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Some fundamental changes in the financial markets reflect an evolution from the rational linear analytical approach of traditional finance to a quite new approach which incorporates nonlinearity as well as a new view into the dynamics of financial markets. Since the return and risk management models use the variance as a key variable for risk, and since the traditional normal model disregards the nonlinearities present in stock markets, the author has improved the fit of the volatility in the German equity market using nonlinear ARCH models. This work focuses on the behaviour of the German equity market, the significance of which is growing in the global financial market. The practical objective is to demonstrate how nonlinear features in stock market volatility can be incorporated in financial theory to improve the forecasting capabilities of financial models.