The main sources of risk that an investor faces are price and volatility risk (vega risk). Price risk is the investor's exposure to changes in the asset price. Volatility risk is the exposure to changes in volatility. The latter type of risk has been responsible for the collapse of major financial institutions in the past fifteen years (e.g. Barings Bank, Long Term Capital Management).
To date, the hedging of volatility risk has been carried out by using the exchange traded standard futures and plain vanilla options. However, these instruments are designed so as to deal with price risk, primarily. A natural candidate to hedge volatility risk is volatility options. These are instruments whose payoff depends explicitly on some measure of volatility.
The growing literature on volatility options has emerged after the 1987 crash. Brenner and Galai (1989, 1993) first suggested options written on a volatility index that would serve as the underlying asset. Towards this end, Whaley (1993) constructed VIX (currently termed VXO), a volatility index based on the S&P 100 option's implied volatilities traded in the Chicago Board of Exchange (CBOE). Ever since, other implied volatility indices have also been developed (e.g., VDAX in Germany, VXN in CBOE, VX1 and VX6 in France) and the properties of some of them have been studied (see e.g., Fleming et al . 1995, Moraux et al . 1999, Whaley 2000, Blair et al . 2001, Corrado and Miller 2003, and Simon 2003).
Various models to price volatility options written on the instantaneous volatility have also been developed (see e.g., Whaley 1993, Grünbichler and Longstaff 1996, and Detemple and Osakwe 2000). These models differ in the specification of the assumed stochastic process, and the assumptions made about the volatility risk premium. In 2003, CBOE adopted a new methodology to calculate the implied volatility index, and it announced the immediate introduction of volatility options in an organized exchange.
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Volatility Options: Hedging Effectiveness, Pricing, and Model Error
