Download This PaperOn American VIX Options under the Generalized 3/2 and 1/2 Models
34 Pages Posted: 8 Feb 2017 Last revised: 4 Apr 2017
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
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