Jointly Modeling of VIX and SPX Options at a Single and Common Maturity with Risk Management Applications

17 Pages Posted: 18 Mar 2013

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Date Written: January 4, 2013

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. Conditionally 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. Calibrating the model jointly to SPX and VIX options a risk management application illustrates a hedge for realized volatility options.

Suggested Citation

Carr, Peter P. and Madan, Dilip B., Jointly Modeling of VIX and SPX Options at a Single and Common Maturity with Risk Management Applications (January 4, 2013). Available at SSRN: https://ssrn.com/abstract=2234761 or http://dx.doi.org/10.2139/ssrn.2234761

Peter P. Carr

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

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