On American VIX Options under the Generalized 3/2 and 1/2 Models

34 Pages Posted: 8 Feb 2017 Last revised: 4 Apr 2017

See all articles by Jerome Detemple

Jerome Detemple

Boston University - Department of Finance & Economics; Center for Interuniversity Research and Analysis on Organization (CIRANO)

Yerkin Kitapbayev

Boston University - Questrom School of Business

Date Written: February 1, 2017

Abstract

In this paper, we extend the 3/2-model for VIX studied by Goard and Mazur (2013) and introduce the generalized 3/2 and 1/2 classes of volatility processes. Under these models, we study the pricing of European and American VIX options and, for the latter, we obtain an early exercise premium representation using a free-boundary approach and local time-space calculus. The optimal exercise boundary for the volatility is obtained as the unique solution to an integral equation of Volterra type.

We also consider a model mixing these two classes and formulate the corresponding optimal stopping problem in terms of the observed factor process. The price of an American VIX call is then represented by an early exercise premium formula. We show the existence of a pair of optimal exercise boundaries for the factor process and characterize them as the unique solution to a system of integral equations.

Keywords: Stochastic Volatility, VIX, Generalized 3/2 and 1/2 Models, Generalized Mixture Models, American Options, Exercise Premium, Exercise Boundaries, Integral Equations, Local Time

JEL Classification: C61, G13, G17

Suggested Citation

Detemple, Jerome and Kitapbayev, Yerkin, On American VIX Options under the Generalized 3/2 and 1/2 Models (February 1, 2017). Available at SSRN: https://ssrn.com/abstract=2909938 or http://dx.doi.org/10.2139/ssrn.2909938

Jerome Detemple

Boston University - Department of Finance & Economics ( email )

595 Commonwealth Avenue
Boston, MA 02215
United States
(617) 353-4297 (Phone)
(617) 353 6667 (Fax)

Center for Interuniversity Research and Analysis on Organization (CIRANO)

2020 rue University, 25th Floor
Montreal, Quebec H3C 3J7
Canada

Yerkin Kitapbayev (Contact Author)

Boston University - Questrom School of Business ( email )

595 Commonwealth Ave
Boston, MA 02466
United States

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