IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2503.08666.html
   My bibliography  Save this paper

Modeling Stock Return Distributions and Pricing Options

Author

Listed:
  • Xinxin Jiang

Abstract

This paper provides evidence that stock returns, after truncation, might be modeled by a special type of continuous mixtures or normals, so-called $q$-Gaussians. Negative binomial distributions might model the counts for extreme returns. A generalized jump-diffusion model is proposed, and an explicit option pricing formula is obtained.

Suggested Citation

  • Xinxin Jiang, 2025. "Modeling Stock Return Distributions and Pricing Options," Papers 2503.08666, arXiv.org.
    • Handle: RePEc:arx:papers:2503.08666
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2503.08666
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    2. Ning Cai & S. G. Kou, 2011. "Option Pricing Under a Mixed-Exponential Jump Diffusion Model," Management Science, INFORMS, vol. 57(11), pages 2067-2081, November.
    3. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    4. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    5. 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.
    6. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    7. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
    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. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    2. Wang, Xiao-Tian & Li, Zhe & Zhuang, Le, 2017. "European option pricing under the Student’s t noise with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 848-858.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Garcia, R. & Renault, E., 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    5. Michael C. Fu & Bingqing Li & Guozhen Li & Rongwen Wu, 2017. "Option Pricing for a Jump-Diffusion Model with General Discrete Jump-Size Distributions," Management Science, INFORMS, vol. 63(11), pages 3961-3977, November.
    6. Bent Jesper Christensen & Morten Ø. Nielsen, 2005. "The Implied-realized Volatility Relation With Jumps In Underlying Asset Prices," Working Paper 1186, Economics Department, Queen's University.
    7. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Reinders, Henk Jan & Schoenmaker, Dirk & van Dijk, Mathijs, 2023. "A finance approach to climate stress testing," Journal of International Money and Finance, Elsevier, vol. 131(C).
    9. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
    10. Chernov, Mikhail, 2007. "On the Role of Risk Premia in Volatility Forecasting," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 411-426, October.
    11. Arismendi, Juan & Genaro, Alan De, 2016. "A Monte Carlo multi-asset option pricing approximation for general stochastic processes," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 75-99.
    12. Patrick Dennis & Stewart Mayhew, 2009. "Microstructural biases in empirical tests of option pricing models," Review of Derivatives Research, Springer, vol. 12(3), pages 169-191, October.
    13. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 2000. "Pricing and hedging long-term options," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 277-318.
    14. Jingzhi Huang & Liuren Wu, 2004. "Specification Analysis of Option Pricing Models Based on Time- Changed Levy Processes," Finance 0401002, University Library of Munich, Germany.
    15. Shu Ling Chiang & Ming Shann Tsai, 2019. "Valuation of an option using non-parametric methods," Review of Derivatives Research, Springer, vol. 22(3), pages 419-447, October.
    16. Peter Carr & Liuren Wu, 2004. "Variance Risk Premia," Finance 0409015, University Library of Munich, Germany.
    17. Pena, Ignacio & Rubio, Gonzalo & Serna, Gregorio, 1999. "Why do we smile? On the determinants of the implied volatility function," Journal of Banking & Finance, Elsevier, vol. 23(8), pages 1151-1179, August.
    18. Schoenmaker, Dirk & Reinders, Henk Jan & Van Dijk, Mathijs, 2020. "Is COVID-19 a threat to financial stability in Europe?," CEPR Discussion Papers 14922, C.E.P.R. Discussion Papers.
    19. Cui, Zhenyu & Lars Kirkby, J. & Nguyen, Duy, 2019. "A general framework for time-changed Markov processes and applications," European Journal of Operational Research, Elsevier, vol. 273(2), pages 785-800.
    20. Xiao, Weilin & Zhang, Xili, 2016. "Pricing equity warrants with a promised lowest price in Merton’s jump–diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 219-238.

    More about this item

    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:arx:papers:2503.08666. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.