GARCH Modeling of Major Global Equity Market Returns

The sample data used in the study consist of daily closing prices from the various markets. The markets are the S&P 500 (U.S.), FOTSE 100 (U.K), DAX40 (Germany), CAC (France), and NIKKEI225 (Japan). The indexes range from November 26th, 1990 to March 21st, 2002. The sample data showed the market daily returns, squared returns, and correlations of the daily returns from the five markets. The daily returns represent the log diff

The ARCH/GARCH family models were used to examine the behavior of the volatility of the return. Factors like the weekend/holiday effect, leverage effects, and asymmetric response to news were looked at more closely. The GARCH model is a more generalized model of the ARCH model first introduced by professor, Robert Engle in 1982 to explain the volatility of inflation rates. The model is considered to be more appropriate for modeling high frequency financial assets and market return data. There are several versions of the GARCH model that have been proposed over the years. The ARCH process uses two equations, the mean and the variance equations. The model indicates that the conditional variance of a shock at time t is a function of the squares of past shocks, where the conditional variance needs to be nonnegative. The nonnegative aspect indicates that a positive or negative market move will result in a big increase in conditional variance. This process captures the conditional variance of financial market returns and it uses the assumption that today’s conditional variance is a weighted average of past squared unexpected returns. Because ARCH model are difficult to estimate and has lagged forecasts, the GARCH model was proposed. It adds autoregressive terms to the equation and focuses on the time-varying variance of the distribution of returns.

The estimates for both the symmetric and asymmetric GARCH models are based on the maximum likelihood method. The sum of á + â in the GARCH equations must be less than 1 if the equity returns process is stationary. Most volatility forecast of financial market returns “mean revert”; which means they eventually adjust back to the value of their mean. Relatively large values of á + â indicate that shocks to the conditional varianc

Some topics in this essay:
TARCH E-GARCH, Robert Engle, ARCH GARCH, France Japan, DAX NIKKEI, CAC France, NIKKEI225 Japan, , daily returns, conditional variance, leverage effect, volatility clustering, s&p 500, garch model, returns markets, arch model, sample data, volatility models, returns arch model, markets s&p 500, á + â, negative price changes, financial market returns,