1 CHAPTER 15 FINANCIAL APPLICATIONS OF TIME-VARYING VOLATILITY Figure 15.1 Value-at-Risk González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc Value-at-Risk (VaR)

2 Figure 15.2 SP500 Daily Returns and Their Conditional 1% VaR Under Conditional Normality González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

3 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 15.3 SP500 Daily Returns and Their Conditional 1% VaR Under Conditional Student-t

4 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. Figure 15.4 Expected Shortfall for VaR Expected Shortfall (ES)

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 5 Figure 15.5 Optimal Weights for AAPL and FCX for 15.2 Portfolio Allocation

6 Table 15.1 Descriptive Statistics of Optimal Weights for AAPL and FCX González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

7 Figure 15.6 Conditional Betas for AAPL and FCX 15.3 Asset Pricing

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 8 Table 15.2 SP500 Index Volatility at the Daily and Weekly Frequencies 15.4 Option Pricing

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 9 Table 15.3 Black-Scholes Call Option Pricing