Volatility Library

Article by: Pawan Madhogarhia
Published by: The Pennsylvania State University

“Why are we interested to forecast the volatility of S&P 500, a proxy for the stock market? If
stock market volatility remained constant over time, forecasting volatility would have been
an easy task. If this were true, volatility measured through a measure such as standard
deviation in the current period could have been applied in the future. There are often wide
swings in the market followed by larger swings. This implies that volatility is not constant
over time and is often referred to as heteroscedasticity. Stock market volatility is important
for several reasons. Detection of volatility-trends would provide insight for designing
investment strategies and for portfolio management. The volatility of S&P 500 is important
to derive the price of an option on S&P 500 index for the remaining life of the option. The
stock market volatility forecast is also an important input for dynamic portfolio insurance
strategies.

“Forecasting stock market volatility would be useful for holders and writers of options on the
S&P 500 index. Gains on straddles or spreads depend on the volatility of underlying security.
The more volatile a security is, the larger the gain to the straddle-trader or the spread-trader.
The spread-trader and the straddle-trader are not concerned about the direction of change;
rather they are concerned about the fluctuations in prices.”

Full article (PDF): Link

Article by: Sassan Alizadeh, Michael W. Brandt, Francis X. Diebold
Published by: University of Pennsylvania, The Wharton School
Date: 20 Dec 1999

“We propose using the price range, a recently-neglected volatility proxy with a long history in finance, in the estimation of stochastic volatility models. We show both theoretically and empirically that the log range is approximately Gaussian, in sharp contrast to popular volatility proxies, such as log absolute or squared returns. Hence Gaussian quasi-maximum likelihood estimation based on the range is not only simple, but also highly efficient. We illustrate and enrich our theoretical results with a Monte Carlo study and a substantive empirical application to daily exchange rate volatility. Our empirical work produces sharp conclusions. In particular, the evidence points strongly to the inadequacy of one-factor volatility models, favoring instead two-factor models with one highly persistent factor and one quickly mean reverting factor.”

Full article (PDF): Link