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经章佳
5 years ago
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2 - i -

3 1 2 W 1 W 2 W W W d(w) = d(p) + d (P) + L+ d(t) + d( σ ) + d(r) 2 P 2 P t σ R 1 2 = d(p) + Γ d (P) + L+ θ d(t) + ν d( σ) + ρ d(r) 2 Delta Delta Leland WW Delta-Gamma Delta-Gamma-Vega Michel Crouhy, Dan Galai & Robert Mark 2 - ii -

4 VaR VaR VaR VaR VaR - iii -

5 ERM 5.1 Delta VaR 7.1 VaR 7.2 VaR 7.3 VaR 7.4 VaR 7.5 VaR - i -

6 VaR VaR

7 Covered Warrant 1 (Equity Warrant) Derivative Warrant synthetic warrant third party warrant - 2 -

8 VaR VaR VaR VaR - 3 -

9 JTB / /

10 American Light Power : NA

11 2 ( ) =8.00 GDP - 6 -

12 - 7 -

13 1994 (Market Risk) Credit Risk (Liquidity Risk) (Operational Risk) (Law Risk) (Market Risk) (Credit Risk) (Liquidity Risk) (Operational Risk) (Law Risk) 1-8 -

14 3 Max(P -X,0) Revenue=W - (1+R) C (1+R) T t 0 T t Revenue W 0 P T X R T Ct

15 2 /

16 - Modiligliani-Miller MM B-S W=P N(d ) X e N(d ) -RT 1 2 d 1 2 P σ ln( ) + (R + ) T = X 2 σ T

17 d = d σ T 2 1 W P X T R Taylor Expansion 2 W 1 W 2 W W W d(w) = d(p) + d (P) + L+ d(t) + d( σ ) + d(r) 2 P 2 P t σ R 1 2 = d(p) + Γ d (P) + L+ θ d(t) + ν d( σ) + ρ d(r) 2 W P t R P t R

18 2 W 1 W 2 W d(w) = d(p) + d (P) + d( σ ) + L 2 P 2 P σ 1 2 W = d(p) + Γ d (P) + d( σ ) + L 2 σ 2 CAPM / Delta Delta Delta Delta Delta Delta Delta Delta Leland 1985 Delta Delta Whalley Wilmott 1999 [Delta-Bt Delta+Bt] 3kP e B t = 2λ R(T t) 2 t Γt

19 Bt K Pt R T t 1 Whally Wilmott Delta Delta-Gamma Gamma Delta Delta Gamma Delta-Gamma Delta-Gamma-Vega Delta Gamma Delta Gamma Vega

20 Delta-Gamma-Vega 3 Delta / / / ETF ETF 3 ETF 80% ETF 80%

21 GARP 4 GARP Generally Accepted Risk Principles(GARP),Cooper s & Lybrand

22 / Money laundering Outsourcing

24 Delta VaR 3 ERM Enterprise-wide Risk Management

25 - 20 -

26 Delta JTB BS % 7 Delta WW = Delta Delta= WW =1 Delta

27 WW = WW = =100% Delta=0 =1 =0.75 =

28 % 1 2 Delta / % dp dt dz P =

29 BS / 400*100 =

30 A1 A A A2 A3 A A A A2 A3 A A1 A2 A3 = A1 -A2/A3 -[max -A1 0 -max -A2/A3 0 ]

31 A3 A

32 ( ) 20 ( ), 2

33 twbbb 20%

34 20% 20% 50%

35 ( ) % % 30% 20%

37 VaR VaR VaR 100% 20% 20% 20%

38 1 VaR VaR VaR(Value at Risk) prob( P > VaR) = α Prob P P t VaR VaR = α σ P t t P Jorion 1997 VaR VaR VaR Delta- Delta-Gamma VaR VaR 21 VaR VaR RiskMetrics CreditMetrics

39 VaR VaR VaR 2 VaR VaR local-valuation method Delta- Delta-Gamma full-valuation method Delta-Gamma VaR 1- Delta-Gamma VaR VaR 9 VaR

40 ARCH GARCH VaR Delta-Gamma VaR Delta-Gamma Delta-Normal 90% Delta-Gamma

41 VaR Delta-Gamma VaR VaR(W) = Z( α) ( σ(p)) + 1/ 2 ( Γ σ(p )) 1 2 VaR(P) Γ VaR(P ) Z( ) P P P P

42 P P VaR P 8 Pr ob(p>var(p)) = α VaR VaR T VaR VaR T T VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR

43 9 3 VaR 1 JP RiskMetric CreditMetric VaR 99% 10 VaR Z( α ) T 1 1 VaR( α1,t 1) = VaR( α2,t 2) Z( α2 ) T 2 Z VaR VaR VaR K VaR 9 95% 20 99% %

44 T 10 99% % % 1 99% JP 1 95% 1 99% UBS 1 99% 1 98% 1 95% 1 99% 1 99% 1 99% CSFP 1 99% VaRPhilippe Jorion VaR [95% 99%] 1 mark to market 4 VaR VaR VaR VaR VaR VaR

45 VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR 5 VaR VaR VaR VaR

46 95% 99% 95% 99% VaR 95% 99% Pi = Ri P0 Ri 95% 99% P0 95% 99% VAR = (P X) N i i Pi 95% 99% X N VaR 2003 VaR VaR =95% =99% 44.78% 65.23% VaR VaR 95% 99% % 99%

47 % 99% VaR VaR 11 VaR % 95% VaR Jarque-Bera 248 P=0 j = cv = Jarque-Bera J

48 Ordinary Least Squares Estimates SSE DFE 624 MSE Root MSE SBC AIC Regress R-Square Total R-Square Durbin-Watson Pr < DW Pr > DW NOTE: Pr<DW is the p-value for testing positive autocorrelation, and Pr>DW is the p-value for testing negative autocorrelation. Q and LM Tests for ARCH Disturbances Order Q Pr > Q LM Pr > LM Standard Approx VaRiable DF Estimate Error t Value Pr > t Intercept Q LM 1-12 P VaR VaR 95% 99% 40.87% 53.78%

49 VaR % VAR 95% VAR 99% VaR 14 VaR VAR VAR(95%) VAR(99%)

50 J P Morgan

51 - 46 -

52 1 Don M. Chance Charles W. Smithson Keith Cuthbertson & Durk Nitzsche, VaR Option pricing and replication with transaction costs, Leland, H.E., Journal of Finance, Optimal Hedging of Options with Small but Arbitrary Transaction Cost Structure A.E.Whalley and P.Wilmott, Mathematical Finance, Michel Crouhy, Dan Galai & Robert Mark

0 1 VaR 2 VaR 3 VaR 4 5 VaR 6 7 VaR 2

VaR B 1 0 1 VaR 2 VaR 3 VaR 4 5 VaR 6 7 VaR 2 VaR VaR VaR _VaR VaR 0.72 VaR 3 2001 VaR _VaR 180 2000 2 60% VaR VaR 4 VaR VaR VaR VaR VaR VaR 5 VaR 1 VaR VaR(Value at Risk) Prob P