Option Pricing Variance Reduction Techniques Under the Levy Process

Li Zhou; Hong Zhang; Jian Guo; Shucong Ming

doi:doi:10.11648/j.acm.20150403.20

| Peer-Reviewed |

Option Pricing Variance Reduction Techniques Under the Levy Process

Li Zhou, Hong Zhang, Jian Guo, Shucong Ming

Received: 8 May 2015 Accepted: 20 May 2015 Published: 29 May 2015

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques.

DOI	10.11648/j.acm.20150403.20
Published in	Applied and Computational Mathematics (Volume 4, Issue 3, June 2015)
Page(s)	174-180
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

Option Pricing, Variance Reduction Techniques, Levy Process

References

[1]	Koponen, I. Analytic approach to the problem of convergence of truncated Levy flights towards the Gaussian stochastic process[J]. Physical Review E, 1995,52: 1197-1199.
[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;

Cite This Article

Plain Text BibTeX RIS

APA Style

Li Zhou, Hong Zhang, Jian Guo, Shucong Ming. (2015). Option Pricing Variance Reduction Techniques Under the Levy Process. Applied and Computational Mathematics, 4(3), 174-180. https://doi.org/10.11648/j.acm.20150403.20

Copy | Download

ACS Style

Li Zhou; Hong Zhang; Jian Guo; Shucong Ming. Option Pricing Variance Reduction Techniques Under the Levy Process. Appl. Comput. Math. 2015, 4(3), 174-180. doi: 10.11648/j.acm.20150403.20

Copy | Download

AMA Style

Li Zhou, Hong Zhang, Jian Guo, Shucong Ming. Option Pricing Variance Reduction Techniques Under the Levy Process. Appl Comput Math. 2015;4(3):174-180. doi: 10.11648/j.acm.20150403.20

Copy | Download

@article{10.11648/j.acm.20150403.20,
  author = {Li Zhou and Hong Zhang and Jian Guo and Shucong Ming},
  title = {Option Pricing Variance Reduction Techniques Under the Levy Process},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {3},
  pages = {174-180},
  doi = {10.11648/j.acm.20150403.20},
  url = {https://doi.org/10.11648/j.acm.20150403.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150403.20},
  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. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Option Pricing Variance Reduction Techniques Under the Levy Process
AU  - Li Zhou
AU  - Hong Zhang
AU  - Jian Guo
AU  - Shucong Ming
Y1  - 2015/05/29
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150403.20
DO  - 10.11648/j.acm.20150403.20
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 174
EP  - 180
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150403.20
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. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques.
VL  - 4
IS  - 3
ER  -

Copy | Download

Author Information

Li Zhou

School of Information, Beijing Wuzi University, Beijing, China
Hong Zhang

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

School of Information, Beijing Wuzi University, Beijing, China
Shucong Ming

Chinese Academy of Finance and Development, Central University of Finance and Economics, Beijing, China

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Li Zhou, Hong Zhang, Jian Guo, Shucong Ming. (2015). Option Pricing Variance Reduction Techniques Under the Levy Process. Applied and Computational Mathematics, 4(3), 174-180. https://doi.org/10.11648/j.acm.20150403.20

Copy | Download

ACS Style

Li Zhou; Hong Zhang; Jian Guo; Shucong Ming. Option Pricing Variance Reduction Techniques Under the Levy Process. Appl. Comput. Math. 2015, 4(3), 174-180. doi: 10.11648/j.acm.20150403.20

Copy | Download

AMA Style

Li Zhou, Hong Zhang, Jian Guo, Shucong Ming. Option Pricing Variance Reduction Techniques Under the Levy Process. Appl Comput Math. 2015;4(3):174-180. doi: 10.11648/j.acm.20150403.20

Copy | Download

@article{10.11648/j.acm.20150403.20,
  author = {Li Zhou and Hong Zhang and Jian Guo and Shucong Ming},
  title = {Option Pricing Variance Reduction Techniques Under the Levy Process},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {3},
  pages = {174-180},
  doi = {10.11648/j.acm.20150403.20},
  url = {https://doi.org/10.11648/j.acm.20150403.20},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150403.20},
  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. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Option Pricing Variance Reduction Techniques Under the Levy Process
AU  - Li Zhou
AU  - Hong Zhang
AU  - Jian Guo
AU  - Shucong Ming
Y1  - 2015/05/29
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150403.20
DO  - 10.11648/j.acm.20150403.20
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 174
EP  - 180
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150403.20
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. Key word: Levy stochastic processes, option pricing models, Chinese warrants market, American option pricing, risk-neutral adjustment, variance reduction techniques.
VL  - 4
IS  - 3
ER  -

Copy | Download