IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1009.5495.html
   My bibliography  Save this paper

American Options Pricing under Stochastic Volatility: Approximation of the Early Exercise Surface and Monte Carlo Simulations

Author

Listed:
  • Yu. A. Kuperin
  • P. A. Poloskov

Abstract

The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling the early exercise surface of the American option. These methods of present work are compared to the complexity of modeling and computation speed. The paper presents the semi-analytic expression for the price of American options with stochastic volatility. The results of numerical computations and their calibration are also presented. The obtained results were compared with results excluding the effect of volatility smile.

Suggested Citation

  • Yu. A. Kuperin & P. A. Poloskov, 2010. "American Options Pricing under Stochastic Volatility: Approximation of the Early Exercise Surface and Monte Carlo Simulations," Papers 1009.5495, arXiv.org.
    • Handle: RePEc:arx:papers:1009.5495
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1009.5495
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Montagna, Guido & Nicrosini, Oreste & Moreni, Nicola, 2002. "A path integral way to option pricing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 310(3), pages 450-466.
    3. Andrew Ziogas & Carl Chiarella, 2005. "Pricing American Options under Stochastic Volatility," Computing in Economics and Finance 2005 77, Society for Computational Economics.
    4. Eleonora Bennati & Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach To Derivative Security Pricing I: Formalism And Analytical Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 381-407.
    5. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: I. Formalism and Analytical Results," Papers cond-mat/9901277, arXiv.org.
    6. Marco Rosa-Clot & Stefano Taddei, 1999. "A Path Integral Approach to Derivative Security Pricing: II. Numerical Methods," Papers cond-mat/9901279, arXiv.org.
    7. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
    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. Ingber, Lester, 2000. "High-resolution path-integral development of financial options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 283(3), pages 529-558.
    2. Zura Kakushadze, 2014. "Path Integral and Asset Pricing," Papers 1410.1611, arXiv.org, revised Aug 2016.
    3. Paolinelli, Giovanni & Arioli, Gianni, 2018. "A path integral based model for stocks and order dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 387-399.
    4. Giovanni Paolinelli & Gianni Arioli, 2018. "A model for stocks dynamics based on a non-Gaussian path integral," Papers 1809.01342, arXiv.org, revised Oct 2018.
    5. Paolinelli, Giovanni & Arioli, Gianni, 2019. "A model for stocks dynamics based on a non-Gaussian path integral," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 499-514.
    6. O. Samimi & Z. Mardani & S. Sharafpour & F. Mehrdoust, 2017. "LSM Algorithm for Pricing American Option Under Heston–Hull–White’s Stochastic Volatility Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 173-187, August.
    7. Yu. A. Kuperin & P. A. Poloskov, 2010. "Analytical and Numerical Approaches to Pricing the Path-Dependent Options with Stochastic Volatility," Papers 1009.4587, arXiv.org.
    8. Moore, Ryleigh A. & Narayan, Akil, 2022. "Adaptive density tracking by quadrature for stochastic differential equations," Applied Mathematics and Computation, Elsevier, vol. 431(C).
    9. Farid AitSahlia & Manisha Goswami & Suchandan Guha, 2010. "American option pricing under stochastic volatility: an efficient numerical approach," Computational Management Science, Springer, vol. 7(2), pages 171-187, April.
    10. Decamps, Marc & De Schepper, Ann & Goovaerts, Marc, 2006. "A path integral approach to asset-liability management," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 404-416.
    11. Igor Halperin, 2021. "Distributional Offline Continuous-Time Reinforcement Learning with Neural Physics-Informed PDEs (SciPhy RL for DOCTR-L)," Papers 2104.01040, arXiv.org.
    12. G., Mauricio Contreras & Peña, Juan Pablo, 2019. "The quantum dark side of the optimal control theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 450-473.
    13. Blessing Taruvinga & Boda Kang & Christina Sklibosios Nikitopoulos, 2018. "Pricing American Options with Jumps in Asset and Volatility," Research Paper Series 394, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Cassagnes, Aurelien & Chen, Yu & Ohashi, Hirotada, 2014. "Path integral pricing of outside barrier Asian options," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 266-276.
    15. Andrew Matacz, 2000. "Path Dependent Option Pricing: the path integral partial averaging method," Papers cond-mat/0005319, arXiv.org.
    16. Andrew Matacz, 2000. "Path dependent option pricing: the path integral partial averaging method," Science & Finance (CFM) working paper archive 500034, Science & Finance, Capital Fund Management.
    17. Grillo, Sebastian & Blanco, Gerardo & Schaerer, Christian E., 2015. "Path integration for real options," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 120-132.
    18. Junkee Jeon & Jeonggyu Huh & Kyunghyun Park, 2020. "An Analytic Approximation for Valuation of the American Option Under the Heston Model in Two Regimes," Computational Economics, Springer;Society for Computational Economics, vol. 56(2), pages 499-528, August.
    19. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
    20. Fabian Dickmann & Nikolaus Schweizer, 2014. "Faster Comparison of Stopping Times by Nested Conditional Monte Carlo," Papers 1402.0243, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:1009.5495. 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.