We will study in our work, the persistence of the beneficial effect of the derivatives on the volatility and the efficiency of the French market. We will refer to the long term memory of FIGARCH type process as well as the breaking down of the anticipated variance of the volatility of the French stock market and the functions of impulse responses of different shocks of the derivatives. We deduced that the volatility is resistant in the market. We also noticed that the beneficial effect of these products is direct. This volatility disappears with the time because the impulse responses of these shocks are low and remaining inside the intervals of confidence and converging asymptotically towards the axis of abscissa. We will reveal in long term that the raise of volumes of transactions that is due to the concentration of the activities of investors on the derivative market is generating a big risk of volatilities in the French financial market. So, and despite the direct beneficial effects of these products on the volatility and the efficiency of the French financial market, it is become clear for the investors to reduce the total confidence granted on the increased use of these products which can lead in long term to the instability situations and of the persistence of the volatility in the financial markets.
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