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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
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    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. Xi Fu & Eser Arisoy & Mark Shackleton & Mehmet Umutlu, 2016. "Option-Implied Volatility Measures and Stock Return Predictability," Post-Print hal-01484672, HAL.
    3. 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.
    4. 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.
    5. Back, Kerry, 1993. "Asymmetric Information and Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 435-472.
    6. Gurdip Bakshi & Nikunj Kapadia, 2003. "Delta-Hedged Gains and the Negative Market Volatility Risk Premium," The Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 527-566.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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".
    15. repec:bla:jfinan:v:59:y:2004:i:2:p:711-753 is not listed on IDEAS
    16. Anthony Neuberger, 2012. "Realized Skewness," The Review of Financial Studies, Society for Financial Studies, vol. 25(11), pages 3423-3455.
    17. 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.
    18. 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.
    19. 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.
    20. Xiaoquan Liu, 2007. "Returns to trading portfolios of FTSE 100 index options," Applied Financial Economics, Taylor & Francis Journals, vol. 17(15), pages 1211-1225.
    21. Gurdip Bakshi & Nikunj Kapadia & Dilip Madan, 2003. "Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 101-143.
    22. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    23. 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.
    24. 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.
    25. 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.
    26. P. Carr & D. Madan, 2001. "Optimal positioning in derivative securities," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 19-37.
    27. 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.
    28. George Skiadopoulos, 2004. "The Greek implied volatility index: construction and properties," Applied Financial Economics, Taylor & Francis Journals, vol. 14(16), pages 1187-1196.
    29. 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.
    30. 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.
    31. Jackwerth, Jens Carsten, 2000. "Recovering Risk Aversion from Option Prices and Realized Returns," The Review of Financial Studies, Society for Financial Studies, vol. 13(2), pages 433-451.
    32. 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.
    33. 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.
    34. 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.
    35. Roman Kozhan & Anthony Neuberger & Paul Schneider, 2013. "The Skew Risk Premium in the Equity Index Market," The Review of Financial Studies, Society for Financial Studies, vol. 26(9), pages 2174-2203.
    36. 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.
    37. 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.
    38. George J. Jiang & Yisong S. Tian, 2005. "The Model-Free Implied Volatility and Its Information Content," The Review of Financial Studies, Society for Financial Studies, vol. 18(4), pages 1305-1342.
    39. 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.
    40. 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.
    41. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    42. 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.
    43. 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".
    44. repec:bla:jfinan:v:53:y:1998:i:2:p:499-547 is not listed on IDEAS
    45. 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.
    46. 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.
    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.
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    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

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