Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model

Yanan Yun; Lingyun Gao

doi:doi:10.11648/j.ijtam.20200602.11

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Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model

Yanan Yun, Lingyun Gao

Published in International Journal of Theoretical and Applied Mathematics (Volume 6, Issue 2)

Received: 5 April 2020 Accepted: 22 April 2020 Published: 15 May 2020

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Abstract

Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.

Published in	International Journal of Theoretical and Applied Mathematics (Volume 6, Issue 2)
DOI	10.11648/j.ijtam.20200602.11
Page(s)	19-27
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), 2020. Published by Science Publishing Group

Keywords

European Chooser Option, Vasicek Model, Fractional Brownian Motion

References

[1]	Rubinstein M. Options for the undecided [J]. Risk, 1991, 4 (4): 43.
[2]	Detemple J, Emmerling T. American chooser options [J]. Journal of Economic Dynamics Control, 2009, 33 (2): 128-153.
[3]	Xuehui Bi, Xueqiao Du. Actuarial pricing of post-determined options [J]. Journal of Hefei University of Technology, 2007, 30 (5): 649-651.
[4]	Guohe Deng. European chooser option pricing and hedging strategy based on Heston model [J]. Journal of Guangxi Normal University (Natural Science Edition), 2012, 30 (3): 36-43.
[5]	Jiangjiang Dong, Kai Gao, Xueru Liu. Complex chooser option pricing for continuous O-U process [J]. Journal of Nanjing Normal University (Natural Science Edition), 2018, 42 (2): 16-22.
[6]	John C Hull. Options, futures and other derivatives [M]. Beijing: Machinery Industry Press, 2011.
[7]	Yan Zhang, Shengwu Zhou, Miao Han, Xinli Suo. European gap option pricing under Vasicek stochastic interest rate model [J]. College Mathematics, 2012, 28 (4): 98-101.
[8]	Sang Wu, Chao Xu, Yinghui Dong. Pricing of vulnerable options under jump-diffusion model with random interest rate [J]. Journal of Applied Mathematics, 2019, 42 (4): 518-532.
[9]	Yingxin Zhan, Yun Xu. Pricing of European complex chooser option under fractional Brownian motion [J]. Mathematical Theory and Application, 2010, 30 (3): 78-82.
[10]	Shucai Yang, Hong Xue, Xiaodong Xue. Fractional compound option pricing model with stochastic interest rate [J]. Journal of Harbin University of Commerce (Natural Sciences Edition), 2014, 30 (1): 98-102.
[11]	Ciprian Necula. Option Pricing in a Fractional Brownian Motion Environment [J]. Pure mathematics, 2002, 2 (1): 63-68.
[12]	Zhang S, Yuan S, Wang L. Prices of Asian options under stochastic rates [J]. Applied Mathematics- A Journal of Chinese Universities, 2006, 21 (2): 135-142.
[13]	Jie Lin, Hong Xue, Xiaodong Wang. Pricing model of gap options under fractional Brownian motion [J]. Journal of Harbin University of Commerce (Natural Sciences Edition), 2012, 28 (5): 616-619.
[14]	Korn R, Korn E. Option Pricing and Portfolio Optimization [M]. New York: American Mathematical Society, 2000.
[15]	Shaoqun Liu, Xiangqun Yang. Pricing European contingent claims under fractional Brownian motion [J]. Chinese Journal of applied probability and statistics, 2004, 20 (4): 429-434.
[16]	Songnan Chen. Financial engineering [M]. Shanghai: Fudan University Press, 2002.

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APA Style

Yanan Yun, Lingyun Gao. (2020). Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model. International Journal of Theoretical and Applied Mathematics, 6(2), 19-27. https://doi.org/10.11648/j.ijtam.20200602.11

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ACS Style

Yanan Yun; Lingyun Gao. Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model. Int. J. Theor. Appl. Math. 2020, 6(2), 19-27. doi: 10.11648/j.ijtam.20200602.11

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AMA Style

Yanan Yun, Lingyun Gao. Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model. Int J Theor Appl Math. 2020;6(2):19-27. doi: 10.11648/j.ijtam.20200602.11

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@article{10.11648/j.ijtam.20200602.11,
  author = {Yanan Yun and Lingyun Gao},
  title = {Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {6},
  number = {2},
  pages = {19-27},
  doi = {10.11648/j.ijtam.20200602.11},
  url = {https://doi.org/10.11648/j.ijtam.20200602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20200602.11},
  abstract = {Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.},
 year = {2020}
}

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TY  - JOUR
T1  - Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model
AU  - Yanan Yun
AU  - Lingyun Gao
Y1  - 2020/05/15
PY  - 2020
N1  - https://doi.org/10.11648/j.ijtam.20200602.11
DO  - 10.11648/j.ijtam.20200602.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 19
EP  - 27
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20200602.11
AB  - Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.
VL  - 6
IS  - 2
ER  -

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Author Information

Yanan Yun

Department of Mathematics, Jinan University, Guangzhou, China
Lingyun Gao

Department of Mathematics, Jinan University, Guangzhou, China

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Plain Text BibTeX RIS

APA Style

Yanan Yun, Lingyun Gao. (2020). Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model. International Journal of Theoretical and Applied Mathematics, 6(2), 19-27. https://doi.org/10.11648/j.ijtam.20200602.11

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ACS Style

Yanan Yun; Lingyun Gao. Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model. Int. J. Theor. Appl. Math. 2020, 6(2), 19-27. doi: 10.11648/j.ijtam.20200602.11

Copy | Download

AMA Style

Yanan Yun, Lingyun Gao. Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model. Int J Theor Appl Math. 2020;6(2):19-27. doi: 10.11648/j.ijtam.20200602.11

Copy | Download

@article{10.11648/j.ijtam.20200602.11,
  author = {Yanan Yun and Lingyun Gao},
  title = {Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model},
  journal = {International Journal of Theoretical and Applied Mathematics},
  volume = {6},
  number = {2},
  pages = {19-27},
  doi = {10.11648/j.ijtam.20200602.11},
  url = {https://doi.org/10.11648/j.ijtam.20200602.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20200602.11},
  abstract = {Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Pricing and Analysis of European Chooser Option Under The Vasicek Interest Rate Model
AU  - Yanan Yun
AU  - Lingyun Gao
Y1  - 2020/05/15
PY  - 2020
N1  - https://doi.org/10.11648/j.ijtam.20200602.11
DO  - 10.11648/j.ijtam.20200602.11
T2  - International Journal of Theoretical and Applied Mathematics
JF  - International Journal of Theoretical and Applied Mathematics
JO  - International Journal of Theoretical and Applied Mathematics
SP  - 19
EP  - 27
PB  - Science Publishing Group
SN  - 2575-5080
UR  - https://doi.org/10.11648/j.ijtam.20200602.11
AB  - Based on the modification of some assumptions in the traditional Black-Scholes option pricing model, we construct a model that is closer to the real financial market in this paper. That is to say, in order to make up for the shortages of using the standard Brownian motion to describe the underlying asset price, we use fractional Brownian motion to replace the standard Brownian motion in the traditional Black-Scholes model. At the same time, we assume that the interest rate satisfies the Vasicek interest rate model under fractional Brownian motion. Under the above market model, we use the stochastic analysis method under fractional Brownian motion to obtain the pricing formulae of European simple option and complex option, which generalize the existing conclusions. It is not only can be closer to the actual financial market but also make the research more practical. In addition, since the sensitivity analysis of options refers to the sensitivity or response of options to the change of its determinants, we use numerical methods to analyze the impact of the stock initial price, the chooser date and Hurst parameter on the price of European complex chooser option, which not only verifies the rationality of the pricing formula but also has guiding value for option trading.
VL  - 6
IS  - 2
ER  -

Copy | Download