Joint modeling of VIX and SPX options at a single and common maturity with risk management applications

Peter Carr; Dilip B. Madan

doi:10.1080/0740817X.2013.857063

Joint modeling of VIX and SPX options at a single and common maturity with risk management applications

Peter Carr, Dilip B. Madan

Finance and Risk Engineering

Research output: Contribution to journal › Article › peer-review

Abstract

A double gamma model is proposed for the VIX. The VIX is modeled as gamma distributed with a mean and variance that respond to a gamma-distributed realized variance over the preceeding month. Conditional on VIX and the realized variance, the logarithm of the stock is variance gamma distributed with affine conditional drift and quadratic variation. The joint density for the triple realized variance, VIX, and the SPX is in closed form. Maximum likelihood estimation on time series data addresses model adequacy. A joint calibration of the model to SPX and VIX options is employed to illustrate a risk management application hedging realized volatility options. © 2014

Original language	English (US)
Pages (from-to)	1125-1131
Number of pages	7
Journal	IIE Transactions (Institute of Industrial Engineers)
Volume	46
Issue number	11
DOIs	https://doi.org/10.1080/0740817X.2013.857063
State	Published - Nov 2 2014

Keywords

Ask price minimizing hedge
distorted expectation
variance gamma model

ASJC Scopus subject areas

Industrial and Manufacturing Engineering

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10.1080/0740817X.2013.857063

Cite this

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abstract = "A double gamma model is proposed for the VIX. The VIX is modeled as gamma distributed with a mean and variance that respond to a gamma-distributed realized variance over the preceeding month. Conditional on VIX and the realized variance, the logarithm of the stock is variance gamma distributed with affine conditional drift and quadratic variation. The joint density for the triple realized variance, VIX, and the SPX is in closed form. Maximum likelihood estimation on time series data addresses model adequacy. A joint calibration of the model to SPX and VIX options is employed to illustrate a risk management application hedging realized volatility options. {\textcopyright} 2014",

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AU - Madan, Dilip B.

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N2 - A double gamma model is proposed for the VIX. The VIX is modeled as gamma distributed with a mean and variance that respond to a gamma-distributed realized variance over the preceeding month. Conditional on VIX and the realized variance, the logarithm of the stock is variance gamma distributed with affine conditional drift and quadratic variation. The joint density for the triple realized variance, VIX, and the SPX is in closed form. Maximum likelihood estimation on time series data addresses model adequacy. A joint calibration of the model to SPX and VIX options is employed to illustrate a risk management application hedging realized volatility options. © 2014

AB - A double gamma model is proposed for the VIX. The VIX is modeled as gamma distributed with a mean and variance that respond to a gamma-distributed realized variance over the preceeding month. Conditional on VIX and the realized variance, the logarithm of the stock is variance gamma distributed with affine conditional drift and quadratic variation. The joint density for the triple realized variance, VIX, and the SPX is in closed form. Maximum likelihood estimation on time series data addresses model adequacy. A joint calibration of the model to SPX and VIX options is employed to illustrate a risk management application hedging realized volatility options. © 2014

KW - Ask price minimizing hedge

KW - distorted expectation

KW - variance gamma model

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Joint modeling of VIX and SPX options at a single and common maturity with risk management applications

Abstract

Keywords

ASJC Scopus subject areas

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