Three Essential Models for Volatility

Nigel Da Costa Lewis

Volatility models are important to traders, investors, and risk managers. Volatility forecasts are used to derive option prices, to update hedge ratios for derivatives portfolios and fed into value-at-risk models. Tools to assist with modelling volatility are therefore of key importance. We will discuss three of the most practical models in this chapter. The first is based on moving averages; the second the generalised autoregressive conditional heteroskedastic (GARCH) model; and the third is the exponentially weighted moving average (EWMA) model.

MASTERING VOLATILITY

Volatility is a measure of variability in price over some period of time. Traders are interested in daily volatility, investors in monthly or quarterly movements, whilst historians and scholars may take measurements over many decades. Asset prices are inherently volatile with long periods of apparent stability followed by abrupt jumps upwards or downwards. On numerous occasions market participants have been surprised by sudden and enormous changes. In October 2008 the Dow Jones 30 Industrial Index fell 19%; on October 19, 1987, it declined by around 23%, and again by 18% on August 31, 1998; the Federal Fund’s