Title page for ETD etd-121611-122959

Document Type	thesis
Author Name	Carr, Justin P
URN	etd-121611-122959
Title	Modeling Volatility Derivatives
Degree	MS
Department	Mathematical Sciences
Advisors	Marcel Blais, Advisor
Keywords	Modeling Volatility Derivatives
Date of Presentation/Defense	2011-12-16
Availability	restricted
Abstract The VIX was introduced in 1993 by the CBOE and has been commonly referred to as the fear gauge due to decreases in market sentiment leading market participants to purchase protection from declining asset prices. As market sentiment improves, declines in the VIX are generally observed. In reality the VIX measures the markets expectations about future volatility with asset prices either rising or falling in value. With the VIX gaining popularity in the marketplace a proliferation of derivative products has emerged allowing investors to trade volatility. In observance of the behavior of the VIX we attempt to model the derivative VXX as a mean reverting process via the Ornstein-Uhlenbeck stochastic differential equation. We extend this analysis by calibrating VIX options with observed market prices in order to extract the market density function. Using these parameters as the diffusion process in our Ornstein-Uhlenbeck model we derive futures prices on the VIX which serves to value our target derivative VXX.
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