IDEAS home Printed from https://ideas.repec.org/a/taf/quantf/v12y2012i5p805-818.html
   My bibliography  Save this article

Coupling index and stocks

Author

Listed:
  • Benjamin Jourdain
  • Mohamed Sbai

Abstract

In this paper, we are interested in continuous-time models in which the index level induces feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the log-returns of each stock may be decomposed into a systemic part proportional to the log-returns of the index plus an idiosyncratic part. We show that, when the number of stocks in the index is large, this model may be approximated by a local volatility model for the index and a stochastic volatility model for each stock with volatility driven by the index. This result is useful from a calibration perspective: it suggests that one should first calibrate the local volatility of the index and then calibrate the dynamics of each stock. We explain how to do so in the limiting simplified model and in the original model.

Suggested Citation

  • Benjamin Jourdain & Mohamed Sbai, 2012. "Coupling index and stocks," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 805-818, March.
    • Handle: RePEc:taf:quantf:v:12:y:2012:i:5:p:805-818
    DOI: 10.1080/14697681003785959
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/14697681003785959
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/14697681003785959?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. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Nicole Branger & Christian Schlag, 2004. "Why is the Index Smile So Steep?," Review of Finance, European Finance Association, vol. 8(1), pages 109-127.
    3. H. Berestycki & J. Busca & I. Florent, 2002. "Asymptotics and calibration of local volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 61-69.
    4. Nicolas P. B. Bollen & Robert E. Whaley, 2004. "Does Net Buying Pressure Affect the Shape of Implied Volatility Functions?," Journal of Finance, American Finance Association, vol. 59(2), pages 711-753, April.
    5. Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Correlation structure of extreme stock returns," Papers cond-mat/0006034, arXiv.org, revised Jan 2001.
    6. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    7. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    8. P. Cizeau & M. Potters & J-P. Bouchaud, 2001. "Correlation structure of extreme stock returns," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 217-222.
    9. 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)

    Citations

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


    Cited by:

    1. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2021. "A model-free approach to multivariate option pricing," Review of Derivatives Research, Springer, vol. 24(2), pages 135-155, July.
    2. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01686114, HAL.
    3. Frédéric Abergel & Rémy Tachet Des Combes & Riadh Zaatour, 2017. "Nonparametric model calibration for derivatives," Post-Print hal-01399542, HAL.

    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. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    2. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    3. Cosma, Antonio & Galluccio, Stefano & Pederzoli, Paola & Scaillet, Olivier, 2020. "Early Exercise Decision in American Options with Dividends, Stochastic Volatility, and Jumps," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 55(1), pages 331-356, February.
    4. Antonio Cosma & Stefano Galluccio & Paola Pederzoli & O. Scaillet, 2012. "Valuing American Options Using Fast Recursive Projections," Swiss Finance Institute Research Paper Series 12-26, Swiss Finance Institute.
    5. Kevin Aretz & Ming-Tsung Lin & Ser-Huang Poon, 2023. "Moneyness, Underlying Asset Volatility, and the Cross-Section of Option Returns," Review of Finance, European Finance Association, vol. 27(1), pages 289-323.
    6. Matthias Raddant & Friedrich Wagner, 2017. "Transitions in the stock markets of the US, UK and Germany," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 289-297, February.
    7. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    8. Raddant, Matthias & Wagner, Friedrich, 2013. "Phase transition in the S&P stock market," Kiel Working Papers 1846, Kiel Institute for the World Economy (IfW Kiel).
    9. Jørgen Vitting Andersen & Andrzej Nowak & Giulia Rotundo & Lael Parrott & Sebastian Martinez, 2011. "“Price-Quakes” Shaking the World's Stock Exchanges," PLOS ONE, Public Library of Science, vol. 6(11), pages 1-8, November.
    10. Tzang, Shyh-Weir & Wang, Chou-Wen & Yu, Min-Teh, 2016. "Systematic risk and volatility skew," International Review of Economics & Finance, Elsevier, vol. 43(C), pages 72-87.
    11. Yu, Xisheng & Xie, Xiaoke, 2015. "Pricing American options: RNMs-constrained entropic least-squares approach," The North American Journal of Economics and Finance, Elsevier, vol. 31(C), pages 155-173.
    12. Alexander, Carol & Chen, Xi & Ward, Charles, 2021. "Risk-adjusted valuation for real option decisions," Journal of Economic Behavior & Organization, Elsevier, vol. 191(C), pages 1046-1064.
    13. Gagliardini, Patrick & Ronchetti, Diego, 2013. "Semi-parametric estimation of American option prices," Journal of Econometrics, Elsevier, vol. 173(1), pages 57-82.
    14. Naji Massad & Jørgen Vitting Andersen, 2019. "Defining an intrinsic "stickiness" parameter of stock price returns," Post-Print halshs-02385901, HAL.
    15. Gonzalez-Hermosillo Gonzalez, B.M., 2008. "Transmission of shocks across global financial markets : The role of contagion and investors' risk appetite," Other publications TiSEM d684f3c7-7ad8-4e93-88cf-a, Tilburg University, School of Economics and Management.
    16. Naji Massad & J{o}rgen Vitting Andersen, 2020. "Defining an intrinsic stickiness parameter of stock price returns," Papers 2005.02351, arXiv.org.
    17. Carlos Andrés Zapata Quimbayo, 2020. "OPCIONES REALES Una guía teórico-práctica para la valoración de inversiones bajo incertidumbre mediante modelos en tiempo discreto y simulación de Monte Carlo," Books, Universidad Externado de Colombia, Facultad de Finanzas, Gobierno y Relaciones Internacionales, number 138, April.
    18. 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).
    19. Lech A. Grzelak & Juliusz Jablecki & Dariusz Gatarek, 2022. "Efficient Pricing and Calibration of High-Dimensional Basket Options," Papers 2206.09877, arXiv.org.
    20. Victor Chang, 2020. "Presenting Cloud Business Performance for Manufacturing Organizations," Information Systems Frontiers, Springer, vol. 22(1), pages 59-75, February.

    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:taf:quantf:v:12:y:2012:i:5:p:805-818. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/RQUF20 .

    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.