Analysis of Financial Data

Chapter 12. Financial volatility

Chapters 8–11 developed several different regression models for time series variables. Throughout, we were always interested in the variables themselves. For instance, we were interested in explaining stock or bond returns, exchange rates and yield spreads. However, there are many cases where we are not interested in the variables themselves, but in their volatility (measured by the variance). For instance, in Chapter 4 we introduced the capital asset pricing model (CAPM) and discussed how risk was important for investment decisions. The risk of investing in the stock of a company was related to the volatility of its share price (and other factors).

Another very important field of research relates to the pricing of financial derivatives (e.g. options and other securities whose payoff is derived from the price of an underlying asset). If you have studied the theory of finance, you may be aware of the Black–Scholes option price formula and other similar derivative pricing methods. In this book, we will not derive such formulae. We note only that, in these formulae, the volatility of the price of the underlying asset plays a crucial role. The methods introduced in this chapter are commonly used to provide estimates of this volatility.

We begin our discussion of volatility in asset prices informally, staying with familiar regression methods. We then discuss a very popular method for estimating financial volatility called autoregressive conditional heteroskedasticity ...