CH20

()

1973~(CBOE)

1975

2001.122003.01

22.1 ()(callput)

(Underlying Asset)(Exercise Price/Strike Price)(Maturity/Expiration Date)(European Option & American Option)

()()(Underlying Asset)()() (CBOE) (ASE)(PHLX) (Over-the-Counter Options)

22.2 (exerci sevalue):

36351(36-35)36350(35-36

30$28$22000

29330(2000)()($30$29)2000$2,000$32000$2,000$4000

>

3050 (1) (2)452,000

481.5482.0

(1)15(30000/2000)(2)453159(152000$3)6(15$22000)396 453015(5301000)12

0.60.061625000.65 (1) (2) (3) (4)

(1)$0.65$0.6$0.06$0.01(2)62500$(0.01)$625(3)X$0.6$0.060 X$0.66(4)$0.06($0.65$0.6)$0.01

20.3:Ct StSt =34 Ct =35.00 35341

: 0MAX(0, St -X) & +=

C0S0 X / (1+rf)T>ST - X>ST - X>0

CoxRos sRubins tein1979(binomial option pricing model)

X=$145$120$220$70$C$75$0 C=(1/2)(-) =(1/2)($120-$64.8148) =$27.59268%$64.8148

$220 $70 -70 -70 $150 $0 $75 $0

Su-SdSuCuSdCd$C$S

2 X=$34$35.3$37.7$32.9$C$3.7$0 C=(3.7/4.8)(-) =(0.7708)($35.3-$32.83) =$1.91.2%$32.9/1.002=32.83

$37.7 $32.9 -32.9 -32.9 $ 4.8 $0 $ 3.7 $0

4 2X=$34$35.3$37.7$32.9$C$1.3$0 Cd=(1.3/4.6)(-) =(0.2826)($32.9-$30.64) =$0.63871.2%$30.7/1.002=30.64$40.3$35.3$30.7$6.3CuCd

$35.3 $30.7 -30.7 -30.7 $ 4.6 $0 $ 1.3 $0

St+ X- (rf)+ (T - t)+

CallPut+--++++++-

Black-Scholes( lognormal distribution) d(,nS) (random walk)(stochastic process)

B-S C=SN(d1)-Xe-rt N(d2) C =S =X =r = ()T = ()ln=s =N()=

Black-Scholes Co = Soe-dTN(d1) - Xe-rTN(d2)d1 = [ln (So / X) + (r d + s2 / 2)T] / (s T1/2)d2 = d1 - (s T1/2)

Co = So = N(d) = d

Black-Scholes X = d = e = 2.71828r = T = ln = s =

So = 100X = 95r = .10T = .25 ()s = .50d = 0d1 = [ln(100/95)+(.10-0+(.5 2/2))]/(.5 .251/2) = .43 d2 = .43 - ((.5)( .251/2) = .18

N (.43) = .6664Table 17.2d N(d) .42 .6628 .43.6664 .44.6700

N (.18) = .5714Table 17.2d N(d) .16 .5636 .18.5714 .20.5793

Co = Soe-dTN(d1) - Xe-rTN(d2)Co = 100 X .6664 - 95 e- .10 X .25 X .5714 Co = 13.70

P=Xe-rT [1-N(d2)] - S0e-dT [1-N(d1)]

P = $95e(-.10X.25)(1-.5714) - $100 (1-.6664)P = $6.35

-P = C + PV (X) - So = C + Xe-rT - So

C = 13.70X = 95S = 100r = .10T = .25P = 13.70 + 95 e -.10 X .25 - 100P = 6.35

G&K

G&K

G&K E= US$1.75/S= US$1.78/ T= 6= 0.56US$r= 1.5%6r= 3.9%= 14%

G&KE= US$0.72/A$S= US$0.73/A$T= 3= 0.253US$r= 1.4%3A$r= 4.2%= 15%

Delta010 1Delta0-1-1 0DeltaITM CallDelta0.5OTM CallDelta0.5ITM PutDelta0.5OTM PutDelta0.5

Theta

Theta

RhoRhoRho

PhiPhiPhi

VegaVega

St XSt XS0StStP00X-StS0+P0StX

St XSt XC0St -X0Xe-rTXXC0+Xe-rTStX

P0=S0=C0=X=r=T=P0+S0=C0+Xe-rTBSP=Xe-rtN(-d2)-SN(d1)

1 4

1 4

1. buy Call2. sell Put3. Bull Call Spread4. Bull Put Spread5. Reversals

1.buy Put2.sell Call 3.Bear Call Spread4.Bear Put Spread5.Conversion

1.sell Straddles2.sell Strangles

1.buy Straddles 2.buy Strangles

(long call)

0-0.00450.750.7545

(long put)

(long put)

0Profit($)Loss

8-6 0+0.015 Profit($)Loss

()()()()()()()

(Protective Put)(Covered Call)Bull Spread StrategyBear Spread StrategyStraddle StrategyStrangle Strategy

91553002.651 12

/Put (Put) (Put)

1. buy Call2. sell Put3. Bull Call Spread4. Bull Put Spread5. Reversals

8900 48800(300)48900(260 ) 40(300-260= 40) 890060(100-40) 40 8840Call

Call()7,500 2047,800 48

Bull Put Spread 5,1001705,300260 90(4,500) 90 110 5,2105,100-1703005,300130-70

Put() 7,500 607,700142

Reversals 5,2003405,200210 130(6,500) 5,3305,2003402105,330

1.buy Put2.sell Call 3.Bear Call Spread4.Bear Put Spread5.Conversion

Call 5,1004005,300290 110(5,500) 110 90 5,210

Call()7,500 2047,300 358

5,1001705,300260 90(4,500) 110 90 5,210-90Put

Put Call/ Call (Call) / Call Call Call

Put()7,500 607,300 24

Conversion 5,2003405,200210 130(6,500) 5,3303402105,2005,330

sell Straddles 5,2003405,200210 550(27,500) 550 5,2005504,6505,750 4,6505,7505,2005,7504,650550

(Straddle) 1CallPut ()

127,600 138127,600 95(Straddle) ()

sell Strangles 5,3004005,100260 660(33,000) 660 5,100~53005300510066044405960 59604440596059604440

(Strangle) 1CallPut () Call Put

(Strangle) ()127,500 204127,700 142

(Straddle) 1CallPut ()

(Straddle) ()127,600 138127,600 95

5,2003405,200210 550(27,500) 550 5,2005504,6505,750 4,6505,7505,7504,650

(Strangle) 1CallPut () Call Put

127,400282127,700 142(Strangle) ()

5,3004005,100260 660(33,000) 660 5,100~53005300510066044405960 44405960

3-5 1Call(Put) +2Call(Put) +1Call(Put) ()

127,300(1)358 127,600(2)138 127,900(1)233-5 ()

3-6 1Call(Put) +2Call(Put) +1Call(Put) ()

-0.04:-0.09+0.05=-0.04:1.88+0.04=1.92(1.974-1.92)=0.054

1.301.26-0.032 0+0.011Buy PutSell Put-0.021+0.0191.279:0.032-0.011=0.021:1.3-0.021=1.279(1.3-0.032) 1.26+0.011=0.019

Profit$

Loss 0:1.82+0.0162=1.8362 1.82-0.0162=1.8038:0.0125+0.0037=0.0162

Profit$

Loss 1.821.8362 1.8038 0 0.0162

(long strangle)11

Buy PutBuy Call -$0.050.660.580.740.630.69

+0.030+0.01 0.68 0.790.61+0.040.750.65

Current Exchange Rate110/US$3PSE Strike Premium (Call) US$0.0086/ US$0.00005/ (Put) US$0.0086/ US$0.00048/

(a)CallPut(b)(a)(c)3130/US$

(a) (b) US$0.00812/(=US$0.0086/-US$0.00048/) (c) US$2,673 0.00812-(1/130) 6,250,000 =US$ 2,673

3PSEUS$0.66/CHFUS$0.0126/CHFUS$0.65/CHF3US$0.71/CHF(a)(b)US$0.71/CHF (0.71 0.6726) 62,500 2 = US$4,6750.660.6726

= US$0.70/C$ = US$0.75/C$ = US$0.03 /C$ = US$0.65/C$ = US$0.02 /C$(a)(Long Strangle)(b)0.750.650.02 0.030.800.6

(Long Straddle)US$1.20/US$0.024/US$0.015/(a)US$1.10/US$1.25/US$1.32/(b)(c)1.201.2240.0240.0150.0391.2391.161

= US$1.10/US$0.061/(-0.024+1.2-1.1-0.015)= US$1.25/US$0.011/(1.25-1.2-0.024-0.015)=US$1.32/US$0.081/ (1.32-1.2-0.024-0.015)

US$0.8/SFrPSEUS$0.035/SFrUS$0.75/SFrPSEUS$0.006/SFr(a)?(b)US$0.76/SFr(c)(d) (a) : 0.8 (0.035 0.006) = US$0.771/SFr (b) US$0.76/SFr (0.760.771) 62,500 5 = US$3,437.5 (c) 0.750.771 = US$0.021/SFr

$0.8$0.035$0.75$-0.006$0.765$-0.021$0.8-0.029=.771$0.035-0.006=0.0290.75-0.006-(0.8-0.035)=-0.021:

PSE(A$)US$0.73/A$US$0.016/A$US$0.75/A$US$0.010/A$(a)(b)(c)US$0.76/A$(d)(a)US$0.73/A$US$0.75/A$US$0.76/A$ (0.760.736)(0.760.75)US$0.014/A$

$0.73$-0.016$0.750.0100.01-0.016=-0.0061$0.75+0.01-(0.73+0.016)=0.014$0.76:0.73+0.006=0.7360.75-0.014=0.736

PSE(SFr)US$0.80/SFrUS$0.018/SFrUS$0.76/SFrUS$0.007/SFr(a)(b)(c)US$0.77/SFr(d)

0.800.760.0180.007$0.8-0.018-(0.76-0.007)=0.0290.007-0.018=-0.011:0.76+0.029=0.7890.8-0.011=0.789

*2**3*3*9*10*11*12*13*14*15***************