利用高頻金融數(shù)據(jù)的已實(shí)現(xiàn)波動率估計及其應(yīng)用

1、(1)tttpm 0(|)ttssE dp F00(|)(|)ttssssIVCov dCov dpmFFtm0(2)ttssdmW ,( ( ), ,1,2,si jsi jK ttt 0ttsIVds0|,(,)tttttsNdsp 10(3)ttNtssiidmWY 0()ttN iYtm111|00 ,lim()()(4)jjjjntttttj p ppppp , ,(5)ttp pm m00 , (6)ttssss tds p pmm sssmmm0,ttsdsm m 0|,(,)tttttsNdsp 111 , ()()(7)iiiiMMMMMtMtip ppppp0lim , ,

2、 tMttsMdsp pp p 0( , )()|( ,)( ,)(8)tMtStM vechpvechdsN 0p L (1)(1):22tK KK K , ,1,0()(9)lkstklkklltsssk k l lKds 0(,)tklMkltsMdspp 0(,)tklMk ltsMds pp t tttsdpdtdW20ttsIVds121 ,lim()iiMMMttMip ppp , ttIVp p1()2 , 1 , ()iiMMM b aMa baaip ppp , , Ma bp p , , bap pp p2bbasaIVIVds2111( , )lim|(10)riiMM

3、MtrtMiV p rpMpp122121111121( ; ,)lim| |(11)rriiiiMMMMMtrrtMiV p r rpMpppp0( , )(12)trtrsV p rds1212120( ; ,)(13)trrtrrsV p r rds 21212 (1)|2,( )rrrrE u(0,1)uN120rr01(0,2)( , ) ,2(14)2trsrttdsrV p rp prr121212011121212max( ,)2( ; ,)( )max( ,)2(15)max(,)2rtrrsrdsr rV p r rX tr rrr 2200 , ttsss tp pdsp

4、 22120( ;1,1)ttV pds( ;1,1)MV p20( ,2)( ;1,1)ss tpV pV p 0ln( , ) ln()|( , )( ,)(16)tMtstttMvechvechdsN 0p pCC L 1ln( , )MttdiagvechCp p10(,)ln()0RVg RVRVttttpp1iiMMMirpp1iiMMMtrppMMMiiierr1iiMMMie2()0,(),tttsEVarst 224()tVar 階數(shù) 自相關(guān)函數(shù) t 值 1 -.47636 -172.31 2 0.03113 11.26 3 0.01161 4.20 第 i 筆交易 第 i-

5、1 筆交易 “+” “0” “-” 邊際和 “+” 612 12840 12985 26437 “0” 12277 52313 12990 77580 “-” 13550 12431 615 26596 邊際和 26439 77584 26590 130613 111(, )()(), 1,0,1,iii hi hMMMMMtMhiX YXXYYhHH ()(,)MMhhXX X011( )( )()( )( ),(17)HMMMMhhhhKppkppH0( )Mp , Mtp p10,020( )kk x dx11,120( )kk xdx12,220( )kkx dx2240/tstds2

6、400/ttssdstds40tsds230()Hc Mt16240,022240000( )(0,4 (0)(1) )(18)ttMssnKpdsNtds c kckk L120(0)(1)0,()kkmHc Mt14240,011,1232,2400000( )(0,42)(19)ttMssnKpdsNtds c kckc k L40tsds0101 , , ,0nnt ttttttG(, )111 21,kK kkkKkKkc Ktttt G1knkcK02,KKn Kntttttppppp11211,KKn Kttttpppp22222,Kn Kttttpppp121311,KKKnt

7、tttpppp11 (1)(, )21 , ()kkiKkiKCK ktttip ppp ()(, )21011 , , ()(20)i KiKn KKK kttttkip pp pppKK(, )()( ) , , (21)K JKJKtttJnTSRVp pp pn(1)/KnnKK(1)/JnnJJ12(,)()()11 , , (22)WiWK KKKalltittiWRVMSRVw p pp pn 最高頻率個低頻加權(quán)和12,WK KK11Wiiw16n14n14n16n()ht t hE0h0h ()0lutttEpp00,luluttttt00022211112(23)MMMMiiiiiiiiirrer e224100()(0,2)(24)ttMissiMrdsNds L2222011()(0,22()(25)MMiitiiMeEeNVar L22010(0,4)(26)tMiisir eNds L1()OM201/(2)MiidiirM,201()/(2)Miid ciirRVMln,000expln/(2)ciidRVM000(27)22llhhMMMMACAClhRVRVRVRV