Volatility tail risk under fractionality

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Volatility tail risk under fractionality. / Morelli, Giacomo; Santucci de Magistris, Paolo.

In: Journal of Banking and Finance, Vol. 108, 105654, 2019.

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Morelli, Giacomo ; Santucci de Magistris, Paolo. / Volatility tail risk under fractionality. In: Journal of Banking and Finance. 2019 ; Vol. 108.

Bibtex

@article{fb8639f60aba4aa29ddd5d5db5162b46,
title = "Volatility tail risk under fractionality",
abstract = "We study the probabilistic properties of the fractional Ornstein–Uhlenbeck process, which is a relevant framework for volatility modeling in continuous time. First, we compute an expression for its variance for any value of the Hurst parameter, H ∈ (0, 1). Second, we derive the density of the process and we calculate the probability of its supremum to be above a given threshold. We provide a number of illustrations based on fractional stochastic volatility models, such as those of Comte and Renault (1998), Bayer et al. (2016) and Gatheral et al. (2018). Finally, the empirical analysis, based on the realized variance series of S&P500, shows the usefulness of these theoretical results for risk management purposes, especially when a characterization of the volatility tail risk is needed.",
keywords = "Fractional Ornstein–Uhlenbeck, Rough volatility, Supremum, VIX, VolaR",
author = "Giacomo Morelli and {Santucci de Magistris}, Paolo",
year = "2019",
doi = "10.1016/j.jbankfin.2019.105654",
language = "English",
volume = "108",
journal = "Journal of Banking & Finance",
issn = "0378-4266",
publisher = "Elsevier BV",

}

RIS

TY - JOUR

T1 - Volatility tail risk under fractionality

AU - Morelli, Giacomo

AU - Santucci de Magistris, Paolo

PY - 2019

Y1 - 2019

N2 - We study the probabilistic properties of the fractional Ornstein–Uhlenbeck process, which is a relevant framework for volatility modeling in continuous time. First, we compute an expression for its variance for any value of the Hurst parameter, H ∈ (0, 1). Second, we derive the density of the process and we calculate the probability of its supremum to be above a given threshold. We provide a number of illustrations based on fractional stochastic volatility models, such as those of Comte and Renault (1998), Bayer et al. (2016) and Gatheral et al. (2018). Finally, the empirical analysis, based on the realized variance series of S&P500, shows the usefulness of these theoretical results for risk management purposes, especially when a characterization of the volatility tail risk is needed.

AB - We study the probabilistic properties of the fractional Ornstein–Uhlenbeck process, which is a relevant framework for volatility modeling in continuous time. First, we compute an expression for its variance for any value of the Hurst parameter, H ∈ (0, 1). Second, we derive the density of the process and we calculate the probability of its supremum to be above a given threshold. We provide a number of illustrations based on fractional stochastic volatility models, such as those of Comte and Renault (1998), Bayer et al. (2016) and Gatheral et al. (2018). Finally, the empirical analysis, based on the realized variance series of S&P500, shows the usefulness of these theoretical results for risk management purposes, especially when a characterization of the volatility tail risk is needed.

KW - Fractional Ornstein–Uhlenbeck

KW - Rough volatility

KW - Supremum

KW - VIX

KW - VolaR

UR - http://www.scopus.com/inward/record.url?scp=85072582833&partnerID=8YFLogxK

U2 - 10.1016/j.jbankfin.2019.105654

DO - 10.1016/j.jbankfin.2019.105654

M3 - Journal article

AN - SCOPUS:85072582833

VL - 108

JO - Journal of Banking & Finance

JF - Journal of Banking & Finance

SN - 0378-4266

M1 - 105654

ER -