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Forward variance dynamics: Bergomi’s model revisited.

Aly, Sidi Mohamed LU (2014) In Applied Mathematical Finance 21(1). p.84-107
Abstract
In this article, we propose an arbitrage-free modelling framework for the joint dynamics of forward variance along with the underlying index, which can be seen as a combination of the two approaches proposed by Bergomi. The difference between our modelling framework and the Bergomi (2008. Smile dynamics III. Risk, October, 90–96) models is mainly the ability to compute the prices of VIX futures and options by using semi-analytic formulas. Also, we can express the sensitivities of the prices of VIX futures and options with respect to the model parameters, which enables us to propose an efficient and easy calibration to the VIX futures and options. The calibrated model allows to Delta-hedge VIX options by trading in VIX futures, the... (More)
In this article, we propose an arbitrage-free modelling framework for the joint dynamics of forward variance along with the underlying index, which can be seen as a combination of the two approaches proposed by Bergomi. The difference between our modelling framework and the Bergomi (2008. Smile dynamics III. Risk, October, 90–96) models is mainly the ability to compute the prices of VIX futures and options by using semi-analytic formulas. Also, we can express the sensitivities of the prices of VIX futures and options with respect to the model parameters, which enables us to propose an efficient and easy calibration to the VIX futures and options. The calibrated model allows to Delta-hedge VIX options by trading in VIX futures, the corresponding hedge ratios can be computed analytically. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
variance swap, forward variance, VIX, VIX futures, VIX options, implied volatility, skew, hedging
in
Applied Mathematical Finance
volume
21
issue
1
pages
84 - 107
publisher
Routledge
external identifiers
  • Scopus:84892678233
ISSN
1466-4313
DOI
10.1080/1350486X.2013.812329
language
English
LU publication?
yes
id
7c586810-76e7-4aeb-bfa7-991e73bf6a37
date added to LUP
2016-04-13 13:21:31
date last changed
2017-01-01 08:22:49
@article{7c586810-76e7-4aeb-bfa7-991e73bf6a37,
  abstract     = {In this article, we propose an arbitrage-free modelling framework for the joint dynamics of forward variance along with the underlying index, which can be seen as a combination of the two approaches proposed by Bergomi. The difference between our modelling framework and the Bergomi (2008. Smile dynamics III. Risk, October, 90–96) models is mainly the ability to compute the prices of VIX futures and options by using semi-analytic formulas. Also, we can express the sensitivities of the prices of VIX futures and options with respect to the model parameters, which enables us to propose an efficient and easy calibration to the VIX futures and options. The calibrated model allows to Delta-hedge VIX options by trading in VIX futures, the corresponding hedge ratios can be computed analytically.},
  author       = {Aly, Sidi Mohamed},
  issn         = {1466-4313},
  keyword      = {variance swap,forward variance,VIX,VIX futures,VIX options,implied volatility,skew,hedging},
  language     = {eng},
  number       = {1},
  pages        = {84--107},
  publisher    = {Routledge},
  series       = {Applied Mathematical Finance},
  title        = {Forward variance dynamics: Bergomi’s model revisited.},
  url          = {http://dx.doi.org/10.1080/1350486X.2013.812329},
  volume       = {21},
  year         = {2014},
}