Figure 3.1 shows the daily returns on the stock market index

Table 3.1 provides some GARCH model specifications for the basic GARCH(1,1) model where the volatility equation is specified as

and the GJR-GARCH model where the volatility is specified as

where S is a dummy which takes the value 1 when

a. Discuss which empirical characteristics of the asset returns do we observe in Figure 3.1? What do these characteristics suggest?

b. Describe the difference between the two volatility specifications. What is the advantage of GJR-GARCH over GARCH? How would you test the hypothesis that there is no asymmetry in the volatility process?

c. Compare the results from the GARCH and GJR-GARCH estimations in Table 3.1. What conclusions can you draw from comparing the specifications so far?

d. Formally define and interpret the Integrated GARCH model.

e. Explain what is the news impact curve (NIC)? How different is the NIC for GJRGARCH and GARCH presented in Table 3.1

f. The relationship between the risk and expected return of an asset depends upon attitudes toward risk from asset holders. Which volatility model would you choose to capture this relationship?

Figure 3.1 Jorcon 2000 2002 2004 2008 2010 2012 2014 Table 3.1. Estimation results, (p-values in parentheses) w V Log-likelihood -4042.15 GARCH 0.12 (0.74) 0.01 (0.03) a 0.1 (0.00) 0.11 (0.00) B 0.94 (0.00) 0.88 (0.00) GJR-GARCH -4041.82 0.03 (0.01) Figure 3.1 Jorcon 2000 2002 2004 2008 2010 2012 2014 Table 3.1. Estimation results, (p-values in parentheses) w V Log-likelihood -4042.15 GARCH 0.12 (0.74) 0.01 (0.03) a 0.1 (0.00) 0.11 (0.00) B 0.94 (0.00) 0.88 (0.00) GJR-GARCH -4041.82 0.03 (0.01)