CU HI N TP MN QUN TR RI RO TI CHNHCHNG 1: NHP MN QUN TR RI RO TI CHNH1. Chng minh cc cng thc chuyn i cc li sut.2. Chng minh cc cng thc quy i li sut theo thi gian.3. Nh u t mua c phiu A vo u nm vi gi mua l 30.000; trong nm nhn c tc 1000; cui nm gi l 40.000. Tnh li sut?4. Nh u t mua c phiu A vo u 1/ 2011 vi gi mua l 30.000; trong thng 1/2011 nhn c tc 1000; cui thng gi l 40.000. Tnh li sut sau 1 thng nm gi? Tnh li sut nm?5. Nh u mua c phiu A vo u 1/2011 vi gi mua l 30.000; trong thng 4/2011 nhn c tc 1000; cui thng 4 gi 40.000. Tnh li sut sau 4 thng nm gi? Tnh li sut nm?6. Mt khon tit kim c li sut 12%/ nm, li theo thng. Tnh li lin tc?7. Ngn hng Techcombank thng bo mc li sut tit kim k hn 3 thng l 14%/ nm. Tnh li gp theo nm v li sut lin tc theo nm?8. Mt tri phiu vi thgian cn li l 2 nm, mnh gi 100 USD. Li coupon 6%/ nm. Tr 6 thng 1 ln. nh gi tri phiu bit li sut th trng:Thi hnLi sut th trng (lin tc)

0.51.01.52.05.05.86.46.8

9. Cng thc Fisher?10. Qua thng k s liu trong qu kh, thy rng li sut ca c phiu PNC t 30% vo nhng thng c thi tit p, 20% vo nhng thng bnh thng, -5% vo nhng thng c thi tit m m. Theo cc kh tng thy vn, xc sut v thi tit p, bnh thng, xu ca nm l 30%, 30%, 40%. D bo v li sut c phiu ny.11. Tnh lch chun ca 1 danh mc u t 2 ti sn c phng sai 30% v 50% vi t trng u t tng ng l 70% vo ti sn 1 v phn cn li vo TS 2. H s tng quan l 0.812. Tnh li sut ca 1 danh mc u t gia ti sn ko c ri ro c li sut 7% nm v ti sn c ri ro c li sut 10% nm. lch chun ca ti sn c ri ro l 20%, lch chun danh mc l 15%.13. Xc nh li sut k vng v ri ro d n sau:K u tLi sut

123411.5-5.32010

14. Tnh li sut k vng v ri ro cc khon u t sau:Li sutKh nng t c li sut

-10%0%5%20%10%25%40%25%

15. Hai c phiu A v B c li sut d bo nh sau:Tnh trng kinh tXc sutLi sut ALi sut B

Suy thoiBnh thngKhHng thnh20%40%30%10%-5%10%-4%7%6%-2%8%-9%

a. Li sut k vng 2 c phiub. Ri ro 2 c phiuc. Hip phng sai?d. Tnh t sut sinh li k vng v ri ro ca danh mc gm 2 cp trn bit 75% t l u t vo A.e. Mi quan h gia t l u t 2 cp t c mc sinh li cao nht vi ri ro thp nht.16. Mt ngn hng cho li sut 14% nm, tr theo qu. Tnh li lin tc v li thc theo nm?17. Mt nh u t nhn c 1100 usd trong 1 nm vi s tin u t ban u 1000 usd. Quy i ra li sut lin tc?18. Tnh li sut lin tc nm cho 1 khon tn dng c li sut 15% nm tr theo thng.19. Mt khon tit kim c li sut lin tc l 12% nm tr theo qu. Tnh li thu c tr hng qu cho khon tit kim 10.000 usd?20. Mt nh u t mua c phiu c gi 68.500 vnd vo 1/7/10. Cui nm nhn c mt khon c tc 1000 vnd/cp. Gi s nh u t bn c phiu ny vo cui nm vi gi 69.000 vnd. Tnh li sut cho 6 thng nm gi? Quy i ra nm? Quy i ra lin tc.21. Tnh t sut sinh li k vng bnh qun v ri ro ca cc c phiu v mc bnh qun trn HOSE trong 1 nm.22. Gi s li sut lin tc k hn 6 thng, 12 thng, 18 thng, 24 thng v 30 thng l 4%, 4.2%, 4.4%, 4.6%, 4.8% nm. Hy tnh gi tr hin ti tri phiu k hn 30 thng mnh gi 100 usd coupon 4% nm, tr 2 ln/ nm.23. Mt tri phiu coupon mnh gi 100 usd k hn 3 nm tr li 8% nm, 2 ln/ nm. Gi s lu sut lin tc k hn 6 thng, 12 thng, 18 thng, 24 thng, 30 thng, 36 thng tng ng l 6%, 6.2%, 6.4%, 6.6%, 6.8%, 7% nm. nh gi tri phiu.24. Li nhun cc v th trong hp ng k hn/ tng lai? V th.25. Ai c quyn la chn thi im giao hng, a im v hng ha c th (nu c nhiu s la chn) trong giao dch tng lai?26. Hp ng tng lai c pht sinh ri ro thanh ton khng?27. Giao dch tng lai k qu ntn? Tc dng k qu?28. Mt nh u t k 1 v th bn k hn 1 nm vi ti sn gi 60 usd khi gi giao ngay l 58 usd. Sau 1 nm gi giao ngay tng ln 63 usd. Li l ra sao?29. Mt cng ty k tng lai mua 1000 v hng ha vi gi 20 usd/ v. Khon k qu ban u 6000 usd, duy tr 4000 usd. Gi tng lai l bao nhiu th cty c php rt 2000 usd?30. Mt v th bn tng lai 50 000 pound bng vi gi 70 cents/pound. K qu ban u 4000 usd, duy tr 3000 usd. Gi tng lai l bao nhiu th cty nhn margin call?31. Li nhun giao dch quyn chn? V th. Ai l ngi k qu? Phn bit quyn chn M v chu u.32. S dng quyn chn trong giao dch bn khng ntn? V th.33. Mt nh u t mua 100 qcm kiu u vi gi thc hin 20 usd, k hn 1 nm. Gi quyn 2 usd. Gi ti sn c s tng ln 25 usd sau 1 nm. Nh u t li l bn?34. Nh u t bn 100 qcb u vi gi thc hin 50 usd, k hn 6 thng. Gi quyn 4 usd. Gi ti sn c s 41 usd sau 6 thng. Li l?35. Mt nh u t c 2000 usd u t. D bo gi cp A s tng trong 2 thng ti. Gi hin ti ca cp l 20 usd. Gi ca 1 qcm tring 2 thng ti vi gi thc hin 22.5 usd l 1 usd. Chin lc u t? Tnh li sut tng chin lc khi gi cp sau 2 thng l 27 usd, 18 usd? Gi cp sau 2 thng l bao nhiu 2 chin lc c li sut bng nhau?36. Mt nh u t bn k hn 100 000 gbp ly usd vi t gi 1 gbp = 1.9 usd. Xc nh li nhun nh u t vo ngy o hn, nu t gi l:a. 1 gbp = 1.8900 usd.b. 1 gbp = 1.9200 usd.37. Mt nh u c mun hng li t d bo v s tng gi c phiu. gi hin ti ca c phiu l 29 usd, mt hp ng quyn chn mua cp c gi thc hin l 30 usd, ph quyn 2.9 usd. Nh u t c 5800 usd u t. Xc nh thu nhp 2 chin lc: t vo cp t vo gi qcmKhi gi cp tng ln 35 usd, gim xung 25 usd.38. Mt qcm vi gi thc hin 50 usd, ph quyn 2.5 usd o hn vo thng 11. V th li nhun?39. Gi vng giao ngay l 1000 usd. Gi k hn 1 nm l 1100 usd. Li sut tin gi usd thi hn 1 nm l 5% nm lin tc. Gi s ko pht sinh thu nhp hay chi ph t vic nm gi vng. C hi arbitrage?40. 1 doanh nghip vit nam cn thanh ton 1 triu usd sau 6 thng na. Gii thch chin lc phng nga ri ro t gi bng:a. K hnb. Tng laic. Quyn chn41. V th m t li nhun 1 danh mc gm Mua k hn Mua qcb u cng ti sn, cng ngy o hn.Bit gi quyn bng gi k hn vo ngy k kt hp ng.42. Gi du 70 usd/ thng. Gi tng lai 1 nm ca du l 80 usd/ thng. Li sut usd k hn 1 nm l 5% nm. Chi ph bo qun lin quan n vic nm gi du l 2% nm. C hi arbitrage?43. Gi du 70 usd/ thng. Gi tng lai 1 nm ca du l 65 usd/ thng. Li sut usd k hn 1 nm l 5% nm. Chi ph bo qun lin quan n vic nm gi du l 2% nm. C hi arbitrage?44. Gi vng giao ngay 1600 usd/oz. Gi k hn 1 nm 1800 usd/oz. Li sut 10% nm. Gi s chi ph bo qun vng l 0, vng ko sinh li. C hi arbitrage?45. (1-18) Mt doanh nghip d tnh tr 1 triu cad trong 6 thng na. Phng nga ri ro t gi ntn nu s dng K hn Quyn chn46. (1-21) Quyn chn v tng lai l tr chi c tng bng 0. ng hay sai?47. (1-23) 1 cty m pht trin mt sn phm l index currency option notes ICONs. y l nhng tri phiu trong lng tin c nhn bi ngi nm gi ti cc k hn khc nhau vi t gi ngoi t. V d n giao dch vi cty nht bn. Icons xc nh rng nu t gi ln hn 169 /$ lc o hn ngi nm gi tri phiu s nhn c 1000$. Nu nh hn ngi nm gi nhn c s tin l: 1000 max [0; 1000(169/ST -1) ]Khi t gi di 84.5 nh u t ko nhn c g c.Chng minh rng ICON = 1 tri phiu + 2 quyn chn.48. (1-24) Vo 1/7/11 mua k hn 1 triu yn nht vo 1/1/12. Vo 1/9/11 bn k hn 1 triu yn nht vo 1/1/2012. M t thu nhp t chin lc ny?49. (1-25) Gi s t gi usd/gbp nh sauGiao ngayK hn 90 ngyK hn 180 ngy1.45801.45561.4518

C hi arbitrage nu: Qcm u 180 ngy mua 1 cho 1.42$ vi ph 2 cents. Qcb u 90 ngy bn 1 cho1.49$ vi ph 2 cents.50. Trader A mua k hn vng 1000$/ounce trong 1 nm. Trader B mua qcm vng 1000$/ounce trong 1 nm. Ph quyn 100$/ounce. S khc bit gia 2 v th ny? Chng minh rng li nhun/ounce l mt hm s bin l gi vng 1 nm cho c 2 traders.51. Cty m d nh tr 3 triu euro trong 3 thng ti. T gi hin ti l 1.4500 usd/eur. S dng k hn v quyn chn th no hedge?52. Vo 15/7/10, mt nh u t s hu 100 cp. Gi cp khong 497$ v 1 qcb vo thng 12 vi gi thc hin l 460$ vi ph l 27.3 usd. C 2 chin lc phng v: Mua 1 qcb Bn 100 cp ngay khi gi t 460$.So snh 2 chin lc?53. C mt tri phiu nh sau: Nh u t ko nhn li. Ti thi im o hn s nhn 1000$ cng thm s tin da vo gi du ti thi im . Lng thm ny bng vi 170 + gi mi barrel du vt mc lc o hn trn 25$. Lng tng thm ny ti a l 2550$ (gi du lc ny l 40/barrel).Chng minh rng tri phiu ny = 1 tri phiu thng + long call vi K = 25 + short call vi K = 4054. Gim c ch th bn s dng quyn chn satisfy him nh sau: Hin c 1 triu bng bn trong 6 thng ti. Nu t gi nh hn 1.41 th ti mun bn cho ti 1.41 Nu ln hn 1.47 th ti chp nhn 1.47 Nu nm gia 2 cc trn ti s bn gbp ti gi giao ngay.Bn s dng chin lc ntn?55. Mt nh u t long call u v short put u vi cng ti sn c s, cng K, v cng k hn. Khi no th gi qcm bng vi gi qcb?56. LIBOR l g, LIBID l g? Ci no cao hn?57. (4-5) Li sut lin tc nh sauK hnLi sut nm

36912151888.28.48.58.68.7

Tnh li sut k hn cho qu th 2, 3 4,5,6.58. (4-7) gi s ng cong li sut i ln. Sp xp cc loi li sut sau: Li sut 5 nm Li sut tri phiu coupon 5 nm Li sut k hn giai on gia 4.75 v 5 nm.59. (4-6) nh gi hp ng li sut k hn nu nh u t kim c 9.5% cho giai on 3 thng bt u trong 1 nm vi vn gc l 1 triu usd. Li sut ghp li theo qu.60. (4-15) nh gi FRA trong tr 5% theo nm cho nm th 3 trn 1 triu usd. Bit:K hn (nm)Li sut nm

123452.03.03.74.24.5

61. (4-16) 1 tri phiu coupon 8% k hn 10 nm bn vi gi 90usd. 1 tri phiu coupon 4% k hn 10 nm bn vi gi 80usd. Hi li sut 10 nm?62. (4-23) Tri phiu chnh ph k hn 6 thng v 1 nm hin bn vi gi 94usd v 89 usd. 1 tri phiu k hn 1.5 nm coupon 4usd/6 thng bn 94.84usd. 1 tri phiu k hn 2 nm coupon 5usd/6 thng bn 97.12usd. Tnh li sut 6 thng, 1 nm, 1.5 nm v 2 nm.

CHNG 2: HP NG TNG LAI V HP NG K HN1. So snh hp ng tng lai v hp ng k hn2. Thot khi v th trong giao dch tng lai ntn? V sao phi lm nh vy?3. V sao gi tng lai tim cn gi giao ngay trong ngy giao hng?4. Khi mt giao dch c thc hin, open interest s chu nh hng ntn?5. Khi lng giao dch trong 1 ngy c th ln hn open interest ko?6. Basis risk l g? Basis risk quan h th no vo ngy o hn? Ti sao lun tn ti basis risk?7. Basis risk nh hng ntn n phng v bn v phng v mua?8. Vo ngy 1 thng 3, gi giao ngay l 20 USD, gi tng lai thng 7 l 19 usd. Vo ngy 1 thng 6, gi giao ngay l 24, gi tng lai thng 7 l 23.4 usd. Cty k hp ng vo 1/3 nhm phng v cho mt hp ng mua hng trn th trng giao ngay vo thng 6. Cty ng v th tng lai vo 1/6. Tnh gi thc cht (effective price) m cty phi tr c hng ha trn?9. Vo ngy 1/3, gi giao ngay l 300, gi tng lai thng 12 l 315 usd. Vo 1/11, gi giao ngay l 280, gi tng lai thng 12 l 281. Mt nh sx k mt v th tng lai giao hng thng 12 nhm phng v cho 1 h bn hh vo 1/11. Tnh gi thc cht?10. Nhm phng v, cn la chn hp ng ntn?11. Mt cty m d kin nhn 50 triu jpy vo thng 7. Hp ng tng lai jpy trn cme c thng giao hng l 3,6,9,12. Chin lc short hedge vo thng no?12. T l phng v l g? Cng thc tnh? S lng hp ng ti u? Chng minh cng thc t l phng v ti u.13. Mt hng hng ko mun mua 2 triu gallon xng nh dng trong my bay trong vng 1 thng ti v nh s dng hp ng tng lai du th phng nga ri ro. Hp ng tng lai du th trn th trng c 42000 gallons du th. Tnh s hp ng cn mua? BitThng Thay i trong gi tng lai duThay i trong gi giao ngay xng

1234567891011121314150.0210.035-0.0460.0010.044-0.029-0.026-0.0290.048-0.006-0.036-0.0110.019-0.0270.0290.0290.020-0.0440.0080.026-0.019-0.010-0.0070.0430.011-0.036-0.0180.009-0.0320.023

14. lch chun gi giao ngay l 0.65; lch chun gi tng lai l 0.81. H s tng quan l 0.8. T l phng v?15. lch chun gi giao ngay l 1.2; gi tng lai l 1.4. H s tng quan l 0.7. 1 nh sx cn mua 200000 pound gia sc sng trong thng ti. Cn mua bao nhiu hp ng bit khi lng 1 hp ng tng lai l 40000 pound.16. Gi tr mt danh mc l 5050 000 usd. H s beta ca danh mc 1.5. Ch s hin ti 1000. Gi tng lai 1010. S lng ch s / hp ng l 250. Li sut phi ri ro 4%/ nm. T l chi tr c tc 1%/ nm. Tnh s lng hp ng cn thit phng nga ri ro danh mc ny? Sau 3 thng, gi tr ch s gim xung 900, gi tng lai gim xung 902. Tnh gi tr ton b danh mc gm v th trn th trng tng lai v gi tr danh mc u t ban u?Nu mun gim gi tr beta danh mc xung cn 0.75 nh u t cn s dng hp ng ntn?Nu mun tng ln 2 th sao?17. Ngy 1/7 nh u t nm gi 50000 c phiu. Gi th trng l 30. Nh u t d kin phng v trong thng ti v quyt nh s dng hp ng tng lai ch s s&p500, giao hng thng 9. Gi tng lai ch s l 1500, 1 hp ng c gi tr bng 50 ln ch s. H s beta l 1.3. Nh u t cn lm ntn?18. (3-7) Mt qu u t c danh mc c phiu tr gi 50 triu usd, beta 0.87 v c nh s dng tng lai ch s 3 thng phng nga 2 thng ti. Ch s hin ti l 1250, gi tr gp 250 ln. Li sut phi ri ro 6%/ nm, t l c tc 3%/ nm. Gi tng lai l 1259. Nn mua hay bn? Bao nhiu hp ng? Gi s sau 2 thng, ch s gim cn 1000, gi tng lai gim cn 1002.5. Tnh gi tr tng th ca danh mc gm danh mc c phiu v v th hp ng tng lai.19. Gi nh trong xc nh gi tng lai?20. Chng minh cng thc F0 = S0erT.Mt c phiu c gi 40, ko c tc trong 3 thng ti. Li sut tri phiu phi ri ro k hn 3 thng l 5%/ nm. Gi k hn l 39. C tn ti arbitrage ko? Nu gi k hn l 43 th sao?21. Chng minh rng: F0 = (S0 I)erT.Gi tri phiu hin ti 900, tr li coupon 40 sau 4 thng. Li sut phi ri ro lin tc 4 thng v 9 thng l 3% v 4%/ nm. Gi k hn 9 thng l 910 usd. C hi arbitrage? Nu gi k hn 870 th sao?22. Xem xt mt hp ng k hn 10 thng, gi c phiu l 50. Li sut phi ri ro lin tc mi k hn l 8%/ nm. C phiu mang li c tc 0.75 usd sau 3 thng, 6 thng. 9 thng. Tnh gi hp ng k hn?23. Chng minh: F0 = S0e(r-q)T.Mt hp ng k hn 6 thng c ti sn c s mang li li tc 2% trn ti sn trong khong thgian 6 thng. Li sut phi ri ro lin tc l 10%/ nm. Ti sn hin c gi 25. Gi k hn 30. C hi arbitrage?24. Mt hp ng k hn c phiu va k, o hn sau 6 thng. C phiu ko tr c tc trong lc ny. Hin gi 30, li sut phi ri ro lin tc 12%/ nm. Xc nh gi k hn?25. Mt hp ng k hn c phiu va k, o hn sau 6 thng, d kin tr 1 usd c tc 1 ln vo 3 thng sau. Hin gi l 50 usd. Li sut phi ri ro lin tc l 10% / nm. C hi arbitrage nu: Gi k hn 49 Gi k hn 5326. Mt c phiu c hin gi 350. Li sut phi ri ro lin tc 12% nm. C tc 4% nm lin tc. nu gi k hn l 360 th c hi arbitrage ntn?27. Gi tr hp ng k hn cho v th mua? V th bn? Chng minh?28. Mt v th mua k hn c phiu ko tr c tc c k trc v hin cn 6 thng l o hn. Li sut phi ri ro lin tc l 10% nm. Gi c phiu l 25, gi giao hng trong hp ng l 24. Tnh gi tr hp ng ny hin nay.29. S khc bit ca gi tr hp ng k hn v tng lai?30. Khi no th gi tng lai v gi k hn bng nhau?31. Arbitrage cho hp ng tng lai ch s chng khon ntn?32. Chng minh cng thc ngang gi li sut. Arbitrage ntn?33. Li sut k hn 2 nm ti c v m l 5% v 7%. T gi aud/usd giao ngay l 0.6200. Xc nh t gi k hn 2 nm ca 2 ng tin trn? Nu t gi k hn 2 nm l 0.6300 th chuyn g xy ra?34. Mt hp ng tng lai k hn 1 nm mt ti sn u t ko mang thu nhp. Ti sn tn 2 usd/ n v lu kho. Ph lu kho thanh ton vo cui nm. Gi giao ngay l 450. Li sut phi ri ro 7% nm mi k hn. Tnh gi tng lai?35. Chng minh rng: F0 (S0 + U)erT v F0 S0e(r+u)T nu ti sn c s l hng ha tiu dng. Li sut tin li nh hng ntn?36. Hin tng normal backwardation v contango l g?37. Mt ch s c phiu c gi tr hin ti l 350. Li sut phi ri ro lin tc l 12% nm. C tc ch s 4% nm. Xc nh gi tng lai k hn 4 thng?38. Li sut phi ri ro lin tc l 7% nm. T l c tc l 3.2% nm. Gi hin ti ch s l 150. Tnh gi tng lai k hn 6 thng.39. (5-11) Li sut phi ri ro lin tc l 9% nm. Ch s c phiu c c tc chi tr trong sut nm nh sau: thng 2,5,8,11 tr 5% nm, cn li 2% nm. Gi tr ch s vo 31/7 l 1300. Tnh gi tng lai o hn vo 31/12 cng nm.40. Mt v th mua k hn mt c phiu thi hn 1 nm. C phiu c gi hin ti 40 v ko tr c tc. Li sut phi ri ro lin tc l 10% nm.Tnh gi k hn? tnh gi tr ban u?6 thng sau, gi c phiu tng ln 45. Li sut phi ri ro ko i. Tnh gi k hn mi, gi tr hp ng mi?41. Mt c phiu c k vng tr c tc 1 usd sau 2 thng, 5 thng. Gi tr hin ti c phiu l 50. Li sut phi ri ro lin tc mi k hn l 8% nm. Mt nh u t va bn k hn 6 thng.Tnh gi k hn v gi tr ban u?3 thng sau, gi c phiu gim xung 48. Li sut ko i. Tnh gi k hn v v th bn?42. (5-12) Li sut phi ri ro lin tc 10% nm, ch s c phiu tr c tc 4% nm. Gi tr hin ti l 400. Gi tng lai 4 thng l 405. Arbitrage?43. (5-14) Li sut k hn 2 thng lin tc ti thy s v m l 2% v 5% nm. Gi giao ngay CHF l 0.8000 usd. Gi tng lai k hn 2 thng l 0.81000 usd. Arbitrage?44. (5-15) Gi giao ngay ca bc l 9 usd/oz. Chi ph lu kho l 0.24 usd nm, tr trc theo tng qu. Li sut phi ri ro lin tc mi k hn l 10% nm. Tnh gi tng lai 9 thng sau. Nu gi ny l 13 th arbitrage ntn?45. Bn k hn thng 7 bc c gi 17.2/ounce. Size l 5000 ounces. K qu ban u l 4000, duy tr 3000. Gi tng lai thay i th no s c margin call?46. Thng 9 nm 2012 mt cty k mua tng lai thng 5 nm 2013 du th. Gi tng lai l 68.3 mi barrel, khi thot khi v th vo thng 3 nm 2013 th gi tng lai l 70.5 v 69.10 lc cui thng 12 nm 2012. Size l 1000 barrels. Tng li nhun cty? Khi no c hin thc ha? Li nhun s b nh thu ntn nu l 1 nh phng v? 1 nh u c.47. Lnh dng bn 2$ l g? Khi no s dng lnh ny? Lnh gii hn bn 2$ l g? Khi no s dng?48. V th bn tng lai thng c quyn chn thi gian, a im giao hng, loi ti sn, vn vn. Nhng quyn ny c lm tng hay gim gi tng lai khng? Ti sao?49. 1 trader mua 2 tng lai thng 7 ti sn l nc p cam. Mi hp ng l 15000 pounds. Gi tng lai hin ti l 160 cents mi pound, k qu ban u l 6000 mi hp ng, duy tr l 4500 mi hp ng. Gi thay i ntn b margin call? Trng hp no c php rt 2000?50. Chng minh rng: nu gi tng lai hng ha > gi giao ngay trong sut thi hn giao hng, s c c hi arbtrage. Nu n nh hn th c arbitrage ko?51. Phn bit lnh th trng v lnh dng.52. Phn bit lnh gii hn dng bn 20.30 v lnh gii hn 20.10 53. Vo cui 1 ngy giao dch, 1 thnh vin ca trung tm thanh ton b tr mua 100 hp ng, v gi iu chnh l 50000 mi hp ng. K qu ban u l 2000 mi hp ng. Vo ngy tip theo, thnh vin ny mua thm 20 hp ng na, vi gi l 51000. Gi iu chnh cui ny ny l 50200. Thnh vin ny s phi thm bao nhiu vo ti khon ca mnh?54. Gi k hn CHF l 1.1000; gi tng lai l 0.9000. Gii thch?55. u c thc cht l 1 canh bc, chnh ph nn cm loi hnh ny. Nu quan im?56. Ti sao open interest thng gim vo thng trc thng giao hng? Hin ti c 2000 giao dch. C 1400 v th mua thot khi v th, 1200 v th bn thot khi v th. Open interest thay i ntn?57. V th no = long forward mua ti sn ti K + short put ti sn ny ti K vo cng 1 thi im.58. Perfect hedge l g? So vi imperfect hedge, perfect hedge lun dn ti 1 dng tin tt hn hay ko?59. Trng hp no ca phng sai nh nht dn n ko cn phng v na?60. Ti sao th qu cng ty thng khng phng v ri ro?61. 1 cty nht bn d nh s xut khu dng in vo m. Nu l th qu cty ny, bn s thit k chin lc phng v ri ro t gi th no? Khi trnh d n ln gim c, bn s l lun th no thc hin chin lc ny?62. Nu phng sai nh nht = 1, l perfect hedge. ng hay sai?63. Nu ko c basis risk, phng sai nh nht lun bng 1. ng hay sai?64. i vi ti sn m gi tng lai < gi giao ngay, long hedge s thu ht hn. Ti sao?65. Mt nng dn l lun rng: ti ko cn s dng tng lai phng v. Ri ro thc s ca ti l khng phi gi bp, m l c v ma c th b thi bay bi cn bo. Theo bn, ngi nng dn c nn d on s bp k vng v phng v n lock in gi ko?66. Kh c th bit gi tng lai du, v c 50% gi nh hn gi giao ngay, 50% gi ln hn gi giao ngay. Tho lun?67. Mt cty mun phng v ri ro cho 1 loi nguyn liu mi m s thay i gi ca n tng quan 0.6 vi s thay i gi tng lai xng. Cty ny s mt 1 triu usd cho mi s tng 1 cent v gi mi gallon ca nguyn liu ny vo 3 thng ti. lch chun ca nguyn liu ny ln hn 50% so vi xng. H s phng v l bao nhiu? Chin lc? Mi hp ng l 42000 gallon th s hp ng cn c l bao nhiu?68. Beta mt danh mc c duy tr mc 0.2. Trong sut nm va ri, li sut phi ri ro l 5% v ti sn vn c mc li sut l -30%. Nh u t nhn c li sut -10% v c nhn nh l mt chin lc u t xut sc. Nhn xt v nhn nh ny.69. Mt qu u t c 1 danh mc tr gi 50 triu usd vi beta l 0.87. Qu ny s dng tng lai 3 thng ch s phng v trong 2 thng ti. Hin ti ch s l 1250, mt hp ng gp 250 ln ch s. Li sut phi ri ro l 6% nm, t l c tc l 3% nm. Gi tng lai 3 thng l 1259.Qu u t s thit k chin lc ca mnh ra sao?Tnh nh hng chin lc ln ti thu nhp ca qu nu ch s 2 thng ti l 1000; 1100; 1200; 1300; 1400 v gi tng lai cao hn mc ch s l 0,25%.70. (5-8) Gi tng lai ch s chng khon s nh hn hay ln hn gi tr tng lai k vng ca ch s? Ti sao?71. (5-16) C 2 hp ng tng lai cng hng ha khc nhau v k hn, t2 > t1. Chng minh rng: F2 F1er(t2-t1). Gi nh khng c chi ph lu kho.72. (5-17) Trong trng hp di y, cng ty nn phng v bng k hn hay tng lai:a. Gi tr ngoi t gim.b. Gi tr ngoi t tngc. Gi tr ngoi t tng ri gim.d. Gi tr ngoi t gim ri tng.73. (5-18) Trong trng hp no th t gi k hn l c lng khng chch ca t gi trong tng lai?74. Chng minh rng t l tng trng ch s gi tng lai bng vi li sut vt mc ca danh mc cha ch s ti li sut phi ri ro. Gi nh rng ng cong li sut nm ngang v t l c tc khng i.75. L lun ca Keynes v Hicks v gi tng lai k vng?76. Gi s cty s dng hp ng n hn T phng nga ri ro t gi AUD/USD ti thi im t (T> t).a. Chng minh rng t l phng v ti u l e(rf-r)(T-t).b. Chng minh rng khi t = 1 ngy, t l phng v ti u l S0/F0.77. Mt ch s l 1200. Li sut phi ri ro lin tc 3 thng l 3% nm v t l c tc lin tc 3 thng ti l 1.2% nm. Li sut phi ri ro 6 thng l 3.5% nm v t l c tc tng ng l 1% nm. D on gi tng lai ch s 3 thng, 6 thng.78. T gi USD/EUR hin ti l 1.4000 USD mi EUR. T gi k hn 6 thng l 1.3950. Li sut USD 6 thng l 1% lin tc. Tnh li sut EUR.79. Gi giao ngay du l 80 mi barrel v chi ph lu kho l 3 mi nm, tr vo cui nm. Li sut phi ri ro l 5% nm lin tc. Cn trn gi tng lai du 1 nm l bao nhiu?80. Mt c phiu d nh tr c tc 1$ trong 2 thng v trong 5 thng. Gi c phiu l 50, li sut phi ri ro lin tc l 8% nm mi k hn. NT k bn k hn 6 thng.Gi k hn, gi tr ban u?3 thng sau, gi c phiu l 48 v li sut phi ri ro ko i. Gi k hn, gi tr mi?81. Mt ngn hng ngh khch hng la chn hoc vay tin li sut 11% nm hoc vay vng li sut 2% nm, ghp li hng nm. Nu vay vng, li phi c tr bng vng. Li sut phi ri ro l 9.25% nm, chi ph lu kho l 0.5% nm ghp lin tc. Hi li sut vay vng c qu cao hay qu thp so vi li sut vay tin?82. (5-29) 1 cty khng chc v thi im chnh xc khi no n tr hay nhn ngoi t c th thng lng vi ngn hng 1 hp ng k hn c xc nh mt giai on m ngy giao hng c th din ra. Cty mun bo lu quyn c chn chnh xc ngy giao hng ph hp vi dng tin ca n. Nu bn l ngn hng, bn s nh gi sn phm m cty mun ntn?83. Mt nh u t s hu vng nh 1 phn ca danh mc u t di hn. NT ny c th mua vng mc 1250 mi ounce v bn ra mc 1249 mi ounce. Nt c th vay vn 6% nm v u t vn 5.5% nm, ghp li theo nm. Gi k hn vng 1 nm trong khong bao nhiu th ko c arbitrage? Gi nh ko c spread gia gi mua v gi bn k hn.84. Mt cty k bn k hn vi ngn hng bn ngoi t vi gi K1 ti T1. T gi ti T1 l S1 > K1. Cty hi ngn hng rng liu n c th gia hn hp ng n T2 > T1 thay v gii quyt hp ng ti T1 khng. V ngn hng ng vi gi giao hng mi l K2. Tnh K2.

CHNG 3: HP NG HON I1. 2 cng ty aaa v bbb cng mun vay mt khon tr gi 10 triu usd trong 5 nm. Cty aaa mun vay li sut th ni, bbb mun vay vi ls c nh.Cty Li sut c nhLi sut th ni

AaaBbb4.0%5.2%LIBOR 6 thng 0.10%LIBOR 6 thng + 0.6%

Thit k hp ng hon i, bit trung gian ti chnh thu ph 0.02% mi bn.2. (7-1) 2 cty a v b c ngn hng cho mc li sut theo nm cho khon tn dng 20 triu usd, thi gian 5 nmCtyC nhTh ni

AB 5.0%6.4%LIBOR + 0.1%LIBOR + 0.6%

Cty A mun vay th ni, B mun vay c nh. Xy dng hp ng hon i nhm tn dng li th so snh bit trung gian hng ph 0.1%.3. (7-9) Cty x v y c cho khon u t tr gi 5 triu usd, k hn 10 nm vi li sut nh sau:Cty C nhTh ni

XY 8%8.8%LIBORLIBOR

X mun c nh, Y mun th ni. Xy dng hp ng hon i, trung gian ti chnh thu ph 0.2%.4. nh gi hp ng hon i nh th no? Gi tr tri phiu tr li sut c nh, th ni ra sao, chng minh?5. Mt trung gian ti chnh ng tr li sut libor 6 thng v nhn li sut c nh 8% nm, trn vn danh ngha l 100 triu usd. Thi hn cn li l 1.25 nm. Li sut libor lin tc k hn 3 thng, 9 thng, 15 thng l 10,10.5,11%. Li sut libor 6 thng ti k tr li trc l 10.2%. Xc nh gi tr ca hp ng hon i li sut ny ng t v tr trung gian ti chnh.6. (7-3) Mt hp ng hon i li sut, 1 nm hon i 2 ln li sut libor 6 thng v c nh 7% nm. Vn danh ngha 100 triu usd. Thi gian cn li 10 thng. Mc bnh qun li sut c nh c hon i vi li sut libor 6 thng l 5% nm lin tc vi mi k hn. Li sut libor 6 thng va c cng b cch y 2 thng l 4.6% nm. Tnh gi tr v th tr li sut th ni v v th tr li sut c nh.7. Ngn hng cho li sut cho vay bng usd v aud thi hn 5 nm cho 2 cty ge v quantas airways nh sau:Cty Usd Aud

Ge Qantas5.0%7.0%7.6%8.0%

FI thu ph mi bn 0.1%. Thit k hp ng hon i bit ge cn 20 triu aud, qantas cn 15 triu usd. T gi hin ti 1 aud = 0.75 usd.8. (7-2) Cty x mun vay usd vi li sut c nh, y mun vay jpy vi li sut c nh. S tin 2 cty mun vay ngang nhau nu quy i theo t gi hin ti. Li sut c cho nh sau:Cty Jpy Usd

X Y 5.0%6.5%9.6%10.0%

Xy dng hp ng hon i, fi thu ph 50 im c bn / nm.9. (7-11) Cty a v b c ngn hng cho cc mc li sut nh sau:ng tinCty aCty b

UsdCad Libor + 0.5%5.0%Libor + 1.0%6.5%

A mun vay usd th ni, b mun vay cad c nh. Fi thu ph 50 im c bn. Xy dng hp ng?10. nh gi hp ng hon i tin t.11. Mt t chc ti chnh tham gia mt hp ng hon i tin t nhn 5% nm jpy v tr 8% nm usd. Thi hn cn li ca hp ng l 3 nm. Khon vn gc ban u l 10 triu usd v 1200 triu jpy. Li sut libor ca yn v usd l khng i theo k hn, ng vi 4% v 9% nm. T gi hin ti 110 jpy = 1 usd. Tnh gi tr hp ng hon i.12. (7-5) Mt hp ng hon i tin t: hon i 20 triu bng 10% vi 30 triu usd 6% nm. Cn 15 thng. Nu hp ng hon i ny c k, mc li sut hon i l 7% nm vi bng v 4% nm vi usd (gp). ng cong li sut nm ngang. T gi hin ti 1 gbp = 1.85 usd. Tnh gi tr v th tr gbp?13. (7-10) 1 fi c hp ng hon i li sut vi cty x. fi nhn 10% nm v tr libor 6 thng trn vn gc l 10 triu cho 5 nm. Cc khon thanh ton 6 thng 1 ln. Cty x ph sn vo ngy thanh ton th 6. Khi li sut ghp li na nm l 8% nm cho mi k hn. Khon l ca fi l bao nhiu? Gi nh rng libor 6 thng l 9% nm sut na nm th 3.14. (7-12) 1 fi c hp ng hon i tin t 10 nm vi cty y. Theo , FI nhn li 3% nm CHF v tr li 8% nm USD. Li thanh ton 1 ln trong nm. Vn gc l 7 triu usd v 10 triu chf. Gi s cty y ph sn vo cui nm 6, khi t gi l 0.80$ mi chf. Chi ph ca FI l bao nhiu? Gi s rng, cui nm 6, li sut l 3% nm chf v 8% nm usd cho mi k hn. Mi li sut ghp theo nm.15. (7-15) Ti sao l k vng trn swap li nh hn l k vng trn khon vay cng 1 s tin gc?16. (7-16) 1 ngn hng c ti sn ko match c vi n phi tr. Ngn hng ny nhn tin gi th ni nhng cho vay c nh. Hp ng hon i c s dng nh th no b p ri ro?17. (7-18) ng cong li sut libor nm ngang mc 5% lin tc n 1.5 nm. T sut swap cho khong tr 2 nm v 3 nm (6 thng 1 ln) l 5.4% v 5.6%. D on li sut libor k hn 2, 2.5 v 3 nm?18. Li sut libor 1 nm l 10% ghp theo nm. 1 ngn hng giao dch swaps trong li sut c nh c trao i vi libor 12 thng vi khong tin trao i 1 nm 1 ln. T sut swap 2 nm v 3 nm (ghp theo nm) l 11% v 12% nm. D on li sut libor 2 nm v 3 nm.19. Cty A anh mun vay usd ti li sut c nh. Cty b m mun vay bng anh mc li c nh. Ngn hng cho li sut nh sauCty Gbp Usd

A B 11%10.6%7%6.2%

Thit k hp ng hon i sao cho: Fi nhn 10 im c bn / nm Gain cho mi cty l 15 im c bn/ nm.20. Trong 1 swap, fi tr 10% nm v nhn libor 3 thng trn vn gc l 100 triu usd, thanh ton mi 3 thng. Swap cn li 14 thng. Li sut bid v offer trung bnh c hon i cho libor 3 thng l 12% nm cho mi k hn. libor 3 thng 1 thng trc cng b l 11.8% nm. Mi li sut ghp theo qu. Gi tr ca swap ny?21. Gi nh cu trc k hn ca li sut l bng nhau m v c. Usd l 7% nm v aud l 9% nm. Gi tr hin ti ca aud l 0.62 usd. Theo iu khon ca swap, fi tr 8% nm aud v nhn 4% nm usd. Vn gc l 12 triu usd v 20 triu aud. Thanh ton 1 nm 1 ln. swap ko di 2 nm. Gi tr swap ny ng di gc ca fi? Ghp li lin tc.22. Cty x anh v mun vay 50 triu usd c nh 5 nm ti qu ca m. V cty ny ko ni ting m, nn kh c ngn hng no m chp nhn cho vay. Tuy nhin, cty c thng bo 12% nm trn vn gbp 5 nm c nh.Cty y m v mun vay tng ng 50 triu usd ti qu ca anh vi li sut c nh cho 5 nm. Cty ny c ngh 10.5% nm usd.Tri phiu chnh ph 5 nm hin c li sut 9.5% nm m v 10.5% anh.Thit k hp ng hon i thch hp v li nhun rng ca fi l 0.5% nm.

CHNG 4: HP NG QUYN CHN1. Thu nhp tng v th trong giao dch quyn chn qua gc nhn th?2. Phn bit cc thut ng: at the money, in the money v out of the money.3. Phn bit cc thut ng: intrinsis value v time value4. Gi thit trong vic nh gi quyn chn?5. (10-1) Cc yu t tc ng n gi tr quyn chn6. (9-13) Quan h v gi ca quyn chn kiu m v chu u?7. Cn trn v cn di ca gi tr quyn chn mua u? Chng minh.8. Cn trn v cn di ca gi tr quyn chn mua m? Chng minh.9. Cn trn v cn di ca gi tr quyn chn bn u? Chng minh.10. Cn trn v cn di ca gi tr quyn chn bn m? Chng minh.11. Mt quyn chn mua u c c=3, gi c phiu c s S0 = 20 o hn sau 1 nm, li sut phi ri ro 10%, gi thc hin 18. C phiu ko tr c tc trong vng i quyn chn. Arbitrage?12. Mt quyn chn mua u c phiu ko c tc, vi gi thc hin 50, thi gian cn li n khi o hn l 6 thng, li sut phi ri ro l 12% nm, gi hin ti c phiu l 51. Tnh cn di ca quyn chn ny.13. Mt quyn chn bn u c phiu vi nhng thng tin sau: S0 = 37, K=40, r=5% nm; T=0.5, p=1. Arbitrage?14. (10-2) Xc nh cn di ca gi 1 call khng c tc, k hn 4 thng, khi gi c phiu l 28, gi thc hin 25, li sut phi ri ro 8% nm.15. (10-3) Xc nh cn di 1 put u khng c tc, k hn 1 thng, gi c phiu l 12 usd, gi thc hin 15, li sut phi ri ro 6% nm.16. (10-10) Xc nh cn di ca gi quyn chn bn c phiu khng c tc, k hn 2 thng, gi c phiu hin nay 58 usd, gi thc hin 65, li sut phi ri ro 5% nm.17. (10-9) Xc nh cn di ca gi quyn chn mua c phiu khng c tc kiu u, k hn 6 thng, gi c phiu hin nay 80 usd, gi thc hin 75, li sut phi ri ro 10% nm.18. (10-12) 1 put u c phiu ko c tc k hn 1 thng, c bn vi gi 2.5 usd, gi c phiu l 47, gi thc hin l 50. Li sut phi ri ro l 6% nm. Arbitrage?19. Cng thc ngang gi quyn chn c phiu ko tr c tc kiu u? Chng minh.20. 2 quyn chn mua v bn kiu u cng 1 c phiu, cng thi hn, cng gi thc hin bit: S0 = 31, K = 30, r = 1% nm T=3 thng, c=3, p=2.25. Nh u t tn dng arbitrage th no?Nu p = 1 th sao?21. (10-18) Ngang gi quyn chn c phiu ko c tc kiu m? Chng minh.22. (10-8, 19) Chng minh cng thc ngang gi quyn chn c phiu tr c tc kiu u v M.Gii thch ti sao l lun cho u ko c p dng cho m?23. (10-7) Gi 1 c phiu ko c tc l 19, gi quyn chn mua u k hn 3 thng gi thc hin 20 l 1. Li sut phi ri ro l 4% nm, xc nh gi quyn chn bn u k hn 3 thng chnh c phiu gi thc hin 20.24. (10-4) C nn thc hin quyn chn kiu m trc thi hn? Ti sao?25. Mt call m, thi hn cn li 1 thng, c phiu ko c tc, gi hin ti 50, gi thc hin 40, gi tr ni ti ca call ny l 10. C nn thc hin quyn hay ko?26. Mi quan h gia gi call v gi c phiu. T rt ra call l mt cng c phi sinh.27. Mi put m c gi thc hin 10 gi cp hin ti gn bng 0. Nn thc hin quyn ngay hay ko?28. Mi quan h gia gi put v gi c phiu, t rt ra put l mt cng c phi sinh.29. Lit k cc chin lc phng v ri ro s dng quyn chn. V th m t tng chin lc.30. Tnh thu nhp v v th li nhun ca chin lc sau: long call c=3, K=30, short call c=1, K=35. B qua yu t thgian.31. 1 nh u t long put 1 cp vi p=3, K=35 v short put p=1 v K=30. V th li nhun?32. V s miu t y v th ca 1 nh u t s dng chin lc butterfly spread vi cc thng tin sau: Call 1: K=25, c=5 Call 2: 30; 3 Call 3: 35; 1 K hn hp ng 1 nm.33. (11-12) 1 call c K=60, c=6. 1 put K=60, p=4. V th m t chin lc straddle. Xc nh khong gi cp khin chin lc ny l.34. V th miu t li nhun butterfly spread gn 3 puts cng ngy o hn v c gi thc hin ln lt 55, 60, 65 v gi quyn tng ng 3,5 v 8. Xc nh khong gi khin cho chin lc l.35. Chng minh m hnh nh thc mt cch khi qut.36. nh gi quyn chn theo quan im xc sut ntn?37. Mt quyn chn u bn cp 2 nm, gi thc hin 52, gi cp 50, mi nm gi tng hoc gim 20%. Gi s li sut phi ri ro l 5%, xc nh gi quyn chn.38. (12-1) Mt c phiu c gi hin ti 40, k vng sau 1 thng gi tng ln 42 hoc gim xung 38. Li sut phi ri ro l 8% nm lin tc. Xc nh gi 1 call u vi gi thc hin 39.39. (12-4) Trn th trng c 1 c phiu cs gi giao ngau l 50, theo d on sau 6 thng th gim cn 45 hoc tng ln ti 55. Li sut phi ri ro l 10%.Tnh gi quyn call v put vi K=50.Chng minh m bo put-call parity.40. (12-5, 6) 1 cp gi 100 sau mi 6 thng ti c phiu dao ng trong khong 20%. Li sut phi ri ro l 8% nm lin tc. Xc nh c vi T=1 v K=100.41. (12-12, 13) 1 cp gi 50 sau mi 3 thng k vng tng 6% hoc gim 5%. Li sut 5% nm lin tc, xc nh c bit T=6 thng K=51.Xc nh p u 6 thng K=51. Chng minh rng gi call v put tha mn ngang gi quyn chn.Nu put l m, liu c ti u khi thc hin sm hn bt k nt no ca cy nh thc ko?42. (12-10) Mt c phiu gi 80 sau 4 thng gi k vng gim 75 hoc tng 85. Li sut 5% nm lin tc. tnh p, T=4 thng, K=80.43. 1 cp gi 40 k vng tng 45 hoc gim 35 sau 3 thng. Li sut 8% nm lin tc. xc nh p, T=3 thng, K=40.44. 1 cp gi 40 k vng tng hoc gim 10% c sau 3 thng, li sut phi ri ro 12% nm lin tc. tnh p, T=6 thng, K=42.45. (9-6) mt cty thng bo chia tch c phiu 2 for 1. iu ny nh hng n call option vi K=60 ntn?46. (9-11) m t gi tr cui cng ca danh mc sau: 1 long forward mi c k trn 1 ti sn v 1 long put u cng ti sn cng k hn v K=F0 (gi lc danh mc c thit lp).Chng minh rng: put u c gi tr bng vi call u vi cng K v T.47. (9-16) So snh vic phng nga ri ro t gi bng k hn v quyn chn.48. (9-17) 1 call mua 500 c phn vi K=40 v T=4 thng. Call s b nh hng ntn nu: C tc l 10% c phiu C tc l 10% tin mt Chia tch 1 c phiu thnh 4.49. (9-18) Nu hu ht call c phiu u ang in the money, gi c phiu s tng nhanh vo nhng thng cui. ng hay sai?50. (9-19) nh hng ca c tc tin mt bt thng ln gi quyn chn mua v bn ntn?51. (9-21) Ti sao spread bid v offer ca market maker li l chi ph tht s ca nh u t quyn chn?52. (9-22) 1 nh u t bn 5 calls bit C=3.5, K=60, S0 = 57. Yu cu k qu ban u l bao nhiu?53. Gi c phiu l 40. 1 put u: K=30, p=7, T=1 nm v 1 call u: K=50, c=5, T=1. Mt nh u t mua 100 cp, bn 100 calls, mua 100 puts. V th li nhun sau 1 nm?54. (10-5) Vic thc hin sm put M l mt s giao dch gia gi tr thi gian tin t v gi tr bo him ca put. Gii thch?55. (10-6) Ti sao mt call m c phiu tr c tc c gi tr ti thiu l gi tr ni ti ca n. iu c ng vi call u khng?56. (10-11) 1 call u 4 thng trn cp tr c tc hin ang bn vi gi 5, hin gi cp l 64, K-60 v D=0.8 c tr trong 1 thng ti. Li sut l 12% nm mi k hn. Arbitrage?57. (10-13) ti sao vic thc hin sm put m tr nn hp dn hn khi li sut phi ri ro tng v s bin ng gim?58. (10-14, 15) 1 call u: T=6 thng, K=30, c=2. S0 = 29, D=0.5 c tr trong 2 thng v 5 thng ti. Cu trc k hn nm ngang mc 10%. Tnh p bit T=6 v K=30.Nu p=3 th arbitrage ntn?59. (10-16, 17) 1 call m ko c tc c C=4, S0 = 31, K=30, T= 3 thng, r=8%. Cn trn v cn di ca put m?Nu P> cn trn arbitrage ntn?60. 1 call v 1 put u u c K=20, T=3 thng, p=c=3, r=10% nm, S0 = 19, D=1 s tr trong 1 thng. Arbitrage?61. Gi s c cc i lng sau: c1, c2, c3 v K1,2,3 trong K3 > K2 > K1 v K3 K2 = K2 K1. Tt c u cng T.Chng minh rng:c2 0.5 (c1 + c3)Gi : xem xt 1 danh mc = long 1 call c K1 + long 1 call c K3 + short 2 calls c K2 => chin lc u t???62. (11-1) Protective put l g? N tng ng vi v th no ca call?63. (11-3) Khi no th nh u t mua 1 butterfly spread?64. (11-4) 3 calls nh sau: K= 15, 17.5, 20 v c = 4, 2, 0.5 vi T= 3 thng. S dng chin lc butterfly spread ntn?65. (11-5) Chin lc ntn s to calendar spread i chiu?66. (11-6) Phn bit strangle v straddle?67. (11-7) 1 call K=50, c=2 v 1 put: K=45 v p=3. Chin lc strangle ntn?68. (11-8) S dng ngang gi quyn chn din t mi quan h ca chin lc bull spread bi calls v puts.69. (11-10) puts: K1= 30, p1 = 4 v K2=35 v p2=7. Chin lc bull spread v bear spread ntn?70. (11-11) S dng ngang gi quyn chn chng minh rng chi ph ca butterfly spread t puts u l xc nh vi chi ph t calls u.71. (11-14) Mt nh u t tin rng gi chng khon s chuyn bin mnh, nhng ko chc chn v hng. Xc nh 6 chin lc khc nhau.72. (11-15) Lm th no 1 hp ng k hn 1 cp vi gi v ngy giao hng xc nh c to t quyn chn?73. (11-16) 1 box spread = 4 options, trong c 2 ci kt hp vi nhau thnh 1 long forward v 2 ci c th kt hp vi nhau thnh short forward. Gii thch?74. (11-17) trong strangle, iu j s xy ra nu Kput > Kcall?75. Chin lc diagonal spread = long 1 call K2, T2 v short 1 call K1, T1 vi T2 > T1. V th li nhun trong trng hp:a. K2 > K1b. Ngc li.76. V th cho danh mc sau:a. 1 cp + 1 short 1 callb. 2 cp + 1 short 1 callc. 1 cp + 1 short 2 callsd. 1 cp + 1 short 4 callsGi nh rng call c K = S0.77. Ci j = 1 long starngle + 1 short straddel cng T? Vi Kstraddle = (2 Kstrangle).78. Ci j = 1 long call K2 + 1 short put K1 khi cng T v K2 > K1. Khi K2=K1 th sao?79. (12-2) Gii thch cch tip cn khng arbitrage v nh gi trung lp ri ro nh gi quyn chn u s dng nh thc 1 bc?80. (12-3) Delta quyn chn l g?81. (12-7) Cng thc ca u v d lin quan n s bt n?82. (12-8) gi c phiu s di ng 2 bc trong vng i quyn chn u. Gii thch ti sao khng th thit lp v th c phiu v quyn chn m phi ri ro cho vng i quyn chn?83. (12-9) 1 c phiu c gi 50, sau 2 thng s l 53 hoc 48. Li sut l 10% nm lin tc. nh gi call u 2 thng vi K=49, s dng l lun khng arbitrage.84. (12-11) 1 c phiu c gi 40, sau 3 thng l 45 hoc 35. Li sut phi ri ro ghp qu l 8% nm. Tnh gi tr put u 3 thng K=40.Chng minh rng l lun khng arbitrage v trung lp ri ro cho cng p s.85. (12-14) Gi c phiu hin l 25, sau 2 thng hoc 23 hoc 27. Li sut 10% nm lin tc. ST l gi c phiu sau 2 thng na. Gi tr ca 1 phi sinh m c thu nhp l ST2 vo lc ny l bao nhiu?86. (12-15) Tnh u, d, p khi cy nh thc p dng cho quyn chn ngoi t. Bit k hn 1 thng, li sut ni a 5% nm, li sut ngoi t l 8% nm, bt n 12% nm.87. 1 c phiu hin gi 30, sau mi giai on 2 thng cho 4 thng ti n s tng 8% hoc gim 10%. Li sut 5%. S dng m hnh 2 bc tnh gi tr ca phi sinh m thu nhp l [ max(30-ST,0) ]2 vi ST l gi cp sau 4 thng. Nu phi sinh ny thuc kiu m, liu n cn ng?