Calibration of Implied Volatility in Generalized Hull-White Model

Fangfang Zhao; Zuoliang Xu; Changjing Li

doi:doi:10.11648/j.jfa.20160402.11

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Calibration of Implied Volatility in Generalized Hull-White Model

Fangfang Zhao, Zuoliang Xu, Changjing Li

Published in Journal of Finance and Accounting (Volume 4, Issue 2)

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

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[7]	I. Bouchouev, V. Isakov, N. Valdivia, Recovery of volatility coefficient by linearization, Quantitive Finance, 2002, 2: 257-263.
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[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.
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[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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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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TY  - JOUR
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
SP  - 25
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

Fangfang Zhao

School of Information, Renmin University of China, Beijing, China
Zuoliang Xu

School of Information, Renmin University of China, Beijing, China
Changjing Li

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

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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

Copy | Download

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

Copy | Download

@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}
}

Copy | Download

TY  - JOUR
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
SP  - 25
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  -

Copy | Download