IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v128y2019icp123-128.html
   My bibliography  Save this article

The pricing and numerical analysis of lookback options for mixed fractional Brownian motion

Author

Listed:
  • Chen, Qisheng
  • Zhang, Qian
  • Liu, Chuan

Abstract

Using the stochastic differential equation driven by the composite Poisson process of mixed fractional Brownian motion, the price model of a mixed jump-diffusion fractional Brownian motion environment is established. Under the condition of Merton’s assumption, the Cauchy initial value problem of stochastic differential equations is iterated. The method is estimated, and the Merton formula of the European put option under the mixed jump-diffusion model is obtained, and the call-back option and the bearish option pricing formula of the mixed jump-diffusion fractional Brownian motion European floating strike price are given.

Suggested Citation

  • Chen, Qisheng & Zhang, Qian & Liu, Chuan, 2019. "The pricing and numerical analysis of lookback options for mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 123-128.
    • Handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:123-128
    DOI: 10.1016/j.chaos.2019.07.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919302905
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.07.038?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    2. Lesigne, Emmanuel & Volný, Dalibor, 2001. "Large deviations for martingales," Stochastic Processes and their Applications, Elsevier, vol. 96(1), pages 143-159, November.
    3. Michel Crouhy & Dan Galai, 2018. "Are Banks Special?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 8(04), pages 1-19, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Deng, Guohe, 2020. "Pricing perpetual American floating strike lookback option under multiscale stochastic volatility model," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    2. Liu, Zhibin & Huang, Shan, 2021. "Carbon option price forecasting based on modified fractional Brownian motion optimized by GARCH model in carbon emission trading," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    3. Shi, Gang & Gao, Jinwu, 2021. "European Option Pricing Problems with Fractional Uncertain Processes," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    4. Wang, Jian & Yan, Yan & Chen, Wenbing & Shao, Wei & Wang, Jian & Tang, Weiwei, 2021. "Equity-linked securities option pricing by fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Boucher, Thomas R., 2016. "A note on martingale deviation bounds," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 8-11.
    2. Fan, Xiequan & Alquier, Pierre & Doukhan, Paul, 2022. "Deviation inequalities for stochastic approximation by averaging," Stochastic Processes and their Applications, Elsevier, vol. 152(C), pages 452-485.
    3. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    4. Giraudo, Davide, 2016. "Holderian weak invariance principle under a Hannan type condition," Stochastic Processes and their Applications, Elsevier, vol. 126(1), pages 290-311.
    5. Emmanuel Rio, 2009. "Moment Inequalities for Sums of Dependent Random Variables under Projective Conditions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 146-163, March.
    6. Kanaya, Shin & Otsu, Taisuke, 2012. "Large deviations of realized volatility," Stochastic Processes and their Applications, Elsevier, vol. 122(2), pages 546-581.
    7. Dedecker, Jérôme & Fan, Xiequan, 2015. "Deviation inequalities for separately Lipschitz functionals of iterated random functions," Stochastic Processes and their Applications, Elsevier, vol. 125(1), pages 60-90.
    8. Anders Bredahl Kock, 2013. "Oracle inequalities for high-dimensional panel data models," CREATES Research Papers 2013-20, Department of Economics and Business Economics, Aarhus University.
    9. Hua-Ming Wang, 2018. "Law of Large Numbers for Random Walk with Unbounded Jumps and Birth and Death Process with Bounded Jumps in Random Environment," Journal of Theoretical Probability, Springer, vol. 31(2), pages 619-642, June.
    10. Xia Wang & Miaomiao Zhang, 2022. "Large Deviations for the Maximum of the Absolute Value of Partial Sums of Random Variable Sequences," Mathematics, MDPI, vol. 10(5), pages 1-11, February.
    11. Stoica, George, 2008. "The Baum-Katz theorem for bounded subsequences," Statistics & Probability Letters, Elsevier, vol. 78(7), pages 924-926, May.
    12. Fan, Xiequan & Grama, Ion & Liu, Quansheng, 2012. "Hoeffding’s inequality for supermartingales," Stochastic Processes and their Applications, Elsevier, vol. 122(10), pages 3545-3559.
    13. Li, Yulin, 2003. "A martingale inequality and large deviations," Statistics & Probability Letters, Elsevier, vol. 62(3), pages 317-321, April.
    14. Eunji Lim, 2011. "On the Convergence Rate for Stochastic Approximation in the Nonsmooth Setting," Mathematics of Operations Research, INFORMS, vol. 36(3), pages 527-537, August.
    15. H. Nooghabi & H. Azarnoosh, 2009. "Exponential inequality for negatively associated random variables," Statistical Papers, Springer, vol. 50(2), pages 419-428, March.
    16. Meng, Yanjiao & Lin, Zhengyan, 2009. "On the weak laws of large numbers for arrays of random variables," Statistics & Probability Letters, Elsevier, vol. 79(23), pages 2405-2414, December.
    17. Liu, Quansheng & Watbled, Frédérique, 2009. "Exponential inequalities for martingales and asymptotic properties of the free energy of directed polymers in a random environment," Stochastic Processes and their Applications, Elsevier, vol. 119(10), pages 3101-3132, October.
    18. Anders Bredahl Kock & Haihan Tang, 2014. "Inference in High-dimensional Dynamic Panel Data Models," CREATES Research Papers 2014-58, Department of Economics and Business Economics, Aarhus University.
    19. Lacoin, Hubert & Moreno, Gregorio, 2010. "Directed polymers on hierarchical lattices with site disorder," Stochastic Processes and their Applications, Elsevier, vol. 120(4), pages 467-493, April.
    20. Li, Bainian & Zhang, Kongsheng & Wu, Libin, 2011. "A sharp inequality for martingales and its applications," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1260-1266, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:128:y:2019:i:c:p:123-128. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.