Since 1982, numerous GARCH (Generalized Autoregressive Conditional Heteroskedascity) models have been developed. Some of the more popular ones include the GJR-GARCH, and EGARCH. Even though these models are effective at mapping out the "true volatility" of an asset, they fail to capture periods of extremely high "true volatility" (0.08). When modeling the American subprime crisis from 2008 to 2009 as out-of-sample data, the maximum volatilities that the GJR-GARCH and GARCH model provided were much less than the maximum "true volatility". Therefore, these GARCH models are not quite suitable for risk management applications as they greatly underestimate the volatility during periods of extremely high volatility (0.08).
In this paper, we modified the GARCH model, while using the GJR-GARCH as inspiration, and proposed a new model named GARCH-S. We used the Nikkei 225 and SP 500 as the two asset inputs required by the GARCH-S model. The GARCH-S makes use of a secondary market (SP 500) to increase the volatility forecast of the target market (Nikkei 225). This is possible when the returns of the secondary market at time t-1 is correlated (0.20) with the returns of the target market at time t. Even though we developed a MLE program to estimate the model arameters, the Gibbs Sampling method was used in general to estimate the parameters of the models.
The GARCH-S is found to effective in modeling the "upper range" of "true volatility". It greatly reduces underestimate errors as compared to the GARCH, GJR-GARCH and EGARCH models.Under the several assumptions we made, the GARCH-S was found to be ranked second best in forecasting accuracy while effectively capturing the peaks of high volatility better than other GARCH type models. Therefore, the GARCH-S model is an excellent candidate for risk management purposes as it greatly reduces the underestimate errors while still providing competitive forecast accuracy against other GARCH type models.

修士学位論文. 2010年度システムエンジニアリング学 第23号