CFEF RR/04/0 CAViaR
RR/04/0 004 CAViaR 00080 VaR VaR Engle Manganelli 999 VaR CAViaR Chow CAViaR B Engle Manganelli CAViaR Absrac: Value-a-Risk (VaR) has become a sandard ool o measure marke risk widely employed by financial insiuions boh for inernal and regulaory purposes. The sabiliy of a VaR modeling is usually imporan for predicion and economeric inference in pracice. In his paper, he CAViaR model, proposed recenly by Engle and Manganelli (999) o calculae VaR is inroduced, and he Chow s es for parameer insabiliy is carried on o explore he model sabiliy of CAViaR modeling of he risk of he Chinese sock markes. The empirical resuls show ha he 4 popular CAViaR models due o Engle and Manganelli do no fi well he real siuaion of he Chinese sock markes. The negligence of he srucural changes of he Chinese sock markes may lead o he reducion of inerpreabiliy in modeling of marke risk. VaR Value-a-Risk VaR (Basel accord) (EU capial adequacy direcive) VaR VaR
VaR ( Manganelli and Engle, 00) ) ) Mone Carlo 3) VaR Jorion 997, Manganelli and Engle (00 003 VaR 003 Engle Manganelli 999 VaR VaR VaR CAViaR VaR Manganelli and Engle (00) Mone Carlo CAViaR CAViaR --- ( Hansen 99) VaR 9. 94 97 8.0 5.9 CAViaR VaR Mone Carlo VaR GARCH GARCH EWMA( ) GARCH ( J.P. Morgan RiskMerics) h = ( ) + 0 < <. ε h, VaR Beder 995 Engle Manganelli 999 GARCH VaR CAViaR CAViaR VaR 3
( x) + = max( x,0) ( x) = min( x,0) Engle Manganelli CAViaR SAV AS : GARCH(,) (Adapive): VaR( ) = + VaR ( ) + 3 y VaR ( ) = + VaR ( ) + ( y ) + ( y ) + 3 4 VaR ( ) = + VaR ( ) + y 3 VaR VaR G y VaR ( ) = ( ) {[ exp( [ ( )])] + + + θ} { y } θ G 0 Koenker Basse(978) G [ I( y VaR ( )) ] I() G θ VaR y SAV GARCH(,) GARCH(,), GARCH(,) VaR y VaR VaR VaR CAViaR CAViaR Fisher Chow (960) θ Chow Chow : H 0 : θ 4
H θ Chow Chow Davies 977 987 0 9. Inclan Tiao(994) AR D k AR AIC AR C k = k=,,t, D0 = D T = 0 k Dk C T T C k k = ˆ ε ˆ ε ˆ ˆ = y c by = y = (ln( P) ln( P ))*00 P / c T T Inclan Tiao D W 0 k ma x k T / Dk CAViaR A B B 998 5 004 6 00 y = (ln( P) ln( P ))*00 5
0.005 0.375%, 50 B 6.367 3 9.970 00000 0.087.0638 9.970 0.48 446 39900 0.005.65 8.6797 0.3089 430 000003 B 0.0503 6.367 6.0800 0.3840 447 Inclan Tiao T B D 999 5 9 000 3 7 00 k 7 30 00 6 4 B 999 3 0 00 3 999 5.9 3 59.40 85.53 00 6.4 (a) / k T D (b) B / T k D 4 6
53 VaR 300 5 9 B 5 6 9 5% CAViaR 5%, 6 9 5% VaR VaR VaR VaR 3 + CAViaR : x 5 ( 6) 0 5 SAV 3 3 4 5 0.347.97-0.046 5.79 0.448 0.0309 0.878 0.553-0.0505 5.433 0.643 0.049 B 0.57.088 0.6334 5.00 0.8705-0.0837 0.895-0.9843 0.8383 0.957 0.8560 0.337 0.95 -.0066 0.890 0.9533 B 0.7943 0.6050 0.7866-0.3975 0.338.35 0.395 0.404 0.476 0.058 0.395.9338 0.75 0.35 0.63 0.400 B 0.4465 0.5979 0.4350 0.5579 7
5 CAViaR VaR + VaR y 99 8 66.64 6.09 regime shif VaR VaR VaR 3 AS 3 4 3 4 5 0.4874.7906 0.050 4.987-0.009-0.039 0.536.3309 0.5 4.586 0.0944 0.033 B 0.40.0580 0.796 0.3373 0.6473 0.49 0.77-0.985 0.977 0.9757 0.7975 0.4467 0.9970-0.5703 0.9473 0.987 B 0.8035 0.646 0.7486 0.8989 0.3689-0.3307 0.56 0.387-0.0673 0.0383 0.97-0.5495 0.46-0.55-0.49 0.0380 B 0.3574 0.336 0.3784-0.543.765.034 0.905 0.3549 0.559 0.846 0.694.663-0.3857 0.666 0.309 0.35 B 0.5547 0.5340 0.7009 0.07 4 GARCH(,) 3 3 4 5 0.7496 5.65-0.3068 3.0574.04 0.0800 0.80 6.450-0.3530-0.03.6 0.00 B 3.8489 4.0477 4.8553 0.834 0.88-0.0089 0.8696-0.9834 0.806 0.9476 0.8409-0.049 0.896.0336 0.8594 0.9555 B 0.76 0.5378 0.77.06 0.969 7.6573 0.833 0.588 0.9485 0.04 0.8090 6.0556 0.6756-0.54 0.546 0.304 B.3386.000.938-0.874 5 Adapive 3 4 5 0.5858 -.648-0.0-0.39-0.646.49 0.83-0.065 0 0-0.8 0.447 8
3 0.5858 -.648-0.0-0.39-0.646.49 0.83-0.065 0 0-0.8 0.447 6 SAV B 5.0396-0.6537-0.67-0.9543 4 5 0.968 0.4607 0.87 0.3544 0.450 0.093 0.337 0.997 0.5 0.8740 4.93 0.0409 B 0.86.04 0.097 0.4 0.7870 0.677 0.706 0.678 0.840 0.875 0.783 0.6560 0.76 0.3679-0.36 0.970 B 0.805 0.558 0.884 0.7976 0.480 0.66 0.3089 0.373 0.0978 0.638 0.448 0.4368 0.357 0.3563-0.84 0.45 B 0.84 0.305 0.394 0.566 VaR y VaR VaR VaR VaR VaR I( y VaR ) θ > 0 5 % B 0 3 0 000 3 7 00 6 4.774.65 5 7 AS 3 4 5 0.439 0.34 0.583 0.55 0.94 0.8 0.37 0.9 0.584 0.9855 0.0380-0.006 B 0.857 0.74 0.0954 0.45 0.869 0.053 0.83 0.665 0.9493 0.8346 0.86 0.7633 0.7978 0.348.0 0.963 B 0.7636 0.5866 0.797 0.86 0.77 0.05 0.85-0.06-0.354 0.303 0.98 0.049 0.340-0.65-0.0874 0.54 B 0.385 0.59 0.84 0.0649 0.3045 0.659 0.07 0.4675 0.33 0.830 0.3870 0.489 0.7 0.905 0.0678 0.47 B 0.5485 0.743 0.493 0.567 8 GARCH(,) 9
3 5 3 4 5 0.503 3.446 0.4 0.337.3689 0.849 0.5304.48 0.334.0088.8083 0.08 B 0.737 4.4897 0.9607 0.4478 0.758-0.03 0.774 0.750 0.7957 0.8536 0.778 0.4975 0.797 0.687 0.7773 0.90 B 0.7784 0.597 0.767 0.7800 0.388 0.386 0.546 0.6975 0.90 0.758 0.368 0.69 0.87 0.367 0.97 0.94 B 0.3840 0.3947 0.4337 0.335 9 Adapive 5 3 4 5 0.695 0.0779.07 0.0453 0.0384 0.4305 0.936 0 0.93 0.046 0.0 0.687 B 0.8463 0.96 0.699 0.76 SAV GARCH(,) GARCH SAV AS Taylor(986), Schwer(988) Engle and Maganelli (999) 3 AS GARCH(,) AS Bea() ( 0.063) GARCH(,) Bea() (.404) CI 0
AS 3 5, AS
GARCH(,) 5 7 8 VaR y y VaR VaR y 4 998 5 004 6 B A CAViaR B B B B B B A 4 CAViaR Chow Inclan Tiao CAViaR A B ( Hamilon, 994) 003 EWMA
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