Chapter 7. Option Greeks
Chapter Seven Option Greeks Multiple Choice 1. Jones and Smith each own 100 shares of ZYX stock (current! sein" for #$0%. Jones writes a &'Y $ ca) whie Smith writes a &'Y 70 ca. *hese are the on! ZYX option positions the two peope ha+e. ,hich of the foowin" statements is most correcta. Jon Jones es has has a hi"her hi"her pos positi ition on deta deta in in ZYX. ZYX. . Smith has a hi"her position deta in ZYX. c. Jon Jones es and Smith Smith ha+e ha+e the same same posit position ion deta deta in in ZYX. d. You You cannot determin determinee which person person has the hi"hest hi"hest position position deta deta in ZYX without more more information aout ZYX stock. '/S,2 3 4. Jones and and Smith each each own 100 shares shares of ZYX stock stock (current (current! ! sein" sein" for #$0%. #$0%. Jones write writess a &'Y $ ca) whie Smith writes a &'Y 70 put. *hese are the on! ZYX option positions the two peope ha+e. ,hich of the foowin" statements is most correcta. Jon Jones es has has a hi"her hi"her pos posit ition ion det detaa in ZYX. ZYX. . Smith has a hi"her position deta in ZYX. c. Jon Jones es and and Smith Smith ha+e ha+e the same same posi positi tion on deta deta in ZYX. ZYX. d. You You cannot determine which which person has the hi"hest position position deta in ZYX without more more information aout ZYX stock. '/S,2 3 5.
Jone Joness and and Smit Smith h each each own 100 100 sha share ress of ZYX ZYX stoc stock k (curr (curren ent t! ! se sein in" " for #$0 #$0%. %. Jon Jones es writes a &'Y $ put) whie Smith writes a &'Y 70 put. *hese are the on! ZYX option positions the two peope ha+e. ,hich of the foowin" statements is most most correcta. Jones has a hi"her position position deta deta in in ZYX. ZYX. . Smith has a hi"her position deta in ZYX. c. Jones and Smith Smith ha+e ha+e the same position position deta deta in ZYX. d. You You cannot determi determine ne which person person has the the hi"hest hi"hest position position deta deta in ZYX without without more more information aout ZYX stock. '/S,2 3
1. 6. ,hich ,hich of the fo foowi owin" n" statem statement entss is truetruea. *heta *heta is posi positi ti+e +e for a a optio option n positi positions ons.. 1. Gamma is awa!s opposite in si"n to theta. 4. eta is is p po ositi+e fo for a ca ca op option po positions. 5. Common stock has a deta of 8ero. '/S,2 3
9:
Chapter 7. Option Greeks . *he i""est sin"e disad+anta"e of writin" puts is a. positi+e "amma. 1. the risk of a stae market. 4. hi"h transaction costs. 5. the risk of a fain" market. '/S,2 $. ,hich of the foowin" proa! has the owest detaa. write in;the;mone! cas 1. write puts 4. u! cas and write cas with a hi"her strikin" price 5. u! out;of;the;mone! puts and write puts with a hi"her strikin" price '/S,2 ' 7. ,hich of the foowin" statements is truea. Stock has a positi+e "amma. 1. *ime +aue can on! increase. 4. *he deta of an in;the;mone! ca increases with time. 5. Stock has a ne"ati+e theta. '/S,2 C :. ,hich of the foowin" strate"ies proa! has the hi"hest detaa. 3u! a ca) write a ca with a hi"her strikin" price. 1. 3u! a ca) write a put. 4. ,rite a ca) write a put. 5. ,rite a ca) u! a put. '/S,2 3 9. ' person e
99
Chapter 7. Option Greeks 11. ,hich of the foowin" statements is true re"ardin" an in;the;mone! ca option) e+er!thin" ese ein" e>uaa. 's time passes its deta wi approach one. . 's time passes its +aue wi approach 8ero. c. 's time passes its theta wi remain constant. d. 's time passes its intrinsic +aue wi decine.
'/S,2 ' 14. eta is the a. theoretica +aue of an option. . e
ua to 8ero. '/S,2 ' 1. ?or a ca option) deta @@@@@ as the strikin" price @@@@@. a. increases) increases . decreases) increases c. increases) approaches the stock price d. decreases) approaches the stock price '/S,2 3 1$. ?or at;the;mone! uropean puts and cas on the same stock) a. the put deta is awa!s ess than the ca deta. . the put deta is awa!s e>ua to the ca deta. c. the put deta is awa!s "reater than the ca deta. d. the put deta is awa!s ess than or e>ua to the ca deta. '/S,2 '
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Chapter 7. Option Greeks 17.
' portfoio contains 10)000 shares of XYZ stockA the portfoio mana"er writes 10 XYZ cas. Bf the ca deta is 0.6) what is the position detaa. 6 . 6 c. 9)6 d. Cannot e determined '/S,2 C
1:.
' portfoio contains 1)000 shares of XYZ stockA the portfoio mana"er u!s 10 XYZ puts. Bf the put deta is 0.440) what is the position detaa. 440 . 7:0 c. 10)440 d. Cannot e determined '/S,2 3
19.
'n '3C JD/ 6) uropean st!e ca has a deta of 0.66A what is the deta of an '3C JD/ 6 puta. 0.66 . 0. c. 0. d. 0.66 '/S,2 C
40.
' of the foowin" wi ower position deta e
True/False 1. Ee"a measures the sensiti+it! of the option premium to chan"es in the anticipated +oatiit! of the under!in" asset. '/S,2 * 4. Ee"a is the most inear of the option pricin" mode deri+ati+es. '/S,2 *
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Chapter 7. Option Greeks
Short Answer/Problem Dse F 5) S F 56) and H F 40 in =roems 1 and 4. 1.
Dsin" the C3O Options Cacuator) prepare a deta tae for 90;da!) 'merican st!e options with strikin" prices of 50) 5) and 5$0. '/S,2
Call Delta Put Delta
4.
Striking Price 355 0.540 − 0.471
350 0.594 − 0.415
360 0.485 − 0.528
epeat =roem 1 for uropean e
'/S,2
Call Delta Put Delta
Striking Price 355 0.538 − 0.462
350 0.594 − 0.406
360 0.482 − 0.518
5. ?i in the anks with the appropriate etter2
=ositi+e deta) positi+e "amma =ositi+e deta) ne"ati+e "amma /e"ati+e deta) positi+e "amma /e"ati+e deta) ne"ati+e "amma
6.
'/S,2
B
a% on" put
C
% on" ca
A
c% short put
D
d% short ca
Suppose !ou u! 4 90;da! 50 ca contracts and write 4 90;da! 5$0 ca contracts. ,hat is !our a. position deta . position "ammac. position theta-
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Chapter 7. Option Greeks '/S,S2 a.
Position delta:
350 Calls: 25 x 100 x 0.594 = 1,485.0 360 Calls: − 25 x 100 x 0.485 = − 1,212.5 272.5 b. Position gamma: (sing t!e C"#$ o%tions &al&lato' 350 Calls: 25 x 100 x 0.011 = 27.5 360 Calls: − 25 x 100 x 0.011 = − 27.5 0 &. Position t!eta: (sing t!e C"#$ o%tions &al&lato' 350 Calls: 25 x 100 x ( − 0.092 = − 230 360 Calls: − 25 x 100 x ( −0 .092 = 230 0
.
'fter 1 da!s) the stock price has increased ! 5. position statistics. a. =osition deta . =osition "amma c. =osition theta )e* de'i+ati+es2
'/S,S2 a.
O ption 350 &all
Delta 0.709
Gamma 0.01
360 &all
0.599
0.011
Theta − 0.093 − 0.103
Position delta:
350 Calls: 25 x 100 x 0.709 = 360 Calls: 25 x 100 x 0.599 =
1,772.5 − 1,497.5 275 b. Position gamma: (sing t!e C"#$ o%tions &al&lato' 350 Calls: 25 x 100 x 0.010 = 25.0 360 Calls: 25 x 100 x 0.011 = − 27.5 − 2.5 &. Position t!eta: (sing t!e C"#$ o%tions &al&lato' 350 Calls: 25 x 100 x (0.093 = − 232.5 360 Calls: 25 x 100 x (0.103 = 257.5 105
Dpdate the foowin"
Chapter 7. Option Greeks 25 $. Suppose someone owns )000 shares of a #$0 stock. *he! aso ha+e written 4 of the #70 cas) 4 of the #$ cas) and ha+e purchased 7 of the #$0 puts.
,rite a para"raph aout the %osition 'is- . *hat is) euences of a ar"e market mo+ement up or down. '/S,2 / t!e ma'-et de&lines sbstantiall, t!e &alls go to e'o, *!i&! is o-a. !e sto&- is %'ote&ted b t!e %ts, %ls t!e'e a'e an additional 25 long %t &ont'a&ts. !is %o't/olio *old bene/it sbstantiall /'om a la'ge de&line in t!e sto&- %'i&e. / t!e ma'-et ad+an&es, t!e sto&- *ill be &alled a*a and t!e %ts *ill ex%i'e *o't!less. !e'e *ill not be a disast'os loss, bt t!e'e *ill be no %'o/it eit!e'.
7.
Suppose !ou wanted to spend #40)000 on a deta neutra 5 stradde with 90; da! options. (See the initia conditions ao+e.% 3ased on 3ack;Schoes +aues) how man! put and ca contracts woud !ou u!'/S,2 !e t!eo'eti&al &all and %t +ales a'e 14.84 and 13.46, 'es%e&ti+el. 1 2 3 4 5 6
.540C .471P = 0 14.874 13.46P = 20,000 /'om 1, C = 0.8722P sbstitte 3 into 2 14.84(.8722P 13.46P = 20000 P = 757.48 bstitte 5 into 1, C = 660.67
onding to *!ole &ont'a&ts, P = an! C = 7. !is o+e's!oots t!e 20,000 ma'- some*!at, so it ma be bette' to 'ond one o' bot! &ont'a&ts do*n.
:.
Bn =roem 7) suppose that after two da!s the stock has risen 7I:. as the position deta increased) decreased) or remained the same'/S,2 'ising nde'ling sto&- %'i&e *ill &ase bot! t!e %t and t!e &all delta to in&'ease. (!e %assage o/ time *ill !a+e a modest e//e&t o/ delta, bt t!e sto&- &!ange *ill o+e'*!elm t!e time e//e&t. !e %osition delta *ill in&'ease.
9.
' portfoio contains 14 contracts of XYZ JD/ 0 ca options (uropean st!e%) which se for #5 and ha+e a deta of 0.40. ow &an! JD/ 0 put contracts (sein" for #4% must !ou u! to e appro
Chapter 7. Option Greeks
10.
' portfoio contains 4)00 shares of '3C common stock. You cacuate the foowin" information2 Option JDK 60 ca JDK 5 put
Price 1 5I6 7I:
Delta 0.56 ;0.514
Theta 0.05 0.04
You decide to write the JDK 60 cas and u! the JDK 5 puts so as to e appro
− .534C − .312P 2500 = 0 1.75C − .875P = 0 1.75C = .875P C = 0.5P
− .534P (.5P − .312P 2500 = 0 − .579P = − 2500 P = 4317.79 C = 2158.89 P
11.
= $3 contract# an! C = 22 contract#
'nother portfoio contains 14)000 shares of '3C stock. ow man! JDK 60 ca contracts must the portfoio mana"er write to remo+e haf of the market risk of '3C stock'/S,2 o need to 'emo+e 6,000 deltas. 6000.534 = 11,236
14.
""2 contract#
?i in the tae with L) ;) 0) or inconcusi+e2 Delta
Bu !"" shares Bu !"" shares# write ! call Bu !"" shares# write ! put $rite ! call# write ! put Bu !"" shares# bu ! put 10
Gamma
Theta
Chapter 7. Option Greeks
'/S,2
Bu !"" shares Bu !"" shares# write ! call Bu !"" shares# write ! put $rite ! call# write ! put Bu !"" shares# bu ! put
Delta
Gamma 0
Theta 0
n&on&lsi+e
15. ' J'/ :0 XYZ uropean ca has a deta of 0.0 and a "amma of 0.01:0. ,hat are a% the position deta) and % the position "amma of a on" stradde composed of one ca contract and one put contract- (/o information is missin" from this proem.% '/S,S2 a. 100 x 0.550 = 55.0 100 x (.550 1 = − 45.0 "0.0 b. 100 x 0.0180 = 1.80 100 x 0.0180 = 1.80 3.60
16. ' 5;month ca has a deta of 0.6. ,hat is the appro
Chapter 7. Option Greeks b. t de&lines. &. )o &!ange
1$. You hear someone sa!) M,e do not write unco+ered options) so our "amma is awa!s positi+e.N uite conser+ati+e whie the other is >uite specuati+e. &ake up an e
gamma <0, delta 0 !is is &onse'+ati+e.
1:. State whether the foowin" statement is true or fase) and e
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