IDEAS home Printed from https://ideas.repec.org/p/hal/journl/hal-01275397.html
   My bibliography  Save this paper

Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling

Author

Listed:
  • Ying Jiao

    (SAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon)

  • Chunhua Ma

    (Nankai University, School of mathematical sciences - NKU - Nankai University)

  • Simone Scotti

    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - UPMC - Université Pierre et Marie Curie - Paris 6 - UPD7 - Université Paris Diderot - Paris 7 - CNRS - Centre National de la Recherche Scientifique)

Abstract

We introduce a class of interest rate models, called the α-CIR model, which gives a natural extension of the standard CIR model by adopting the α-stable Lévy process and preserving the branching property. This model allows to describe in a unified and parsimonious way several recent observations on the sovereign bond market such as the persistency of low interest rate together with the presence of large jumps at local extent. We emphasize on a general integral representation of the model by using random fields, with which we establish the link to the CBI processes and the affine models. Finally we analyze the jump behaviors and in particular the large jumps, and we provide numerical illustrations.

Suggested Citation

  • Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Post-Print hal-01275397, HAL.
    • Handle: RePEc:hal:journl:hal-01275397
    Note: View the original document on HAL open archive server: https://hal.science/hal-01275397v2
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01275397v2/document
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Gibbons, Michael R & Ramaswamy, Krishna, 1993. "A Test of the Cox, Ingersoll, and Ross Model of the Term Structure," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 619-658.
    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. Thibault Jaisson & Mathieu Rosenbaum, 2013. "Limit theorems for nearly unstable Hawkes processes," Papers 1310.2033, arXiv.org, revised Mar 2015.
    4. Damir Filipovic, 2001. "A general characterization of one factor affine term structure models," Finance and Stochastics, Springer, vol. 5(3), pages 389-412.
    5. Duhalde, Xan & Foucart, Clément & Ma, Chunhua, 2014. "On the hitting times of continuous-state branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 124(12), pages 4182-4201.
    6. Fu, Zongfei & Li, Zenghu, 2010. "Stochastic equations of non-negative processes with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(3), pages 306-330, March.
    7. Brown, Stephen J & Dybvig, Philip H, 1986. "The Empirical Implications of the Cox, Ingersoll, Ross Theory of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 41(3), pages 617-630, July.
    8. D. P. Kennedy, 1994. "The Term Structure Of Interest Rates As A Gaussian Random Field," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 247-258, July.
    9. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    10. Kallsen, Jan & Muhle-Karbe, Johannes, 2010. "Exponentially affine martingales, affine measure changes and exponential moments of affine processes," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 163-181, February.
    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. Alessandro Bondi & Sergio Pulido & Simone Scotti, 2022. "The rough Hawkes Heston stochastic volatility model," Working Papers hal-03827332, HAL.
    2. Fontana, Claudio & Gnoatto, Alessandro & Szulda, Guillaume, 2023. "CBI-time-changed Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 323-349.
    3. Jianhai Bao & Jian Wang, 2023. "Coupling methods and exponential ergodicity for two‐factor affine processes," Mathematische Nachrichten, Wiley Blackwell, vol. 296(5), pages 1716-1736, May.
    4. Riccardo Brignone & Carlo Sgarra, 2020. "Asian options pricing in Hawkes-type jump-diffusion models," Annals of Finance, Springer, vol. 16(1), pages 101-119, March.
    5. repec:uts:finphd:41 is not listed on IDEAS
    6. Micha{l} Barski & Rafa{l} {L}ochowski, 2024. "Affine term structure models driven by independent L\'evy processes," Papers 2402.07503, arXiv.org.
    7. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2021. "CBI-time-changed Lévy processes for multi-currency modeling," Working Papers 14/2021, University of Verona, Department of Economics.
    8. Frikha, Noufel & Li, Libo, 2021. "Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs," Stochastic Processes and their Applications, Elsevier, vol. 132(C), pages 76-107.
    9. Aur'elien Alfonsi & Guillaume Szulda, 2024. "On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients," Papers 2402.19203, arXiv.org.
    10. 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.
    11. Li, Libo & Taguchi, Dai, 2019. "On the Euler–Maruyama scheme for spectrally one-sided Lévy driven SDEs with Hölder continuous coefficients," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 15-26.
    12. Pingping Jiang & Bo Li & Yongjin Wang, 2020. "Exit Times, Undershoots and Overshoots for Reflected CIR Process with Two-Sided Jumps," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 693-710, June.
    13. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2021. "The Alpha‐Heston stochastic volatility model," Mathematical Finance, Wiley Blackwell, vol. 31(3), pages 943-978, July.
    14. M.E. Mancino & S. Scotti & G. Toscano, 2020. "Is the Variance Swap Rate Affine in the Spot Variance? Evidence from S&P500 Data," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(4), pages 288-316, July.
    15. Alessandro Bondi & Sergio Pulido & Simone Scotti, 2022. "The rough Hawkes Heston stochastic volatility model," Papers 2210.12393, arXiv.org.
    16. Claudio Fontana & Alessandro Gnoatto & Guillaume Szulda, 2022. "CBI-time-changed Lévy processes," Working Papers 05/2022, University of Verona, Department of Economics.
    17. Jiao, Ying & Ma, Chunhua & Scotti, Simone & Sgarra, Carlo, 2019. "A branching process approach to power markets," Energy Economics, Elsevier, vol. 79(C), pages 144-156.
    18. Backwell, Alex & Hayes, Joshua, 2022. "Expected and Unexpected Jumps in the Overnight Rate: Consistent Management of the Libor Transition," Journal of Banking & Finance, Elsevier, vol. 145(C).
    19. Chen, Li & Ma, Yong & Xiao, Weilin, 2022. "Pricing defaultable bonds under Hawkes jump-diffusion processes," Finance Research Letters, Elsevier, vol. 47(PB).
    20. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2017. "Asymptotic properties of maximum likelihood estimator for the growth rate of a stable CIR process based on continuous time observations," Papers 1711.02140, arXiv.org, revised Feb 2019.
    21. Micha{l} Barski & Rafa{l} {L}ochowski, 2023. "Classification and calibration of affine models driven by independent L\'evy processes," Papers 2303.08477, arXiv.org.

    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. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Working Papers hal-01275397, HAL.
    2. Ying Jiao & Chunhua Ma & Simone Scotti, 2016. "Alpha-CIR Model with Branching Processes in Sovereign Interest Rate Modelling," Papers 1602.05541, arXiv.org, revised Feb 2016.
    3. Ying Jiao & Chunhua Ma & Simone Scotti, 2017. "Alpha-CIR model with branching processes in sovereign interest rate modeling," Finance and Stochastics, Springer, vol. 21(3), pages 789-813, July.
    4. Ying Jiao & Chunhua Ma & Simone Scotti & Chao Zhou, 2018. "The Alpha-Heston Stochastic Volatility Model," Papers 1812.01914, arXiv.org.
    5. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    6. Matyas Barczy & Mohamed Ben Alaya & Ahmed Kebaier & Gyula Pap, 2016. "Asymptotic properties of maximum likelihood estimator for the growth rate for a jump-type CIR process based on continuous time observations," Papers 1609.05865, arXiv.org, revised Aug 2017.
    7. Isaac Kleshchelski & Nicolas Vincent, 2007. "Robust Equilibrium Yield Curves," Cahiers de recherche 08-02, HEC Montréal, Institut d'économie appliquée.
    8. Micha{l} Barski & Rafa{l} {L}ochowski, 2024. "Affine term structure models driven by independent L\'evy processes," Papers 2402.07503, arXiv.org.
    9. 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.
    10. 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.
    11. Gil-Bazo Javier & Rubio Gonzalo, 2004. "A Nonparametric Dimension Test of the Term Structure," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(3), pages 1-28, September.
    12. Tao Zou & Song Xi Chen, 2017. "Enhancing Estimation for Interest Rate Diffusion Models With Bond Prices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 486-498, July.
    13. Jacob Boudoukh & Matthew Richardson & Richard Stanton & Robert Whitelaw, 1999. "A Multifactor, Nonlinear, Continuous-Time Model of Interest Rate Volatility," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-042, New York University, Leonard N. Stern School of Business-.
    14. Angelos Dassios & Jiwook Jang & Hongbiao Zhao, 2019. "A Generalised CIR Process with Externally-Exciting and Self-Exciting Jumps and Its Applications in Insurance and Finance," Risks, MDPI, vol. 7(4), pages 1-18, October.
    15. Steven Heston, 2007. "A model of discontinuous interest rate behavior, yield curves, and volatility," Review of Derivatives Research, Springer, vol. 10(3), pages 205-225, December.
    16. Francesco Drudi & Roberto Violi, 1999. "Structure par terme des taux d'intérêt, volatilité et primes de risque : applications au marché de l'Eurolire," Économie et Prévision, Programme National Persée, vol. 140(4), pages 21-34.
    17. Dahlquist, Magnus, 1996. "On alternative interest rate processes," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 1093-1119, July.
    18. Longstaff, Francis A. & Santa-Clara, Pedro & Schwartz, Eduardo S., 2001. "Throwing away a billion dollars: the cost of suboptimal exercise strategies in the swaptions market," Journal of Financial Economics, Elsevier, vol. 62(1), pages 39-66, October.
    19. repec:wyi:journl:002109 is not listed on IDEAS
    20. Berardi, Andrea, 1995. "Estimating the Cox, ingersoll and Ross model of the term structure: a multivariate approach," Ricerche Economiche, Elsevier, vol. 49(1), pages 51-74, March.
    21. Robert Faff & Sirimon Treepongkaruna, 2013. "A re-examination of the empirical performance of the Longstaff and Schwartz two-factor term structure model using real yield data," Australian Journal of Management, Australian School of Business, vol. 38(2), pages 333-352, August.

    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:hal:journl:hal-01275397. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.