Implied Volatility Indexes and Daily Value at Risk Models

Abstract

Value at risk, though flawed as a concept, has become one of the most common ways to summarize risk exposure for an investment position. Computing VaR requires the volatility of the underlying asset as an input. The two general approaches are to use historical volatility or some other estimator based on past returns, such as GARCH; or, alternatively, to compute implied volatility from observed market option prices. The Chicago Board Options Exchange computes and publishes indexes of implied volatilities from options on the stocks in the S&P 500 (VIX) and the Nasdaq index (VXN), respectively. In this article, Giot compares the performance of volatility forecasts drawn from historical returns and from option implied volatilities, using metrics that are appropriate for VaR estimates, such as the empirical failure rate relative to the target VaR percentage, independence, and conditional coverage. Implied volatility is found to perform relatively well, but combining GARCH and implied volatility often improves on the results from either one alone.