Department of Economics and Business Economics

The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework

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The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework. / Barletta, Andrea; Nicolato, Elisa; Pagliarani, Stefano.

In: Mathematical Finance, Vol. 29, No. 3, 2019, p. 928-966.

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Barletta, Andrea ; Nicolato, Elisa ; Pagliarani, Stefano. / The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework. In: Mathematical Finance. 2019 ; Vol. 29, No. 3. pp. 928-966.

Bibtex

@article{491ebd22fcd440b5a2f530159cdd8b29,
title = "The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework",
abstract = "We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed-form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX-implied volatilities, and their sensitivities, in the joint limit of short time-to-maturity and small log-moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol-of-vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications.",
keywords = "C60, G12, G13, VIX options, asymptotic expansions, implied volatility asymptotics, multifactor stochastic volatility, CALIBRATION, EXPANSIONS, MODEL, OPTIONS, HESTON, TERM STRUCTURE, DYNAMICS, VARIANCE, SMILE, DEVIATIONS",
author = "Andrea Barletta and Elisa Nicolato and Stefano Pagliarani",
year = "2019",
doi = "10.1111/mafi.12196",
language = "English",
volume = "29",
pages = "928--966",
journal = "Mathematical Finance",
issn = "0960-1627",
publisher = "Wiley-Blackwell Publishing, Inc",
number = "3",

}

RIS

TY - JOUR

T1 - The short-time behavior of VIX-implied volatilities in a multifactor stochastic volatility framework

AU - Barletta, Andrea

AU - Nicolato, Elisa

AU - Pagliarani, Stefano

PY - 2019

Y1 - 2019

N2 - We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed-form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX-implied volatilities, and their sensitivities, in the joint limit of short time-to-maturity and small log-moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol-of-vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications.

AB - We consider a modeling setup where the volatility index (VIX) dynamics are explicitly computable as a smooth transformation of a purely diffusive, multidimensional Markov process. The framework is general enough to embed many popular stochastic volatility models. We develop closed-form expansions and sharp error bounds for VIX futures, options, and implied volatilities. In particular, we derive exact asymptotic results for VIX-implied volatilities, and their sensitivities, in the joint limit of short time-to-maturity and small log-moneyness. The expansions obtained are explicit based on elementary functions and they neatly uncover how the VIX skew depends on the specific choice of the volatility and the vol-of-vol processes. Our results are based on perturbation techniques applied to the infinitesimal generator of the underlying process. This methodology has previously been adopted to derive approximations of equity (SPX) options. However, the generalizations needed to cover the case of VIX options are by no means straightforward as the dynamics of the underlying VIX futures are not explicitly known. To illustrate the accuracy of our technique, we provide numerical implementations for a selection of model specifications.

KW - C60

KW - G12

KW - G13

KW - VIX options

KW - asymptotic expansions

KW - implied volatility asymptotics

KW - multifactor stochastic volatility

KW - CALIBRATION

KW - EXPANSIONS

KW - MODEL

KW - OPTIONS

KW - HESTON

KW - TERM STRUCTURE

KW - DYNAMICS

KW - VARIANCE

KW - SMILE

KW - DEVIATIONS

U2 - 10.1111/mafi.12196

DO - 10.1111/mafi.12196

M3 - Journal article

VL - 29

SP - 928

EP - 966

JO - Mathematical Finance

JF - Mathematical Finance

SN - 0960-1627

IS - 3

ER -