# Garch Models Essay

927 WordsNov 4, 20104 Pages
Case 4 - Sample Answers APS 425 - Advanced Managerial Data Analysis APS 425 Case 4 – Winter 2008 Sample A S l Answers 3/11/2008 Instructor: G Willi Schwert I G. William S h 585-275-2470 schwert@schwert.ssb.rochester.edu GARCH(1,1) Model for S&P500 Typical GARCH(1,1) Lots of persistence .07 .06 .05 .04 .03 .02 .01 .00 1000 2000 3000 4000 5000 Conditional standard deviation (c) Prof. G. William Schwert, 2003-2008 1 Case 4 - Sample Answers APS 425 - Advanced Managerial Data Analysis EGARCH(1,1) Model for S&P500 Asymmetric coefficient, c(4) is negative, so crashes => more volatility .06 .05 .04 04 .03 .02 .01 .00 1000 2000 3000 4000 5000 Conditional standard deviation EGARCH(1,1) Model for S&P500 2000-2008 Results are certainly y affected by 87 crash, but general tenor is similar .030 .025 .020 .015 .010 .005 .000 3750 4000 4250 4500 4750 5000 5250 5500 Conditional standard deviation (c) Prof. G. William Schwert, 2003-2008 2 Case 4 - Sample Answers APS 425 - Advanced Managerial Data Analysis Plot EGARCH(1,1) Estimate of Conditional SD vs VIX sd01 = sqr(253*GARCH01), where GARCH01 is the estimate of the variance of the daily stock return Note that VIX looks generally higher than EGARCH for most of these periods .5 5 .4 .3 .2 .1 .0 3750 4000 4250 4500 4750 5000 5250 5500 SD01 VIX Combine VIX with EGARCH (1,1) Model for S&P500 Include yesterday’s VIX y y (squared, divided by 253) in the equation to predict today’s variance of returns Coefficient is ..29, and tstat is 4.1 Suggests that VIX contains information beyond the EGARCH model (c) Prof. G. William Schwert, 2003-2008 3 Case 4 - Sample Answers APS 425 - Advanced Managerial Data Analysis Combine VIX with EGARCH (1,1) Model for S&P500 - Diagnostics Residual diagnostics look good g g Combine VIX with EGARCH (1,1) Model