VaR 3.1 VaR 3.2 VaR

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格邀融
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1 D 1

2 VaR 3.1 VaR 3.2 VaR

3 VaR VaR a-garch VaR Black-Scholes 1., 1998 VaR VaR-covered porfolio insurance 3

4 Upside Capure 2 Perold and Sharpe 1988 Rubinsein 1985 Black and Scholes 1973 opion-based porfolio insurance OBPI proecive pu synheic pu buy-and-hold consan proporion porfolio insurance CPPI ime-invarian porfolio proecion TIPP sop-loss sraegy consan mix, 4

5 2.1 Bird Demnis & Tippe

6 2.2 Black & Scholes1973 rt qt P = Ke N d Se 2 N d1 1 2 ln S / K + r q + σ / 2 T d 1 = σ T d 2 = 2 ln S / K + rq σ / 2 T = d1 σ T σ T S K r σ N d 1 = T = q = = e q T [ N d1 1] 2 Dela 1 6

7 7 2.3 Rubinsein & Leland 1981 Black & Scholes ] [1 ] [1 ] [ T r T q T r T q T r T q T r T q Ke d N Se d N Ke d N Se d N Ke d N Se d N Ke d N Se d N S P S + = + = + = + + = + = 3 3 Nd 1 Se -q 1-Nd 2 Ke -r S

8 T K Nd 1 1- Nd 1 S Nd 1 d 1 Nd 1 Self-financing 2.4 8

9 Black, Jones & Perold1986 M : E = M * A-F E M A F M=1 M>1 1/M 9

10 Andre F. Perold & William F. Sharpe Esep & Krizman1988 TIPP CPPI TIPP : F ' = MaxA*f F f 90% F TIPP CPPI

11 1973 Black Scholes 1981 Rubinsein Leland 11

12 CPPI TIPP CPPI TIPP 3. VaR 3.1 VaR VaR VaR W 0 EW * * W δ R δ µ VaR=EW-W * =W 0 1+µ-W 0 1+R * =W 0 µ-r * =-W 0 R * -µ 4 R f R * δ R * < = P R R f R dr = δ R 2 N µ, σ R * = µ + sσ s δ VaR 12

13 VaR= W sσ 5 0 Gauss-VaR VaR * R R VaR J.P.Morgan RiskMerics, GARCH Hisorical Simulaion, Mone Carlo Simulaion Tail index VaR, VaR Pownall R.A. Koedijk,K.G α α Huisman e al α θ = s / α 2 s α Gauss-VaR s θ Garch 1 1 σ VaR = W θσ 6 0 α σ Garch a-garch VaR VaR 13

14 a-garch VaR 3.2 VaR VaR VaR VaR A r w V VaR A w[ e r T w = [ e 1] = A1 w V r T VT + V T 1] T 7 w A1-w V VaR ' V = Max{0,[ V Max0, AR ]} AR T- T T T VaR T 14

15 T- AR VaR VaR T VaR VaR VaR VaR 10 VaR 3.3 VaR CPPI A 1 90% 90% 10% 2 3 VaR 95% 10 VaR 10 VaR 10 4 CPPI M=1 15

16 B

17 1 CPPI VaR D

18 D D D VaR VaR VaR VaR D CPPI VaR 18

19 VaR VaR VaR 4. VaR VaR VaR VaR VaR a-garch VaR Black-Scholes 19

20 VaR VaR VaR 1. [M] Black, Fischer and Rober Jones, 1987, Simplifying Porfolio Insurance [J]. Journal of Porfolio Managemen, Black, Fisher and Myron Scholes, 1973, The Pricing of Opions and 20

21 Corporae Liabiliies [J]. Journal of Poliical Economy, Bird Demnis & Tippe 1988 A Sop Loss Approach o Porfolio Insurance [J]. Journal of Porfolio Managemen, Fall, Bollerslev, T. Generalized Auoregressive Condiional Heeroskedasiciy [J]. Journal of Economerics : Brennan, J. Michael and Eduardo S. Schwarz, 1988, Time-Invarian Porfolio Insurance Sraegies [J]. Journal of Finance, Choie, Kenneh S. and Eric J. Seff, 1989, TIPP: Insurance wihou complexiy: Commen [J]. Journal of Porfolio Managemen, Campbell,R., Huisman,R., Koedijk,K. Opimal porfolio selecion in a Value a Risk framework [J]. Journal of banking & Finance, 2001,25, Esep,Tony and Mark Krizman,1986,TIPP:Insurance wihou Complexiy [J]. Journal of Porfolio Managemen,Fall, Huisman, R.Koedijk, K.G., Pownall, R.A.. VaR-x: fa ails in financial risk managemen [J]. Journal of Risk, fall, Jansen,D.W.K,Koedijk,K.G.,de Vries,C.G. Porfolio selecion wih limied downside risk[j]. Journal of Empirical Finance, 2000,7, JP Morgan. RiskMerics echnology documen [M].4 h ediion, RiskMerics Group,New York, Perold, Andre F. and William F. Sharpe, 1988, Dynamic Sraegies 21

22 for Asse Allocaion [J]. Financial Analyss Journal, Pownall,R.A.,Koedijk,K.G. Capuring downside risk in financial markes: he case of he Asian Crisis [J]. Journal of Inernaional Money and Finance 1999,18, Rubinsein, Mark, 1985, Alernaive Pahs o Porfolio Insurance[J]. Financial Analyss Journal, Rubinsein,Mark,and Hayne E.Leland,1981,Replicaing Opions wih Posiion in Sock and Cash[J]. Financial Analyss Journal, July-Aug,

报告总结

报告总结 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