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Calibration of Implied Volatility in Generalized Hull-White Model

Received: 6 March 2016     Published: 6 March 2016
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Abstract

This paper concerns a problem of calibrating implied volatility in generalized Hull-White model from the market prices of zero-coupon bonds. By using the regularization method, we establish the existence and stability of the optimal solution, and give the necessary condition that the solution satisfies. Finally numerical results show that the method is stable and effective.

Published in Journal of Finance and Accounting (Volume 4, Issue 2)
DOI 10.11648/j.jfa.20160402.11
Page(s) 25-32
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2016. Published by Science Publishing Group

Keywords

Calibration, Implied Volatility, Generalized Hull-White Model, Regularization

References
[1] O. Vasicek, An equilibriurm characterization of the term structure, Jounal of Financial Economics, 1977, 5(2): 177-188.
[2] J. C. Cox, J. E. Ingersoll, S. A. Ross, A Theory of the Term Structure of Interest Rates, Econometrica, 1985, 53(2): 385-407.
[3] J. Hull, A. White, Pricing Interest-Rate-Derivative Securitites, The Review of Financial Studies, 1990, 3(4): 573-392.
[4] K. R. Chan, G. A. Karolyi, F. Longstaff, A. B. Sanders, An Empirical Comparison of Alternative Models of the Short-Term Interest Rate, Journal of Finance, 1992, 47(3): 1209-1228.
[5] J. Hull, A. White, Numerical Procedures for Implementing Term Structure Models I: Single-Factor Models, Journal of Derivatives, 1994, 2(1): 7-16.
[6] J. Hull, A. White, The general Hull-White model and super calibration, Finance Analysts Journal, 2001, 57(6): 34-43.
[7] I. Bouchouev, V. Isakov, N. Valdivia, Recovery of volatility coefficient by linearization, Quantitive Finance, 2002, 2: 257-263.
[8] I. Bouchouev, V. Isakov, Uniqueness, stability and numerical methods for the inverse problem that arises in fnancial markets, Inverse Problems, 1999, 15(3): 95-116.
[9] H. Egger, T. Hein, B. Hofmann, On decoupling of volatility smile and term structure in inverse option pricing, Inverse Problem, 2006, 22(4): 1247-1259.
[10] R. Kramer, M. Richter, Ill-posedness versus ill-conditioning -an example from inverse option pricing, Applicable Analysis, 2008, 87(4): 465-477.
[11] J. Hull, A. White, A generalized procedure for building trees for the short rate and its application to determining market implied volatility functions, Quantitative Finance, 2015, 15(3): 443-454.
[12] A. M. Ferreiro, J. A. García-Rodríguez, J. G. López-Salas, C. Vázquez, SABR/LIBOR market models: Pricing and calibration for some interest rate derivatives, Applied Mathematics and Computation, 2014, 242: 65-89.
[13] Y. F. Wang, Computational Methods for Inverse Problems and Their Applications, Higher Education Press, Beijing, 2007. (In chinese)
[14] H. Egger, H. W. Engl, Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates, Inverse Problems, 2005, 21(3): 1027-1045.
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[16] C. Y. Tang, S. X. Chen, Parameter estimation and bias Correction for diffusion processes, Journal of Econometrics, 2009, 149(1): 65-81.
[17] M. Rainer, Calibration of stochastic models for interest rate derivatives, Optimization, 2009, 58(3): 373-388.
[18] M. Rodrigo, R. Mamon, An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions, Quantitative Finance, 2014, 14(11): 1961-1970.
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  • APA Style

    Fangfang Zhao, Zuoliang Xu, Changjing Li. (2016). Calibration of Implied Volatility in Generalized Hull-White Model. Journal of Finance and Accounting, 4(2), 25-32. https://doi.org/10.11648/j.jfa.20160402.11

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    ACS Style

    Fangfang Zhao; Zuoliang Xu; Changjing Li. Calibration of Implied Volatility in Generalized Hull-White Model. J. Finance Account. 2016, 4(2), 25-32. doi: 10.11648/j.jfa.20160402.11

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    AMA Style

    Fangfang Zhao, Zuoliang Xu, Changjing Li. Calibration of Implied Volatility in Generalized Hull-White Model. J Finance Account. 2016;4(2):25-32. doi: 10.11648/j.jfa.20160402.11

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  • @article{10.11648/j.jfa.20160402.11,
      author = {Fangfang Zhao and Zuoliang Xu and Changjing Li},
      title = {Calibration of Implied Volatility in Generalized Hull-White Model},
      journal = {Journal of Finance and Accounting},
      volume = {4},
      number = {2},
      pages = {25-32},
      doi = {10.11648/j.jfa.20160402.11},
      url = {https://doi.org/10.11648/j.jfa.20160402.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.jfa.20160402.11},
      abstract = {This paper concerns a problem of calibrating implied volatility in generalized Hull-White model from the market prices of zero-coupon bonds. By using the regularization method, we establish the existence and stability of the optimal solution, and give the necessary condition that the solution satisfies. Finally numerical results show that the method is stable and effective.},
     year = {2016}
    }
    

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    T1  - Calibration of Implied Volatility in Generalized Hull-White Model
    AU  - Fangfang Zhao
    AU  - Zuoliang Xu
    AU  - Changjing Li
    Y1  - 2016/03/06
    PY  - 2016
    N1  - https://doi.org/10.11648/j.jfa.20160402.11
    DO  - 10.11648/j.jfa.20160402.11
    T2  - Journal of Finance and Accounting
    JF  - Journal of Finance and Accounting
    JO  - Journal of Finance and Accounting
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    EP  - 32
    PB  - Science Publishing Group
    SN  - 2330-7323
    UR  - https://doi.org/10.11648/j.jfa.20160402.11
    AB  - This paper concerns a problem of calibrating implied volatility in generalized Hull-White model from the market prices of zero-coupon bonds. By using the regularization method, we establish the existence and stability of the optimal solution, and give the necessary condition that the solution satisfies. Finally numerical results show that the method is stable and effective.
    VL  - 4
    IS  - 2
    ER  - 

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Author Information
  • School of Information, Renmin University of China, Beijing, China

  • School of Information, Renmin University of China, Beijing, China

  • School of Mathematical Sciences, Shandong Normal University, Jinan, China

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