stalingrado 45, 40128 Bologna, Italy
    These authors contributed equally to this work.)

  • Kevin Kamm

    (Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, we propose a new exogenous model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox–Ingersoll–Ross (CIR) model with a perfect fit to the observed term-structure. We use the difference between two independent CIR processes and apply the deterministic-shift extension technique. To allow for a fast calibration to the market swaption surface, we apply the Gram–Charlier expansion to calculate the swaption prices in our model. We run several numerical tests to demonstrate the strengths of this model by using Monte-Carlo techniques. In particular, the model produces close Bermudan swaption prices compared to Bloomberg’s Hull–White one-factor model. Moreover, it finds constant maturity swap (CMS) rates very close to Bloomberg’s CMS rates.

Suggested Citation

  • Marco Di Francesco & Kevin Kamm, 2022. "On the Deterministic-Shift Extended CIR Model in a Negative Interest Rate Framework," IJFS, MDPI, vol. 10(2), pages 1-26, May.
    • Handle: RePEc:gam:jijfss:v:10:y:2022:i:2:p:38-:d:820074
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7072/10/2/38/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7072/10/2/38/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
    3. Cornelis W Oosterlee & Lech A Grzelak, 2019. "Mathematical Modeling and Computation in Finance:With Exercises and Python and MATLAB Computer Codes," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0236, February.
    4. 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.
    5. Keiichi Tanaka & Takeshi Yamada & Toshiaki Watanabe, 2010. "Applications of Gram-Charlier expansion and bond moments for pricing of interest rates and credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 645-662.
    6. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. 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.
    3. He, Jie-Cao & Hsieh, Chang-Chieh & Huang, Zi-Wei & Lin, Shih-Kuei, 2023. "Valuation of callable range accrual linked to CMS Spread under generalized swap market model," International Review of Financial Analysis, Elsevier, vol. 90(C).
    4. Raoul Pietersz & Antoon Pelsser, 2010. "A comparison of single factor Markov-functional and multi factor market models," Review of Derivatives Research, Springer, vol. 13(3), pages 245-272, October.
    5. Xiao Lin, 2016. "The Zero-Coupon Rate Model for Derivatives Pricing," Papers 1606.01343, arXiv.org, revised Feb 2022.
    6. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    7. Bueno-Guerrero, Alberto & Moreno, Manuel & Navas, Javier F., 2015. "Stochastic string models with continuous semimartingales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 229-246.
    8. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    9. Ronald Hochreiter & Georg Pflug, 2006. "Polynomial Algorithms for Pricing Path-Dependent Interest Rate Instruments," Computational Economics, Springer;Society for Computational Economics, vol. 28(3), pages 291-309, October.
    10. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    11. Robert R. Bliss & Ehud I. Ronn, 1997. "Callable U.S. Treasury bonds: optimal calls, anomalies, and implied volatilities," FRB Atlanta Working Paper 97-1, Federal Reserve Bank of Atlanta.
    12. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    13. Prakash Chakraborty & Kiseop Lee, 2022. "Bond Prices Under Information Asymmetry and a Short Rate with Instantaneous Feedback," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 613-634, June.
    14. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    15. Frank De Jong & Joost Driessen & Antoon Pelsser, 2001. "Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis," Review of Finance, European Finance Association, vol. 5(3), pages 201-237.
    16. Dong-Mei Zhu & Jiejun Lu & Wai-Ki Ching & Tak-Kuen Siu, 2019. "Option Pricing Under a Stochastic Interest Rate and Volatility Model with Hidden Markovian Regime-Switching," Computational Economics, Springer;Society for Computational Economics, vol. 53(2), pages 555-586, February.
    17. 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.
    18. Fan, Longzhen & Johansson, Anders C., 2010. "China's official rates and bond yields," Journal of Banking & Finance, Elsevier, vol. 34(5), pages 996-1007, May.
    19. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    20. repec:uts:finphd:40 is not listed on IDEAS
    21. R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26, March.

    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:gam:jijfss:v:10:y:2022:i:2:p:38-:d:820074. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.