IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v145y2021ics0960077921001077.html
   My bibliography  Save this article

Pricing geometric asian power options in the sub-fractional brownian motion environment

Author

Listed:
  • WANG, WEI
  • CAI, GUANGHUI
  • TAO, XIANGXING

Abstract

This paper aims of obtaining the closed form expressions for the prices of the geometric Asian options and power options when the payoff function is a power function. After discussing the option pricing in the sub-fractional Brownian motion environment, by the fractional Ito^ formula which is based on the theory of stochastic differential equation, the sub-fractional Ito^ formula is derived. Furthermore, the solution of the stochastic differential equation satisfied by stock prices is obtained. The stock price process is modeled well with the driving force as the sub-fractional Brownian motion. The empirical results show that the fitting effect is better than the Brownian motion.

Suggested Citation

  • Wang, Wei & Cai, Guanghui & Tao, Xiangxing, 2021. "Pricing geometric asian power options in the sub-fractional brownian motion environment," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001077
    DOI: 10.1016/j.chaos.2021.110754
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077921001077
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.110754?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. Tomasz Bojdecki & Luis G. Gorostiza & Anna Talarczyk, 2004. "Sub-fractional Brownian motion and its relation to occupation times," RePAd Working Paper Series lrsp-TRS376, Département des sciences administratives, UQO.
    2. Bojdecki, Tomasz & Gorostiza, Luis G. & Talarczyk, Anna, 2004. "Sub-fractional Brownian motion and its relation to occupation times," Statistics & Probability Letters, Elsevier, vol. 69(4), pages 405-419, October.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. Khan, Mair & El Shafey, A.M. & Salahuddin, T. & Khan, Farzana, 2020. "Chemically Homann stagnation point flow of Carreau fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    5. Salahuddin, T. & Siddique, Nazim & Arshad, Maryam, 2020. "Insight into the dynamics of the Non-Newtonian Casson fluid on a horizontal object with variable thickness," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 177(C), pages 211-231.
    6. Cipian Necula, 2008. "Option Pricing in a Fractional Brownian Motion Environment," Advances in Economic and Financial Research - DOFIN Working Paper Series 2, Bucharest University of Economics, Center for Advanced Research in Finance and Banking - CARFIB.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Wang, Lu & Zhang, Rong & Yang, Lin & Su, Yang & Ma, Feng, 2018. "Pricing geometric Asian rainbow options under fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 8-16.
    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. Axel A. Araneda, 2021. "Price modelling under generalized fractional Brownian motion," Papers 2108.12042, arXiv.org, revised Nov 2023.

    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. Axel A. Araneda, 2021. "Price modelling under generalized fractional Brownian motion," Papers 2108.12042, arXiv.org, revised Nov 2023.
    2. Araneda, Axel A. & Bertschinger, Nils, 2021. "The sub-fractional CEV model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).
    3. Wang, XiaoTian & Yang, ZiJian & Cao, PiYao & Wang, ShiLin, 2021. "The closed-form option pricing formulas under the sub-fractional Poisson volatility models," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    4. Zhaoqiang Yang, 2017. "Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-29, June.
    5. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    6. Gordian Rättich & Kim Clark & Evi Hartmann, 2011. "Performance measurement and antecedents of early internationalizing firms: A systematic assessment," Working Papers 0031, College of Business, University of Texas at San Antonio.
    7. Jeremy Leake, 2003. "Credit spreads on sterling corporate bonds and the term structure of UK interest rates," Bank of England working papers 202, Bank of England.
    8. Boulanouar, Zakaria & Alqahtani, Faisal & Hamdi, Besma, 2021. "Bank ownership, institutional quality and financial stability: evidence from the GCC region," Pacific-Basin Finance Journal, Elsevier, vol. 66(C).
    9. Richardson, Grant & Taylor, Grantley & Lanis, Roman, 2015. "The impact of financial distress on corporate tax avoidance spanning the global financial crisis: Evidence from Australia," Economic Modelling, Elsevier, vol. 44(C), pages 44-53.
    10. Zhijian (James) Huang & Yuchen Luo, 2016. "Revisiting Structural Modeling of Credit Risk—Evidence from the Credit Default Swap (CDS) Market," JRFM, MDPI, vol. 9(2), pages 1-20, May.
    11. Sandrine Lardic & Claire Gauthier, 2003. "Un modèle multifactoriel des spreads de crédit : estimation sur panels complets et incomplets," Économie et Prévision, Programme National Persée, vol. 159(3), pages 53-69.
    12. Polito, Vito & Wickens, Michael, 2015. "Sovereign credit ratings in the European Union: A model-based fiscal analysis," European Economic Review, Elsevier, vol. 78(C), pages 220-247.
    13. Hilscher, Jens & Raviv, Alon, 2014. "Bank stability and market discipline: The effect of contingent capital on risk taking and default probability," Journal of Corporate Finance, Elsevier, vol. 29(C), pages 542-560.
    14. Andres, Christian & Cumming, Douglas & Karabiber, Timur & Schweizer, Denis, 2014. "Do markets anticipate capital structure decisions? — Feedback effects in equity liquidity," Journal of Corporate Finance, Elsevier, vol. 27(C), pages 133-156.
    15. Anna Kovner & Chenyang Wei, 2012. "The private premium in public bonds," Staff Reports 553, Federal Reserve Bank of New York.
    16. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    17. Wen Su, 2021. "Default Distances Based on the CEV-KMV Model," Papers 2107.10226, arXiv.org, revised May 2022.
    18. Klomp, Jeroen, 2013. "Government interventions and default risk: Does one size fit all?," Journal of Financial Stability, Elsevier, vol. 9(4), pages 641-653.
    19. Muhammad Suhail Rizwan & Asifa Obaid & Dawood Ashraf, 2017. "The Impact of Corporate Social Responsibility on Default Risk: Empirical evidence from US Firms," Business & Economic Review, Institute of Management Sciences, Peshawar, Pakistan, vol. 9(3), pages 36-70, September.
    20. Jobst, Andreas A., 2014. "Measuring systemic risk-adjusted liquidity (SRL)—A model approach," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 270-287.

    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:145:y:2021:i:c:s0960077921001077. 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.