An Introduction to Analysis of Financial Data with R

An important measure in finance is the risk associated with an asset and asset volatility is perhaps the most commonly used risk measure. There are several types of asset volatility, however. We define them in the next section. The goal of this chapter is to understand the characteristics of asset volatility, to study volatility models, and to gain experience in modeling and using asset volatility.

Volatility has many important applications in finance. It is a key factor in options pricing and asset allocation. It plays an important role in value at risk calculation for risk management. More recently, some volatility indices have become a financial instrument. For example, the VIX index of the Chicago Board Options Exchange (CBOE) started to trade in futures on March 26, 2004.

Although asset volatility is well defined, it is not directly observable in practice. What we observe are the prices of an asset and its derivatives. One must estimate the volatility from these observed prices. The fact that volatility is not directly observable has several important implications in studying and modeling volatility. We shall discuss these implications throughout the chapter.

There are many volatility models available in the literature. The univariate models discussed in this chapter include the autoregressive conditional heteroscedastic (ARCH) model of Engle (1982), the generalized autoregressive ...