Yaw-Huei Wang National Central University Co-authored with Chih-Chiang Hsu

1. The Performance of GARCH Models with Short-memory, Long-memory, or Jump Dynamics: Evidence from Global Financial Markets Yaw-Huei Wang National Central University Co-authored with Chih-Chiang Hsu National Central University

2. Motivation • Volatility is a key input for both risk management and derivative pricing. • ARCH-type models are the most successful and popular framework for describing volatility. • In the past two decades, the model has been developed to be more realistic, but more complicated unfortunately.

3. Research Questions • Would the more complicated model performs any better for a particular purpose? • Conditional distribution: skewed, fat-tailed • Memory: short or long • If so, can such improved performance be globally valid for different markets?

4. Objectives • Develop a nested volatility model based on the EGARCH framework to investigate the performance of (1)short-memory, (2)long-memory, and (3)jump models in terms of (1)model fitting, (2)volatility forecasting, and (3)VaR prediction for 8 relatively large stock markets.

5. The Model

6. The Model • Estimation: MLE • Maximize the log likelihood function

7. The Model • Short-memory: EGARCH (Nelson, 1991) • λt = d = 0. • Long-memory: FIEGARCH (Bollerslev & Mikkelsen, 1996) • λt = 0. • Jump dynamics: EGARCH-jump (Maheu & McCurdy, 2004) • d = 0. • EGARCH-skewed-t (Hansen, 1994)

8. Measures of Performance • Model fitting: • Likelihood ratio test: • Akaike information criteria (AIC) • Volatility forecasting: • Mean squared errors (MSEs)

9. Measures of Performance • VaR prediction: • Likelihood ratio test • In practice, a preferred model should have a violation rate which is no greater than the threshold.

10. Data • The Datastream stock market indices of US, Japan, the UK, Germany, France, Canada, Italy and Spain . • From July 1990 to June 2005. • Excluding holiday, there are, on average, about 3,785 observations. • Preliminary tests for the absolute values of returns support the existence of long memory in volatility, particularly clear for US and Canada.

11. Empirical Results • Model fitting: • The EGARCH-jump model has the smallest AIC and the highest LR statistic globally. • The EGARCH-skewed-t model, with two more parameters, can also provide substantial improvements. • The FIEGARCH model does not necessarily result in any significant improvement.

13. Empirical Results • Volatility forecasting • The EGARCH-jump performs best for some countries, particularly good for German and Canadian markets. • FIEGARCH has fairly satisfactory improvement as well (but with higher variation), although the performance in model fitting is bad. • By contrast, the EGARCH-skewed-t model does not provide any improvement, although the performance in model fitting is good.

15. Empirical Results • VaR prediction • Almost of all models pass the LR tests for all countries at the 5% significance level. • Both the EGARCH-jump model and the EGARCH-skewed-t model pass the LR tests for all countries and at all significance levels. • However, for the EGARCH-jump model, 87.5% of all violation rates are lower than the corresponding significance levels, while 62.5% for the EGARCH-skewed-t model.

17. Conclusions • The EGARCH-jump model outperforms all other models in all aspects, with the single exception of volatility forecasting for some indices. • However, the computation load is substantially increased.

18. Conclusions • If less-expensive volatility are preferred, alternative models include • the use of the EGARCH-skew-t model for model fitting and VaR prediction. • the FIEGARCH model for volatility forecasting, since these models also demonstrate fairly good performance for these particular purposes. • Interestingly, the FIEGARCH model performs relatively satisfactory for the US market only.