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Indices for financial market volatility obtained through fuzzy regression

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Abstract
The measurement of volatility is of fundamental importance in finance. Standard market practice adopted for volatility estimation from option prices leads to a considerable loss of information and the introduction of an element of arbitrariness in the volatility index computation. We propose to adopt fuzzy regression methods in order to include all the available information from option prices, and to obtain an informative volatility index. In fact, the obtained fuzzy volatility indices not only offer a most possible value, but also a lower and an upper bound for the interval of possible values, providing investors with an additional source of information. We also propose a defuzzification procedure to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in volatility index computation by adopting an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility.
Keywords
Fuzzy volatility index, fuzzy regression methods, defuzzification procedure, volatility forecasting, implied volatility, IMPLIED VOLATILITY, OPTIONS, MODEL, PERFORMANCE

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MLA
Muzzioli, Silvia, Luca Gambarelli, and Bernard De Baets. “Indices for Financial Market Volatility Obtained Through Fuzzy Regression.” INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING 17.6 (2018): 1659–1691. Print.
APA
Muzzioli, Silvia, Gambarelli, L., & De Baets, B. (2018). Indices for financial market volatility obtained through fuzzy regression. INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING, 17(6), 1659–1691.
Chicago author-date
Muzzioli, Silvia, Luca Gambarelli, and Bernard De Baets. 2018. “Indices for Financial Market Volatility Obtained Through Fuzzy Regression.” International Journal of Information Technology & Decision Making 17 (6): 1659–1691.
Chicago author-date (all authors)
Muzzioli, Silvia, Luca Gambarelli, and Bernard De Baets. 2018. “Indices for Financial Market Volatility Obtained Through Fuzzy Regression.” International Journal of Information Technology & Decision Making 17 (6): 1659–1691.
Vancouver
1.
Muzzioli S, Gambarelli L, De Baets B. Indices for financial market volatility obtained through fuzzy regression. INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING. 2018;17(6):1659–91.
IEEE
[1]
S. Muzzioli, L. Gambarelli, and B. De Baets, “Indices for financial market volatility obtained through fuzzy regression,” INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING, vol. 17, no. 6, pp. 1659–1691, 2018.
@article{8607181,
  abstract     = {The measurement of volatility is of fundamental importance in finance. Standard market practice adopted for volatility estimation from option prices leads to a considerable loss of information and the introduction of an element of arbitrariness in the volatility index computation. We propose to adopt fuzzy regression methods in order to include all the available information from option prices, and to obtain an informative volatility index. In fact, the obtained fuzzy volatility indices not only offer a most possible value, but also a lower and an upper bound for the interval of possible values, providing investors with an additional source of information. We also propose a defuzzification procedure to select a representative value within this interval. Moreover, we investigate the occurrence of truncation and discretization errors in volatility index computation by adopting an interpolation-extrapolation method. We also test the forecasting power of each volatility index on future realized volatility.},
  author       = {Muzzioli, Silvia and Gambarelli, Luca and De Baets, Bernard},
  issn         = {0219-6220},
  journal      = {INTERNATIONAL JOURNAL OF INFORMATION TECHNOLOGY & DECISION MAKING},
  keywords     = {Fuzzy volatility index,fuzzy regression methods,defuzzification procedure,volatility forecasting,implied volatility,IMPLIED VOLATILITY,OPTIONS,MODEL,PERFORMANCE},
  language     = {eng},
  number       = {6},
  pages        = {1659--1691},
  title        = {Indices for financial market volatility obtained through fuzzy regression},
  url          = {http://dx.doi.org/10.1142/s0219622018500335},
  volume       = {17},
  year         = {2018},
}

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