Implicit expectiles and measures of implied volatility

References

• Bakshi, G. , Kapadia, N. and Madan, D. , Stock return characteristics, skew laws, and the differential pricing of individual equity. Rev. Financ. Stud. , 2003, 16 , 101–143.
   Web of Science ®Google Scholar
• Banerjee, P.S. , Doran, J. and Peterson, D. , Implied volatility and future portfolio returns. J. Bank. Finance , 2007, 31 , 3183–3199.
   Web of Science ®Google Scholar
• Barndorff-Nielsen, O.E. and Shephard, N. , Non-Gaussian Ornstein Uhlenbeck-based models and some of their uses in financial economics. J. Roy. Stat. Soc.: Ser. B (Stat. Methodol.) , 2001, 63 , 167–241.
   Web of Science ®Google Scholar
• Barone Adesi, G. , VaR and CVaR implied in option prices. J. Risk Financ. Manage. , 2016, 9 , 19–24.
   Web of Science ®Google Scholar
• Barone Adesi, G. , Legnazzi, C. and Sala, C. , SP500 index, an option-implied risk analysis. Working paper SSRN, 2016a.
   Google Scholar
• Barone Adesi, G. , Legnazzi, C. and Sala, C. , WTI crude oil option-implied VaR and CVaR: An empirical application. Working paper SSRN, 2016b.
   Google Scholar
• Bellini, F. and Bignozzi, V. , On elicitable risk measures. Quant. Finance , 2015, 15 , 725–733.
   Web of Science ®Google Scholar
• Bellini, F. and Di Bernardino, E. , Risk management with expectiles. Eur. J. Finance , 2017, 23 , 487–506.
   Web of Science ®Google Scholar
• Bellini, F. , Klar, B. , Müller, A. , and Rosazza Gianin, E. , Generalized quantiles as risk measures. Insur.: Math. Econ. 2014, 54 , 41–48.
   Web of Science ®Google Scholar
• Bellini, F. , Klar, B. and Müller, A. , Expectiles, omega ratios and stochastic ordering. Methodol. Comput. Appl. Probab. , 2016. Available online at: https://doi.org/10.1007/s11009-016-9527-2.
   Web of Science ®Google Scholar
• Breeden, D. and Litzenberger, R. , Prices of state-contingent claims implicit in option prices. J. Bus. , 1978, 55 , 839–866.
   Google Scholar
• Britten-Jones, M. and Neuberger, A. , Option prices, implied price processes, and stochastic volatility. J. Finance , 2000, 51 , 621–651.
   Google Scholar
• Brouste, A. , Fukasawa, M. , Hino, H. , Iacus, S.M. , Kamatani, K. , Koike, Y. , Masuda, H. , Nomura, R. , Ogihara, T. , Shimuzu, Y. , Uchida, M. and Yoshida, N. , The YUIMA project: A computational framework for simulation and inference of stochastic differential equations. J. Stat. Softw. , 2014, 57 , 1–51.
   PubMed Web of Science ®Google Scholar
• CBOE , The CBOE volatility index: VIX. CBOE White Paper, 2009.
   Google Scholar
• CBOE , The CBOE skewness index. CBOE White Paper, 2010.
   Google Scholar
• Delbaen, F. , Bellini, F. , Bignozzi, V. and Ziegel, J. , Risk measures with the CxLS property. Finance Stoch. , 2016, 20 , 433–453.
   Web of Science ®Google Scholar
• Demeterfi, K. , Derman, E. , Kamal, K. and Zou, J. , More than You Ever Wanted to Know about Volatility Swaps , Quantitative Strategies Research Notes, 1999 (Goldman Sachs & Co: New York).
   Google Scholar
• Dickey, D.A. and Fuller, W.A. , Distribution of the estimators for autoregressive time series with a unit root. J. Amer. Stat. Assoc. , 1979, 74 , 427–431.
   Web of Science ®Google Scholar
• Elyasiani, E. , Gambarelli, L. and Muzzioli, S. , The risk-asymmetry index. Working Paper SSRN, 2016.
   Google Scholar
• Fukasawa, M. , Ishida, I. , Maghrebi, N. , Oya, K. , Ubukata, M. and Yamazaki, K. , Model-free implied volatility: From surface to index. Int. J. Theor. Appl. Finance , 2011, 14 , 433–463.
   Google Scholar
• Giot, P. , Relationships between implied volatility indexes and stock index returns. J. Portfolio Manage. , 2005, 26 , 12–17.
   Google Scholar
• Iacus, S.M. and Mercuri, L. , Implementation of Lévy CARMA model in Yuima package. Comput. Stat. , 2015, 30 , 1111–1141.
   Web of Science ®Google Scholar
• Jiang, G. and Tian, Y. , Extracting model-free volatility from option prices: an estimation of the VIX index. J. Derivatives , 2007, 14 , 1–26.
   Web of Science ®Google Scholar
• Jolliffe, I.T. , Principal Component Analysis , 2002 (Springer: New York).
   Google Scholar
• Newey, W. and Powell, J. , Asymmetric least squares estimation and testing. Econometrica , 1987, 55 , 819–847.
   Web of Science ®Google Scholar
• Ng, S. and Perron, P. , Unit root tests in ARMA models with data-dependent methods for the selection of the truncation lag. J. Amer. Stat. Assoc. , 1995, 90 , 268–281.
   Web of Science ®Google Scholar
• Pfaff, B. , Analysis of Integrated and Cointegrated Time Series with R , 2nd ed., 2008 (Springer: New York).
   Google Scholar
• Rockafellar, R.T. , Uryasev, S. and Zabarankin, M. , Generalized deviations in risk analysis. Finance Stoch. , 2006, 10 , 51–74.
   Web of Science ®Google Scholar
• Rubbaniy, G. , Asmerom, R. , Rizvi, S.K.A. and Naqvi, B. , Do fear indices help predict stock returns? Quant. Finance , 2014, 14 , 831–847.
   Web of Science ®Google Scholar
• Shimko, D. , Bounds of probability. Risk , 1993, 6 , 33–37.
   Google Scholar