IDEAS home Printed from https://ideas.repec.org/p/hhs/oruesi/2024_001.html
   My bibliography  Save this paper

Subdiffusive option price model with Inverse Gaussian subordinator

Author

Listed:
  • Shchestyuk, Nataliya

    (Örebro University School of Business)

  • Tyshchenkob, Sergii

    (National University of Kyiv-Mohyla Academy)

Abstract

The paper focuses on the option price subdiffusive model under the unusual behavior of the market, when the price may not be changed for some time which is quite a common situation in the modern financial markets or during global crises. In the model, the risk-free bond motion and classical GBM are time-changed by an inverted inverse Gaussian (IG) subordinator. We explore the correlation structure of the subdiffusive GBM stock returns process, discuss option pricing techniques based on the fractal Dupire equation, and demonstrate how it applies in the case of the IG subordinator.

Suggested Citation

  • Shchestyuk, Nataliya & Tyshchenkob, Sergii, 2024. "Subdiffusive option price model with Inverse Gaussian subordinator," Working Papers 2024:1, Örebro University, School of Business.
    • Handle: RePEc:hhs:oruesi:2024_001
    as

    Download full text from publisher

    File URL: https://www.oru.se/globalassets/oru-sv/institutioner/hh/workingpapers/workingpapers2024/wp-1-2024.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lehar, Alfred & Scheicher, Martin & Schittenkopf, Christian, 2002. "GARCH vs. stochastic volatility: Option pricing and risk management," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 323-345, March.
    2. Marcin Magdziarz & Sebastian Orzel & Aleksander Weron, 2011. "Option pricing in subdiffusive Bachelier model," HSC Research Reports HSC/11/05, Hugo Steinhaus Center, Wroclaw University of Science and Technology.
    Full references (including those not matched with items on IDEAS)

    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. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    2. Shi-jie Jiang & Mujun Lei & Cheng-Huang Chung, 2018. "An Improvement of Gain-Loss Price Bounds on Options Based on Binomial Tree and Market-Implied Risk-Neutral Distribution," Sustainability, MDPI, vol. 10(6), pages 1-17, June.
    3. Lv, Longjin & Xiao, Jianbin & Fan, Liangzhong & Ren, Fuyao, 2016. "Correlated continuous time random walk and option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 100-107.
    4. Nikola Radivojevic & Milena Cvjetkovic & Saša Stepanov, 2016. "The new hybrid value at risk approach based on the extreme value theory," Estudios de Economia, University of Chile, Department of Economics, vol. 43(1 Year 20), pages 29-52, June.
    5. Mustafa Caglayan & Ozge Kandemir & Kostas Mouratidis, 2011. "Real effects of inflation uncertainty in the US," Working Papers 2011002, The University of Sheffield, Department of Economics, revised Feb 2015.
    6. Chuan-Hsiang Han & Wei-Han Liu & Tzu-Ying Chen, 2014. "VaR/CVaR ESTIMATION UNDER STOCHASTIC VOLATILITY MODELS," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(02), pages 1-35.
    7. Ben R. Craig & Ernst Glatzer & Joachim G. Keller & Martin Scheicher, 2003. "The forecasting performance of German stock option densities," Working Papers (Old Series) 0312, Federal Reserve Bank of Cleveland.
    8. Kevin Z. Tong & Allen Liu, 2019. "Option pricing in a subdiffusive constant elasticity of variance (CEV) model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-21, June.
    9. Felor Ghorashi & Roya Darabi, 2017. "Compare Value at Risk and Return of Assets Portfolio Stock, Gold, REIT, U.S. & Iran Market Indices," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 5(1), pages 44-48, March.
    10. Yow-Jen Jou & Chih-Wei Wang & Wan-Chien Chiu, 2013. "Is the realized volatility good for option pricing during the recent financial crisis?," Review of Quantitative Finance and Accounting, Springer, vol. 40(1), pages 171-188, January.
    11. Kyungwon Kim & Jae Wook Song, 2020. "Detecting Possible Reduction of the Housing Bubble in Korea for Different Residential Types and Regions," Sustainability, MDPI, vol. 12(3), pages 1-31, February.
    12. Asai, Manabu & Caporin, Massimiliano & McAleer, Michael, 2015. "Forecasting Value-at-Risk using block structure multivariate stochastic volatility models," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 40-50.
    13. Mahringer, Steffen & Prokopczuk, Marcel, 2015. "An empirical model comparison for valuing crack spread options," Energy Economics, Elsevier, vol. 51(C), pages 177-187.
    14. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Pricing individual stock options using both stock and market index information," Journal of Banking & Finance, Elsevier, vol. 111(C).
    15. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    16. Felor Ghorashi & Roya Darabi, 2016. "Compare Value at Risk and Return of Assets Portfolio Stock, Gold, REIT, U.S. & Iran Market Indices," Asian Journal of Economic Modelling, Asian Economic and Social Society, vol. 5(1), pages 44-48, March.
    17. Joanna Górka, 2014. "Option Pricing under Sign RCA-GARCH Models," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 14, pages 145-160.
    18. Papantonis, Ioannis, 2016. "Volatility risk premium implications of GARCH option pricing models," Economic Modelling, Elsevier, vol. 58(C), pages 104-115.
    19. Puja Padhi & Imlak Shaikh, 2014. "On the relationship of implied, realized and historical volatility: evidence from NSE equity index options," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 15(5), pages 915-934, November.
    20. Cheng, Hung-Wen & Lo, Chien-Ling & Tsai, Jeffrey Tzuhao, 2020. "Model specification of conditional jump intensity: Evidence from S&P 500 returns and option prices," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).

    More about this item

    Keywords

    Option pricing; Subdiffusion models; Subordinator; Inverse subordinator; Time-changed process; Hitting time;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    Statistics

    Access and download statistics

    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:hhs:oruesi:2024_001. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/ieoruse.html .

    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.