IDEAS home Printed from https://ideas.repec.org/p/mod/depeco/0064.html
   My bibliography  Save this paper

Towards a skewness index for the Italian stock market

Author

Listed:
  • Elyas Elyasiani
  • Luca Gambarelli
  • Silvia Muzzioli

Abstract

The present paper is a first attempt of computing a skewness index for the Italian stock market. We compare and contrast different measures of asymmetry of the distribution: an index computed with the CBOE SKEW index formula and two other asymmetry indexes, the SIX indexes, as proposed in Faff and Liu (2014). We analyze the properties of the skewness indexes, by investigating their relationship with model-free implied volatility and the returns on the underlying stock index. Moreover, we assess the profitability of skewness trades and disentangle the contribution of the left and the right part of the risk neutral distribution to the profitability of the latter strategies. The data set consists of FTSE MIB index options data and covers the years 2011-2014, allowing us to address the behavior of skewness measures both in bullish and bearish market periods. We find that the Italian SKEW index presents many advantages with respect to other asymmetry measures: it has a significant contemporaneous relation with both returns, model-free implied volatility and has explanatory power on returns, after controlling for volatility. We find a negative relation between volatility changes and changes in the Italian SKEW index: an increase in model-free implied volatility is associated with a decrease in the Italian SKEW index. Moreover, the SKEW index acts as a measure of market greed, since returns react more negatively to a decrease in the SKEW index (increase in risk neutral skewness) than they react positively to an increase of the latter (decrease in risk neutral skewness). The results of the paper point to the existence of a skewness risk premium in the Italian market. This emerges both from the fact that implied skewness is more negative than physical one in the sample period and from the profitability of skewness trading strategies. In addition, the higher performance of the portfolio composed by only put options indicates that the mispricing of options is mainly focused on the left part of the distribution.

Suggested Citation

  • Elyas Elyasiani & Luca Gambarelli & Silvia Muzzioli, 2015. "Towards a skewness index for the Italian stock market," Department of Economics 0064, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    • Handle: RePEc:mod:depeco:0064
    as

    Download full text from publisher

    File URL: http://155.185.68.2/wpdemb/0064.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Mark Britten‐Jones & Anthony Neuberger, 2000. "Option Prices, Implied Price Processes, and Stochastic Volatility," Journal of Finance, American Finance Association, vol. 55(2), pages 839-866, April.
    2. Anthony Neuberger, 2012. "Realized Skewness," Review of Financial Studies, Society for Financial Studies, vol. 25(11), pages 3423-3455.
    3. Conrad, Jennifer & Kapadia, Nishad & Xing, Yuhang, 2014. "Death and jackpot: Why do individual investors hold overpriced stocks?," Journal of Financial Economics, Elsevier, vol. 113(3), pages 455-475.
    4. Jun Pan & Allen M. Poteshman, 2006. "The Information in Option Volume for Future Stock Prices," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 871-908.
    5. Dennis, Patrick & Mayhew, Stewart, 2002. "Risk-Neutral Skewness: Evidence from Stock Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(3), pages 471-493, September.
    6. Xi Fu & Eser Arisoy & Mark Shackleton & Mehmet Umutlu, 2016. "Option-Implied Volatility Measures and Stock Return Predictability," Post-Print hal-01484672, HAL.
    7. George Skiadopoulos, 2004. "The Greek implied volatility index: construction and properties," Applied Financial Economics, Taylor & Francis Journals, vol. 14(16), pages 1187-1196.
    8. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51.
    9. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    10. Moriggia, V. & Muzzioli, S. & Torricelli, C., 2009. "On the no-arbitrage condition in option implied trees," European Journal of Operational Research, Elsevier, vol. 193(1), pages 212-221, February.
    11. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
    12. Rubinstein, Mark, 1985. "Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes on the 30 Most Active CBOE Option Classes from August 23, 1976 through August 31, 1978," Journal of Finance, American Finance Association, vol. 40(2), pages 455-480, June.
    13. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    14. Diavatopoulos, Dean & Doran, James S. & Fodor, Andy & Peterson, David R., 2012. "The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns," Journal of Banking & Finance, Elsevier, vol. 36(3), pages 786-802.
    15. Jennifer Conrad & Robert F. Dittmar & Eric Ghysels, 2013. "Ex Ante Skewness and Expected Stock Returns," Journal of Finance, American Finance Association, vol. 68(1), pages 85-124, February.
    16. Xiaoquan Liu, 2007. "Returns to trading portfolios of FTSE 100 index options," Applied Financial Economics, Taylor & Francis Journals, vol. 17(15), pages 1211-1225.
    17. Neumann, Michael & Skiadopoulos, George, 2013. "Predictable Dynamics in Higher-Order Risk-Neutral Moments: Evidence from the S&P 500 Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(3), pages 947-977, June.
    18. 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.
    19. 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.
    20. Back, Kerry, 1993. "Asymmetric Information and Options," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    21. Amaya, Diego & Christoffersen, Peter & Jacobs, Kris & Vasquez, Aurelio, 2015. "Does realized skewness predict the cross-section of equity returns?," Journal of Financial Economics, Elsevier, vol. 118(1), pages 135-167.
    22. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
    23. K. J. Arrow, 1964. "The Role of Securities in the Optimal Allocation of Risk-bearing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 31(2), pages 91-96.
    24. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    25. Huimin Zhao & Jin E. Zhang & Eric C. Chang, 2013. "The Relation between Physical and Risk-neutral Cumulants," International Review of Finance, International Review of Finance Ltd., vol. 13(3), pages 345-381, September.
    26. Muzzioli, S. & Torricelli, C., 2005. "The pricing of options on an interval binomial tree. An application to the DAX-index option market," European Journal of Operational Research, Elsevier, vol. 163(1), pages 192-200, May.
    27. Xing, Yuhang & Zhang, Xiaoyan & Zhao, Rui, 2010. "What Does the Individual Option Volatility Smirk Tell Us About Future Equity Returns?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(3), pages 641-662, June.
    28. silvia Muzzioli & Alessio Ruggieri, 2013. "Option Implied Trees and Implied Moments," Department of Economics (DEMB) 0015, University of Modena and Reggio Emilia, Department of Economics "Marco Biagi".
    29. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    30. Yacine Aït-Sahalia & Andrew W. Lo, 1998. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," Journal of Finance, American Finance Association, vol. 53(2), pages 499-547, April.
    31. Panigirtzoglou, Nikolaos & Skiadopoulos, George, 2004. "A new approach to modeling the dynamics of implied distributions: Theory and evidence from the S&P 500 options," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1499-1520, July.
    32. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. "Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-1632, December.
    33. Manaster, Steven & Rendleman, Richard J, Jr, 1982. "Option Prices as Predictors of Equilibrium Stock Prices," Journal of Finance, American Finance Association, vol. 37(4), pages 1043-1057, September.
    34. Yan, Shu, 2011. "Jump risk, stock returns, and slope of implied volatility smile," Journal of Financial Economics, Elsevier, vol. 99(1), pages 216-233, January.
    35. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    36. Muzzioli, Silvia, 2015. "The optimal corridor for implied volatility: From periods of calm to turmoil," Journal of Economics and Business, Elsevier, vol. 81(C), pages 77-94.
    37. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    38. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    39. Bing‐Huei Lin & Ing‐Jye Chang & Dean A. Paxson, 2008. "Smiling less at LIFFE," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 28(1), pages 57-81, January.
    40. Bali, Turan G. & Murray, Scott, 2013. "Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(4), pages 1145-1171, August.
    41. Roman Kozhan & Anthony Neuberger & Paul Schneider, 2013. "The Skew Risk Premium in the Equity Index Market," Review of Financial Studies, Society for Financial Studies, vol. 26(9), pages 2174-2203.
    42. Silvia Muzzioli, 2013. "The Optimal Corridor for Implied Volatility: from Calm to Turmoil Periods," Department of Economics (DEMB) 0029, University of Modena and Reggio Emilia, Department of Economics "Marco Biagi".
    43. 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.
    44. S. Muzzioli, 2010. "Option-based forecasts of volatility: an empirical study in the DAX-index options market," The European Journal of Finance, Taylor & Francis Journals, vol. 16(6), pages 561-586.
    45. Cremers, Martijn & Weinbaum, David, 2010. "Deviations from Put-Call Parity and Stock Return Predictability," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 335-367, April.
    46. P. Carr & D. Madan, 2001. "Optimal positioning in derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 19-37.
    47. Silvia Muzzioli, 2013. "The Forecasting Performance of Corridor Implied Volatility in the Italian Market," Computational Economics, Springer;Society for Computational Economics, vol. 41(3), pages 359-386, March.
    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. Elyas Elyasiani & Luca Gambarelli & Silvia Muzzioli, 2016. "Fear or greed? What does a skewness index measure?," Department of Economics 0102, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    2. Elyas Elyasiani & Silvia Muzzioli & Alessio Ruggieri, 2016. "Forecasting and pricing powers of option-implied tree models: Tranquil and volatile market conditions," Department of Economics 0099, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    3. Elyas Elyasiani & Luca Gambarelli & Silvia Muzzioli, 2018. "The properties of a skewness index and its relation with volatility and returns," Department of Economics 0133, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    4. Christoffersen, Peter & Jacobs, Kris & Chang, Bo Young, 2013. "Forecasting with Option-Implied Information," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 581-656, Elsevier.
    5. Liu, Zhangxin (Frank) & Faff, Robert, 2017. "Hitting SKEW for SIX," Economic Modelling, Elsevier, vol. 64(C), pages 449-464.
    6. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    7. Chin‐Ho Chen, 2021. "Investor sentiment, misreaction, and the skewness‐return relationship," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(9), pages 1427-1455, September.
    8. Elyas Elyasiani & Luca Gambarelli & Silvia Muzzioli, 2018. "The use of option prices in order to evaluate the skewness risk premium," Department of Economics 0132, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    9. Elyas Elyasani & Luca Gambarelli & Silvia Muzzioli, 2016. "The risk asymmetry index," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 16212, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    10. Elyas Elyasani & Luca Gambarelli & Silvia Muzzioli, 2016. "The risk asymmetry index," Centro Studi di Banca e Finanza (CEFIN) (Center for Studies in Banking and Finance) 0061, Universita di Modena e Reggio Emilia, Dipartimento di Economia "Marco Biagi".
    11. 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.
    12. Elyas Elyasiani & Luca Gambarelli & Silvia Muzzioli, 2018. "The Risk-Asymmetry Index as a new Measure of Risk," Multinational Finance Journal, Multinational Finance Journal, vol. 22(3-4), pages 173-210, September.
    13. Sirio Aramonte & Mohammad R. Jahan-Parvar & Samuel Rosen & John W. Schindler, 2022. "Firm-Specific Risk-Neutral Distributions with Options and CDS," Management Science, INFORMS, vol. 68(9), pages 7018-7033, September.
    14. Silvia Muzzioli, 2013. "The Information Content of Option-Based Forecasts of Volatility: Evidence from the Italian Stock Market," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-46.
    15. Yue, Tian & Gehricke, Sebastian A. & Zhang, Jin E. & Pan, Zheyao, 2021. "The implied volatility smirk in the Chinese equity options market," Pacific-Basin Finance Journal, Elsevier, vol. 69(C).
    16. Luca Gambarelli & Silvia Muzzioli, 2019. "Risk-asymmetry indices in Europe," Department of Economics 0157, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    17. Hollstein, Fabian & Nguyen, Duc Binh Benno & Prokopczuk, Marcel, 2019. "Asset prices and “the devil(s) you know”," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 20-35.
    18. Felix Brinkmann & Olaf Korn, 2018. "Risk-adjusted option-implied moments," Review of Derivatives Research, Springer, vol. 21(2), pages 149-173, July.
    19. Alexander Kempf & Olaf Korn & Sven Saßning, 2015. "Portfolio Optimization Using Forward-Looking Information," Review of Finance, European Finance Association, vol. 19(1), pages 467-490.
    20. Kempf, Alexander & Korn, Olaf & Saßning, Sven, 2011. "Portfolio optimization using forward-looking information," CFR Working Papers 11-10, University of Cologne, Centre for Financial Research (CFR).

    More about this item

    Keywords

    risk-neutral moments; volatility; skewness; risk-premia; market fear;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

    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:mod:depeco:0064. 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: Sara Colombini (email available below). General contact details of provider: https://edirc.repec.org/data/demodit.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.