Figure 12.1 illustrates how volatility can vary dramatically over time in financial markets. This figure is a semilog plot of the absolute values of weekly changes in AAA bond interest rates. Larger absolute changes occur in periods of higher volatility. In fact, the expected absolute change is proportional to the standard deviation. Because many changes were zero, 0.005% was added so that all data could plot on the log scale. A spline was added to show changes in volatility more clearly. The volatility varies by an order of magnitude over time; e.g., the spline (without the 0.005% added) varies between 0.017% and 0.20%. Accurate modeling of time-varying volatility is of utmost importance in financial engineering. The ARMA time series models studied in Chapter 4 are unsatisfactory for modeling volatility changes and other models are needed when volatility is not constant.
KeywordsOption Price Conditional Variance Implied Volatility GARCH Model ARMA Model
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