Modeling Volatility Derivatives

Friday, October 28, 2011
Hall 1-2 (San Jose Convention Center)
Nathan Belete , San Francisco State University, San Francisco , CA
Raymond Perkins , Morehouse College, Atlanta, GA
Kendra Pleasant , North Carolina State A&T University, Greensboro, NC
Stephanie Somersille, PhD , Mathematics, University of Texas, Austin, TX
Marcel Blais, PhD , Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA
The Chicago Board Options Exchange introduced the Market's Volatility Index

(VIX) in 1993.  It is a financial instrument which uses Standard & Poor's

500 Index options to measure market volatility.  The first VIX derivatives

were introduced in 2004. We are interested in modeling these derivatives.

After observing mean regressing characteristics of the VIX derivatives, we

use the Ornstein-Uhlenbeck process to model these derivatives.  We then

implement two different methods to estimate the model's parameters using

daily market data. We compare the modeling accuracy of an Ornstein-Uhlenbeck

process with a geometric Brownian motion model.  Our results confirm the

Ornstein-Uhlenbeck process can model VIX derivatives more accurately than a

geometric Brownian motion.

We show it is possible to model VIX derivatives with reasonable accuracy

looking one month forward. Our results can potentially aid investors using

volatility derivatives and influence strategies to hedge against risk.