1

CHAPTER 15FINANCIAL APPLICATIONS OF TIME-VARYING VOLATILITY

Figure 15.1 Value-at-Risk

González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

15.1.1 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.

3González-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

4González-Rivera: Forecasting for Economics and Business,

Copyright © 2013 Pearson Education, Inc.

Figure 15.4 Expected Shortfall for VaR

15.1.2 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.

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