Study of American Option Pricing Based on Levy Process

Hong Zhang; Jie Zhu; Jian Guo; Li Zhou

doi:doi:10.11648/j.ajam.20150303.22

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Study of American Option Pricing Based on Levy Process

Hong Zhang, Jie Zhu, Jian Guo, Li Zhou

Published in American Journal of Applied Mathematics (Volume 3, Issue 3)

Received: 8 May 2015 Accepted: 22 May 2015 Published: 1 June 2015

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Abstract

After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models.

Published in	American Journal of Applied Mathematics (Volume 3, Issue 3)
DOI	10.11648/j.ajam.20150303.22
Page(s)	151-156
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), 2024. Published by Science Publishing Group

Keywords

Levy Stochastic Processes, Option Pricing Models, Chinese Warrants Market, American Option Pricing, Risk-Neutral Adjustment, Variance Reduction Techniques

References

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[2]	Lays Stentoft. American option pricing using simulation: an introduction with to the GARCH option pricing model[C]. CREATES working paper, 2012.
[3]	Lehar A, Scheicher M, Schittenkopf C. GARCH vs. stochastic volatility: option pricing and risk management [J]. Journal of Banking & Finance, 2002, 160(1): 246-256.
[4]	Longstaff F A, Schwartz E S. Valuing American options by simulation: a simple least-squares approach [J]. The Review of Financial Studies, 2001, 14(1): 113-147.
[5]	Lydia W. American Monte Carlo option pricing under pure jump Levy models [D]. Stellenbosch University, 2013.
[6]	Kim J, Jang B G, Kim K T. A simple iterative method for the valuation of American options [J). Quantitative Finance, 2013, 13(6): 885-895.
[7]	Chorro C, Guegan D, hyperbolic Lelpo F. Option pricing for GARCH-type models with innovation [J]. Finance, 2012, 12(7): 1079-1094.
[8]	Christoffersen P, Jacobs K, Ornthanalai C. GARCH option valuation: and evidence [Z]. Aarhus University, Working Paper, 2012. theory
[9]	Byun SJ, Min B. Conditional volatility and the GARCH option pricing model with non-normal innovations [J]. 3ournal of Futures Market, 2413, 33(1): 1-28.
[10]	Carr P, Madan D B. Option valuation using the fast Fourier transform [J]. Journal of Computational Finance, 1999, 2(4): 61-73.
[11]	Carr P, Geman H, Madan D H and Yor M. The fine structure of asset returns: an empirical investigation [J]. Journal of Business, 2002, 75(2): 305-332.
[12]	Carr P and Wu L R. The finite moment log stable process and option pricing [J]. Journal of Finance, 2003, 58(2): 753-777.
[13]	Carriere J F. Valuation of the early exercise price for options using simulations and nonparametric regression[J]. Insurance: Mathematics and Economics, 1996, 19(1): 19-30.

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APA Style

Hong Zhang, Jie Zhu, Jian Guo, Li Zhou. (2015). Study of American Option Pricing Based on Levy Process. American Journal of Applied Mathematics, 3(3), 151-156. https://doi.org/10.11648/j.ajam.20150303.22

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ACS Style

Hong Zhang; Jie Zhu; Jian Guo; Li Zhou. Study of American Option Pricing Based on Levy Process. Am. J. Appl. Math. 2015, 3(3), 151-156. doi: 10.11648/j.ajam.20150303.22

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AMA Style

Hong Zhang, Jie Zhu, Jian Guo, Li Zhou. Study of American Option Pricing Based on Levy Process. Am J Appl Math. 2015;3(3):151-156. doi: 10.11648/j.ajam.20150303.22

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@article{10.11648/j.ajam.20150303.22,
  author = {Hong Zhang and Jie Zhu and Jian Guo and Li Zhou},
  title = {Study of American Option Pricing Based on Levy Process},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {151-156},
  doi = {10.11648/j.ajam.20150303.22},
  url = {https://doi.org/10.11648/j.ajam.20150303.22},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.22},
  abstract = {After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models.},
 year = {2015}
}

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TY  - JOUR
T1  - Study of American Option Pricing Based on Levy Process
AU  - Hong Zhang
AU  - Jie Zhu
AU  - Jian Guo
AU  - Li Zhou
Y1  - 2015/06/01
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.22
DO  - 10.11648/j.ajam.20150303.22
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 151
EP  - 156
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.22
AB  - After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models.
VL  - 3
IS  - 3
ER  -

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Author Information

Hong Zhang

School of Information, Beijing Wuzi University, Beijing, China
Jie Zhu

School of Information, Beijing Wuzi University, Beijing, China
Jian Guo

School of Information, Beijing Wuzi University, Beijing, China
Li Zhou

School of Information, Beijing Wuzi University, Beijing, China

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APA Style

Hong Zhang, Jie Zhu, Jian Guo, Li Zhou. (2015). Study of American Option Pricing Based on Levy Process. American Journal of Applied Mathematics, 3(3), 151-156. https://doi.org/10.11648/j.ajam.20150303.22

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ACS Style

Hong Zhang; Jie Zhu; Jian Guo; Li Zhou. Study of American Option Pricing Based on Levy Process. Am. J. Appl. Math. 2015, 3(3), 151-156. doi: 10.11648/j.ajam.20150303.22

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AMA Style

Hong Zhang, Jie Zhu, Jian Guo, Li Zhou. Study of American Option Pricing Based on Levy Process. Am J Appl Math. 2015;3(3):151-156. doi: 10.11648/j.ajam.20150303.22

Copy | Download

@article{10.11648/j.ajam.20150303.22,
  author = {Hong Zhang and Jie Zhu and Jian Guo and Li Zhou},
  title = {Study of American Option Pricing Based on Levy Process},
  journal = {American Journal of Applied Mathematics},
  volume = {3},
  number = {3},
  pages = {151-156},
  doi = {10.11648/j.ajam.20150303.22},
  url = {https://doi.org/10.11648/j.ajam.20150303.22},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20150303.22},
  abstract = {After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Study of American Option Pricing Based on Levy Process
AU  - Hong Zhang
AU  - Jie Zhu
AU  - Jian Guo
AU  - Li Zhou
Y1  - 2015/06/01
PY  - 2015
N1  - https://doi.org/10.11648/j.ajam.20150303.22
DO  - 10.11648/j.ajam.20150303.22
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 151
EP  - 156
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20150303.22
AB  - After the 2008 financial crisis, the global derivatives trading volume in options proportion is growing, more and more investors build portfolios using options to hedge or arbitrage, our futures and stock options will soon open. Theoretical research of options is also changing, option pricing models under Levy processes developed rapidly. In this context, a review of the China's warrants market and the introduction of option pricing models can not only help us to reflect Chinese financial derivatives market regulation, but also to explore the option pricing theory for China`s financial market environment. In the framework of Monte Carlo simulation pricing, we established mufti-Levy process option pricing models, the structural model for the given parameter estimation and risk-neutral adjustment method are discussed, the last part of this chapter is an empirical analysis of China warrants trading data in order to prove the validate of Levy models.
VL  - 3
IS  - 3
ER  -

Copy | Download