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Least squares estimation for the subcritical Heston model based on continuous time observations

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  • Matyas Barczy
  • Balazs Nyul
  • Gyula Pap

Abstract

We prove strong consistency and asymptotic normality of least squares estimators for the subcritical Heston model based on continuous time observations. We also present some numerical illustrations of our results.

Suggested Citation

  • Matyas Barczy & Balazs Nyul & Gyula Pap, 2015. "Least squares estimation for the subcritical Heston model based on continuous time observations," Papers 1511.05948, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1511.05948
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    References listed on IDEAS

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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: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    2. Hurn, A.S. & Lindsay, K.A. & McClelland, A.J., 2013. "A quasi-maximum likelihood method for estimating the parameters of multivariate diffusions," Journal of Econometrics, Elsevier, vol. 172(1), pages 106-126.
    3. Griselda Deelstra & Freddy Delbaen, 1998. "Convergence of discretised stochastic interest rate: processes with stochastic drift term," ULB Institutional Repository 2013/7584, ULB -- Universite Libre de Bruxelles.
    4. G. Deelstra & F. Delbaen, 1998. "Convergence of discretized stochastic (interest rate) processes with stochastic drift term," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 14(1), pages 77-84, March.
    5. Matyas Barczy & Gyula Pap & Tamas T. Szabo, 2014. "Parameter estimation for the subcritical Heston model based on discrete time observations," Papers 1403.0527, arXiv.org, revised Feb 2016.
    6. Mark Broadie & Özgür Kaya, 2006. "Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes," Operations Research, INFORMS, vol. 54(2), pages 217-231, April.
    7. Overbeck, Ludger & Rydén, Tobias, 1997. "Estimation in the Cox-Ingersoll-Ross Model," Econometric Theory, Cambridge University Press, vol. 13(3), pages 430-461, June.
    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. Matyas Barczy & Gyula Pap, 2013. "Asymptotic properties of maximum likelihood estimators for Heston models based on continuous time observations," Papers 1310.4783, arXiv.org, revised Jun 2015.
    10. Aurélien Alfonsi, 2015. "Affine Diffusions and Related Processes: Simulation, Theory and Applications," Post-Print hal-03127212, HAL.
    11. Matyas Barczy & Leif Doering & Zenghu Li & Gyula Pap, 2012. "On parameter estimation for critical affine processes," Papers 1210.1866, arXiv.org, revised Mar 2013.
    12. van Zanten, Harry, 2000. "A multivariate central limit theorem for continuous local martingales," Statistics & Probability Letters, Elsevier, vol. 50(3), pages 229-235, November.
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