- i -

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 -

VaR VaR VaR VaR VaR - iii -

1.1 1.2 1.3 2.1 2.2 3.1 3.2 4.1 4.2 4.3 ERM 5.1 Delta 5.2 5.3 6.1 6.2 6.3 VaR 7.1 VaR 7.2 VaR 7.3 VaR 7.4 VaR 7.5 VaR - i -

1 2005 VaR VaR 2 1-1 -

Covered Warrant 1 (Equity Warrant) 2 3 3 1 Derivative Warrant synthetic warrant third party warrant - 2 -

VaR VaR VaR VaR - 3 -

1 2 1992-1993 207 12 2005 8 22 JTB1 29 2006 10 30 24 / / 29 28 2-4 -

2005 12 2 2006 42.29 2006-10-30 2 1911 American Light Power 100 2000 1 : 2002 2003 2004 2005 18059 21431 46627 69457 3571 2594 3021 4076 4595 3770 4991 4913 3511 2662 3682 6246 1509 1056 1308 1344 311 545 644 213 4 3 347 530 863 1304 1201 1395 1771 2447 102 272 191 540 3 3 146 455 NA 1 3 72-5 -

http://www.world-exchanges.org 2 ( ) 2002 2003 2004 2005 2117 3679 8608 13641 1385 985 1676 4973 1219 828 455 1313 1323 1224 1620 2069 85 146 214 212 34 65 49 1763 425 1157 2714 5387 8813 138 131 225 399 172 275 500 354 2 1 74 522 0.0 0.9 0.5 3.3 http://www.world-exchanges.org 1 =8.00 GDP - 6 -

- 7 -

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

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 4 5 3 4 5-9 -

2 / - 10 -

- Modiligliani-Miller MM 21 1 1 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 - 11 -

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 - 12 -

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 - 13 -

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 - 14 -

Delta-Gamma-Vega 3 Delta / / / ETF ETF 3 ETF 80% ETF 80% 2-15 -

GARP 4 GARP Generally Accepted Risk Principles(GARP),Cooper s & Lybrand. 5-16 -

- 17 - / Money laundering Outsourcing 6 1 2 6 -------------------- ---------------- ----------------

2 - - - 18 -

Delta VaR 3 ERM Enterprise-wide Risk Management 21-19 -

- 20 -

Delta JTB1 580000 1 2 1 3 BS 0.705 7050 4 0.1% 7 Delta WW =1 0.75 0.5 3 Delta Delta=0 6000 0.8 4000 2000 0 0.4-2000 -4000 0.0 4 WW =1 Delta 7-21 -

1.2 0.8 0.4 0.0 5 WW =0.75 1.2 0.8 0.4 0.0 6 WW =0.5 1.6 1.2 0.8 0.4 0.0-0.4 5 =100% Delta=0 =1 =0.75 =0.5 7050-2240 -2693.09-1354.65-1198.36-811.00-46100 -18614.40-22694.88-19738.34-13837.76 2560 1796.13 1246.72 1070.08 719.36 41300 14125.18 20093.51 17469.90 12307.40-22 -

4810 4356.91 5695.35 5851.64 6239.00 1 100% 1 2 Delta 3 1 300 1550 1500 1/400 120 300 100 10% dp 300 0.000883dt 0.013515dz P = + - 23 -

120 300 BS 0.229 1450 1500 1550 7 300 2000 1800 1600 1400 1200 1 100000000/ 400*100 =2500 2 2500 1500 60000000 55000000 50000000 45000000 40000000 35000000 30000000 25000000 20000000 2290 438.27-811.73-2061.73-36250 -37500-38750 -36250-37500 -38750-36250 1450-24 -

-37500 1500-38750 1550 36688.27 0 0 2728.27 1478.27 228.27-33960 -35210-36460 -33960-35210 -36460 1 A1 A 1 11 1 1 A A2 A3 A1 10.5 12 1 1 A 10 0.15 A1 0.314 A2 A3 A1 0.482 0.119 A1 A2 A3 = A1 -A2/A3 -[max -A1 0 -max -A2/A3 0 ] - 25 -

8 8 0.332 0.195 A3 A2-0.168 10.5 11 12-0.805-26 -

- 27-1 2 1 ( ) 20 ( ), 2

5 5 3 1 30 2 10 30 3 30 3 twbbb 20% - 28 -

20% 20% 50% 4-29 -

( ) 6 1 40 100 2 20% 10 1 3 20% 30% 20% - 30 -

3 2005-31 -

VaR VaR VaR 100% 20% 20% 20% - 32 -

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 - 33 -

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 - 34 -

ARCH GARCH VaR Delta-Gamma VaR Delta-Gamma Delta-Normal 90% Delta-Gamma - 35 -

VaR Delta-Gamma VaR VaR(W) = Z( α) ( σ(p)) + 1/ 2 ( Γ σ(p )) 1 2 VaR(P) Γ VaR(P ) 2 2 2 2 Z( ) P P P P - 36 -

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 8-37 -

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 4 0 5 7 K 4 0.00 5 6 7 8 9 0.40 0.50 0.65 0.75 0.85 10 1.00 2 8 VaR 9 95% 20 99% 100 99.99% 10000-38 -

T 10 99% 1 97.5% 1 97.7% 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 - 39 -

VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR VaR 5 VaR 1 4.63 VaR VaR VaR - 40 -

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% 6.70 7.65 2.20 3.15 VaR -2.20-3.15 248 VaR 95% 99% 10 10 95% 99% - 41 -

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 95% 99% VaR VaR 11 VaR 4 3 2 1 0 99% 95% VaR Jarque-Bera 248 P=0 j =76.5044 cv =5.9915 Jarque-Bera J 248 12-42 -

Ordinary Least Squares Estimates SSE 0.37825036 DFE 624 MSE 0.0006062 Root MSE 0.02462 SBC -2851.1082 AIC -2855.546 Regress R-Square 0.0000 Total R-Square 0.0000 Durbin-Watson 2.0735 Pr < DW 0.8209 Pr > DW 0.1791 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 1 0.0062 0.9371 0.0063 0.9365 2 0.0205 0.9898 0.0132 0.9934 3 0.3593 0.9485 0.3117 0.9578 4 7.7751 0.1002 7.4387 0.1144 5 7.9259 0.1604 7.5752 0.1813 6 8.2488 0.2204 7.8300 0.2508 7 8.5985 0.2828 8.3717 0.3010 8 8.7187 0.3666 8.4250 0.3931 9 8.7188 0.4636 8.5643 0.4784 10 8.7878 0.5524 8.9333 0.5384 11 8.8078 0.6396 8.9333 0.6280 12 9.1683 0.6885 9.6212 0.6492 Standard Approx VaRiable DF Estimate Error t Value Pr > t Intercept 1-0.000995 0.000985-1.01 0.3125 Q LM 1-12 P 0.10 248 VaR VaR 95% 99% 40.87% 53.78% 6.52 7.12-43 -

2.02 2.62 VaR -2.02-2.62 13 % 0.60 0.50 0.40 0.30 0.20 0.10 0.00 VAR 95% VAR 99% VaR 14 VaR VAR 3 2.5 2 1.5 1 0.5 0 VAR(95%) VAR(99%) - 44 -

J P Morgan - 45 -

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1 Don M. Chance 2004 5 2 Charles W. Smithson 2003 9 3 Keith Cuthbertson & Durk Nitzsche, 2004 7 4 www.hkex.com.hk 5VaR 2005 6 Option pricing and replication with transaction costs, Leland, H.E., Journal of Finance, 1985 7 Optimal Hedging of Options with Small but Arbitrary Transaction Cost Structure A.E.Whalley and P.Wilmott, Mathematical Finance, 1999 8 2002.12 9 Michel Crouhy, Dan Galai & Robert Mark 2005 1 10 2001 4 11 2006 3-47 -