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8.Using GARCH to forecast future volatility. 2221()(ntLntLntLVuVVσαβ σ++ −+ −−=−+−1)2), since the expected value of is , hence: 21ntu+ −21ntσ+ −221[]()[]() (tntLntLnLEVEVσαβσαβσ++ −−=+−=+−V9.Volatility term structures– the relationship between the implied volatilities of the options and their maturities. -Define 21( )() and a=ln+ntV tEσαβ+=Æ-011( )[(0)]atTLLeV t dtVVVTaT−−=+−∫, or in per yearÆ-21()252[(0)]atLeTVVaTσ−LV⎧⎫−=+−⎨⎬⎩⎭Æcan be used to estimate a volatility term structure based on the GARCH (1,1) model. 10.Impact of volatility changes. - 221(0)()252[]252atLLeTVaTσσ−⎧⎫−=+−⎨⎬⎩⎭V. - 6 -
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