This thesis examines the pricing of volatility on organized U.S. options exchanges from October 31, 2005 through November 1, 2007. The research is motivated in part by the rapid growth of hedge funds that trade volatility and in part by the growing importance that the financial markets place on the VIX as a measure of investor risk aversion.;The first half of the study speaks to the efficiency with which the market prices index volatility (as derivable from index options) relative to the individual volatilities of the index's components (as derivable from equity options). This has important implications for a particular type of volatility trading, known as dispersion trading. The study required the development of a novel extension of the Markowitz variance equation and, in the process, provides an alternative way to measure systematic and unsystematic risk. Consistent with research claims, it is shown that U.S. options markets tend to overprice index volatility and to underprice index component volatilities. Even allowing for reasonable transaction costs, potentially profitable trading opportunities arise far more frequently than one would expect if markets were perfectly efficient. Further, cluster analysis reveals that the frequency of profitable opportunities is positively correlated with both the level of index volatility and the volatility of index volatility.;The second half of the study compares the implied volatilities of individual stocks derived in two different ways. The first is the now traditional method of simply extracting the implied volatility directly from an option's price (option-implied volatility or OIV). This measure is, of course, model dependent. The second method involves deriving the implied volatility of a stock from the stock's historical beta and from the implied volatility of an index of which the stock is a part (beta-implied volatility or BIV). It is shown that BIV is, on average, slightly higher than OIV, that the two measures are highly correlated, that BIV is more volatile than OIV, and that the ratio of BIV to OIV is mean reverting for nearly all stocks studied. These results suggest that profitable pairs trading of a stock's BIV against its OIV might be possible.
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