This　paper　considers　adaptive　point-wise　estimations　of　density　functions　in　GARCHtype　model　under　the　local　Ho　center　dot　lder　condition　by　wavelet　methods.　A　point-wise　lower　bound　estimation　of　that　model　is　first　investigated;　then　we　provide　a　linear　wavelet　estimate　to　obtain　the　optimal　convergence　rate,　which　means　that　the　convergence　rate　coincides　with　the　lower　bound.　The　non-linear　wavelet　estimator　is　introduced　for　adaptivity,　although　it　is　nearly-optimal.　However,　the　non-linear　wavelet　one　depends　on　an　upper　bound　of　the　smoothness　index　of　unknown　functions,　we　finally　discuss　a　data　driven　version　without　any　assumptions　on　the　estimated　functions.