quyỀn chỌn vÀ quyỀn chỌn thỰc Ứng dỤng trÊn thỊ trƯỜng tÀi chÍnh viỆt nam

8/2/2019 QUYN CHN V QUYN CHN THC NG DNG TRN TH TRNG TI CHNH VIT NAM

1/93

www.empirics.net

QUYN CHN V QUYN CHN THCNG DNG TRN TH TRNG TI CHNH VIT NAM

Sn phm nghin cu

Cng ty TNHH Dan Houtte, Vng vi tc

DHVP Empirics.net
http://www.empirics.net/http://www.empirics.net/


2/93

Mc lc

I Quyn chn 4

1 Tng quan v quyn chn 51 Tng quan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.1 Qu trnh hnh thnh th trng quyn chn . . . . . . . . . . . . 51.2 Mc pht trin hin nay . . . . . . . . . . . . . . . . . . . . . . 51.3 Mt s khi nim . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Cc c trng ca quyn chn trn c phiu . . . . . . . . . . . . . . . . . 72.1 Cc yu t nh hng n gi quyn chn c phiu . . . . . . . . 72.2 Cc gi nh v k hiu . . . . . . . . . . . . . . . . . . . . . . . . 9

3 Giao dch quyn chn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2 Cc chin lc kinh doanh hp ng quyn chn 121 Trng hp mt quyn chn ca mt c phiu duy nht . . . . . . . . . . 12

2 Mua bn song hnh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1 Mua bn theo chiu ln . . . . . . . . . . . . . . . . . . . . . . . . 142.2 Mua bn theo chiu xung . . . . . . . . . . . . . . . . . . . . . . 162.3 Mua bn quyn chn lin hp . . . . . . . . . . . . . . . . . . . . 182.4 Mua bn song hnh theo lch . . . . . . . . . . . . . . . . . . . . . 202.5 Mua bn theo t l . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.6 Chin lc mua bn chnh lch theo ng cho . . . . . . . . . . 23

3 Chin lc kinh doanh kt hp . . . . . . . . . . . . . . . . . . . . . . . . 233.1 Chin lc mua hng hai . . . . . . . . . . . . . . . . . . . . . . . 243.2 Chin lc Strips v Straps . . . . . . . . . . . . . . . . . . . . . . 253.3 Chin lc mua bn hn hp . . . . . . . . . . . . . . . . . . . . . 25

3 nh gi quyn chn 271 Mt s tnh cht c bn ca hp ng quyn chn c phiu . . . . . . . . 28

1.1 Cc gii hn trn . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281.2 Gii hn di ca quyn chn khng tr c tc . . . . . . . . . . . 281.3 Gii hn di ca quyn chn tr c tc . . . . . . . . . . . . . . . 301.4 Mi quan h gia quyn chn mua v quyn chn bn . . . . . . . 30

2 nh gi quyn chn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

2.1 nh gi quyn chn cy nh phn . . . . . . . . . . . . . . . . . . 312.2 M hnh Black-Scholes . . . . . . . . . . . . . . . . . . . . . . . . 41

2

Dan Houtte, Vuong & Partners - Empirics.net

DHVP - Empirics.net


3/93

MC LC

II Quyn chn thc 55

4 Tng quan v quyn chn thc: mt cch nhn mi v u t 561 Cch tip cn theo quan im quyn chn . . . . . . . . . . . . . . . . . . 56

2 Tnh khng th o ngc v Kh nng tr hon . . . . . . . . . . . . . . 573 Dao ng gi hai thi k. . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.1 Tnh cht tng t nh mt quyn chn ti chnh . . . . . . . . . 614 C hi u t khi chi ph thay i . . . . . . . . . . . . . . . . . . . . . . 635 C hi u t khi li sut thay i . . . . . . . . . . . . . . . . . . . . . . 64

5 Quyt nh u t ca doanh nghip 671 C hi v thi im u t . . . . . . . . . . . . . . . . . . . . . . . . . . 67

1.1 M hnh ban u . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681.2 Tip cn m hnh bng quy hoch ng . . . . . . . . . . . . . . . 69

1.3 Tip cn m hnh bng phng php phn tch Nhu cu ti chnhngu nhin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 701.4 Cc tnh cht ca nguyn tc u t ti u . . . . . . . . . . . . . 72

2 nh gi d n v ra quyt nh u t. . . . . . . . . . . . . . . . . . . . 772.1 Chi ph vn hnh v s tr hon tm thi . . . . . . . . . . . . . . 772.2 nh gi d n khi u ra thay i . . . . . . . . . . . . . . . . . . 77

3 Chin lc ra nhp hoc t b . . . . . . . . . . . . . . . . . . . . . . . . 783.1 Chin lc ra nhp v t b hn hp . . . . . . . . . . . . . . . . . 793.2 nh gi hai quyn chn . . . . . . . . . . . . . . . . . . . . . . . 80

6 ng dng phn tch v nh gi 82

1 nh gi c hi u t khi chi ph u t thay i . . . . . . . . . . . . . . 821.1 Gii thiu m hnh . . . . . . . . . . . . . . . . . . . . . . . . . . . 821.2 Phng php . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

2 nh gi c hi u t khi thi im thc hin khng xc nh . . . . . . 862.1 Gii thiu m hnh . . . . . . . . . . . . . . . . . . . . . . . . . . . 862.2 M hnh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

Ph lc tra cu 92

http://www.emiscom.com3

c EMISCOM, 4/2006


DHVP - Empirics.net
http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/


4/93

Phn I

Quyn chn

4


DHVP - Empirics.net


5/93

Chng 1

Tng quan v quyn chn

1 Tng quan

1.1 Qu trnh hnh thnh th trng quyn chn

Vo u nhng nm 1900, hip hi nhng nh mi gii v kinh doanh quyn chn(1) rai. Nh u t mun mua quyn chn s lin h vi mt cng ty thnh vin, cng tyny s tm ngi bn quyn chn t khch hng ca cng ty hoc ca cc cng ty thnh

vin khc. Nu khng c ngi bn, cng ty s t pht hnh quyn chn vi gi cthch hp. Th trng hot ng theo cch ny gi l th trng phi tp trung OTC (2),cc nh kinh doanh khng gp nhau trn sn giao dch.

Vic mua bn quyn chn tr nn ph bin u tin Chicago Board of OptionsExchange. Vo thi k ch yu trao i cc c phiu thng mi n l.

Nm 1982, quyn chn bt u giao dch trn cc hp ng tng lai vi tri phiuchnh ph, v loi giao dch ny pht trin rt nhanh. Giao dch trn th trng u gim, vic mua bn quyn chn cung cp rt nhiu cng c u c v phng h gi chocng ng thng mi. S thnh cng ca hp ng quyn chn m li cho vic rai quyn chn trn v s cc hng ho tiu dng, nh ng, u nnh v cc sn phmkhc.

1.2 Mc pht trin hin nay

Khi x hi ngy cng pht trin, giao dch quyn chn ngy cng tr nn ph bin hn,lan rng sang Anh, Brasil, c, Php, Nht Bn, Singapore, Hng Kng v Australia.

Vic ton cu ho th trng th gii to ra nhu cu lin kt in t v thngmi 24/24 trong ngy. Th trng M p ng nhu cu ny bng cch to ra nhngsnphmgiaodchquct,mrnggigiaodchvtrinkhaimtsngiaodchint.

(1)Option(2)Over-the-counter

5


DHVP - Empirics.net


6/93

CHNG 1. TNG QUAN V QUYN CHN

Nhng h thng ng ch nht l GLOBEX (c CME pht trin) v Project A(c CBOT) pht trin. c, Deutsche Terminborse Exchange b kiu giao dchu gi m, thay vo vn hnh sn giao dch in t.

Trn h thng GLOBEX, cc nh u t c th c th giao dch da trn ch s SP500,SP500 mini v NASDAQ 100 v cc hp ng con. Cc nh u t c th cng c thmua bn ngoi hi trn GLOBEX.

Trn h thng Project A (hin ti l h thng Eurex (3)), cc nh u t c th c thmua bn tri phiu T-bonds v tn phiu, quyn chn, v tt c cc sn phm ng cctrn CBOT. Giao dch in t c thit k h tr vic u gi m ngoi gi giao dchchnh thc.

1.3 Mt s khi nim

Quyn chn

Mt quyn chn l mt phng tin u t cho php ngi mua quyn chn ny cquyn, nhng khng b bt buc phi, bn hoc mua mt ti sn no.

Quyn chn mua (4) Ngi s hu mt quyn chn mua c quyn mua mt ti sn,ti mt mc gi nht nh, vo mt thi im nht nh.

Quyn chn bn (5) Ngi s hu mt quyn chn bn c quyn bn mt ti sn,ti mt mc gi nht nh, vo mt thi im nht nh.

Gi thc hin (6) Gi thc hin cn c gi l gi im l mc gi ti ti sntrong mt quyn chn c th c mua hoc bn.

Ti sn c s (7) L loi ti sn s c giao trn c s mua hoc bn khi quyn chnc thc hin.

In-the-Money Numtquynchncgitrniti (8), n c gi l in-the-money.

Quyn chn mua. Mt quyn chn mua c gi l in-the-money khi gi tisn c s cao hn gi thc hin.

Quyn chn bn. Mt quyn chn bn c gi l in-the-money khi gi ti snc s thp hn gi thc hin.

(3)Thng 8 nm 2000, CBOT xy dng Eurex, tt c cc giao dch trn Project A hin ti u thc hintrn Eurex

(4)Call(5)Put(6)Strike price

(7)Underlying Asset(8)intrinsic value


c EMISCOM, 4/2006


DHVP - Empirics.net


7/93

2. CC C TRNG CA QUYN CHN TRN C PHIU

Out-of-the-Money

Quyn chn mua. Mt quyn chn mua l out-of-the-money nu gi ti sn cs hin ti thp hn gi thc hin.

Quyn chn bn. Mt quyn chn mua l out-of-the-money nu gi ti sn cs hin ti cao hn gi thc hin.

Quyn chn kiu Chu u Quyn chn kiu Chu u l quyn chn c thchin vo cui k hn.

Quyn chn kiu M Quyn chn kiu M l quyn chn c th c thc hin vobt k thi im no trc khi o hn. Quyn chn ny c tnh linh ng hn so vi

quyn chn kiu Chu u.

Th trng v (9) L v th khi nh u t mua ti sn, y l mua mt quyn chntrn ti sn do d bo rng gi ti sn s tng phiu tng.

Th on v (10) Nhn chung v th ca nh u t khi bn mt ti sn m ngi khng s hu. V th ny tri ngc vi th trng v.

2 Cc c trng ca quyn chn trn c phiu

2.1 Cc yu t nh hng n gi quyn chn c phiu

C 6 yu t tc ng n gi quyn chn c phiu:

1. Gi c phiu thi im hin ti;

2. Gi thc hin;

3. Khong thi gian t thi im hin ti cho n khi o hn quyn;

4. bt n ca gi c phiu;

5. Li sut phi ri ro;

6. C tc k vng s thanh ton trong khong thi gian quyn c hiu lc;

Bocostinhnhphntchtcngtigiquynchnkhithayimiyutktrn trong iukincc yu t cn li khng i. Kt qu chung c trnh by bng1.1

(9)Long position(10)Short position


c EMISCOM, 4/2006


DHVP - Empirics.net


8/93


Bng 1.1: Tm tt tc ng ca cc yu t n gi quyn chn c phiu

Quyn chn Quyn chn Quyn chn Quyn chn

Bin mua Chu u bn Chu u mua kiu M bn kiu MGi c phiu + - + -Gi thc hin - + - +Thi gian o hn ? ? + + bt n + + + +Li sut phi ri ro + - + -C tc - + - +

Gi c phiu v gi thc hin

Nu mt quyn chn mua c thc hin mt thi im trong tng lai th khon linhun thu c s bng khong ln hn ca gi c phiu so vi gi thc hin. Do nu gi c phiu tng th gi ca quyn chn mua s tng v nu gi thc hin tng thgi ca quyn chn mua s gim. Vi mt quyn chn bn, li nhun thu v nu quynchn c thc hin s bng khong ln hn ca gi thc hin so vi gi c phiu. Nhth gi quyn chn bn s tng nu nh gi thc hin tng v gim nu nh gi c phiutng.

Thi gian n lc o hn

Yu t ny c tc ng r rng hn n quyn chn kiu M (c mua v bn), nu nhthi gian cn li cho n lc o hn cng di th gi ca quyn chn s cng cao. Xtvi hai quyn chn ging nhau v c yu t khc ngoi tr thi gian cho n ngy ohn. Ngi s hu quyn chn c thi gian di hn r rng c nhiu thi gian lachn thc hin quyn hn ngi s hu quyn chn ngn hn.

Vi quyn chn kiu Chu u, thi gian n ngy o hn khng thc s c nhhng n gi quyn chn do c 2 quyn ni trn u ch c th thc hin thi cngmt thi im l ngy o hn. Thm ch trong nhiu trng hp quyn chn ngnhn c th c gi cao hn, chng hn nh hai quyn chn mua c chung mi c tnh,

mt quyn s o hn trong 1 thng na, quyn cn li o hn trong 2 thng. Nu cphiu c tr c tc v thi im thanh ton l 6 tun na, th do tc ng ca vic trc tc, quyn chn o hn trong 1 thng hn s c gi cao hn.

bt n

nh ngha chnh xc v bt n s c gii thiu trong phn m hnh Black-Scholes, y c th hiu n gin nht bt n l mt thc o mc khng chc chn ca

bn thn nh u t vo bin ng trong tng lai ca gi c phiu. bt n cng caoth kh nng gi c phiu c th ln rt cao hoc xung rt thp cng tng cao. Ngi shu c phiu c th coi hai xu hng ny trit tiu ln nhau v khng qu lo lng. Tuy

nhin ngi s hu quyn mua hay quyn bn th khng nh vy. Ngi s hu quynmua s c li nu nh gi c phiu tng ln nhng h ch phi chu ri ro c gii hn


c EMISCOM, 4/2006


DHVP - Empirics.net


9/93

2. CC C TRNG CA QUYN CHN TRN C PHIU

nu gi gim, mc l cao nht h phi chu chnh bng gi ca quyn mua. Vi ngis hu quyn bn, h s c li nu nh gi ca c phiu gim mnh v h ch phi churi ro c gii hn nu gi tng, l cao nht phi chu cng chnh l gi ca quyn mua.

V l do ny, gi ca quyn chn mua v quyn chn bn s tng cao nu nh bt nca c phiu tng.

Li sut phi ri ro

Tc ng ca li sut phi ri ro n gi ca quyn chn c phiu khng thc s r rngnh nhng trng hp trc. Khi li sut phi ri ro trong nn kinh t tng t l tngtrng k vng vi gi c phiu cng s c xu hng tng. ng thi gi tr hin tica cc dng tin m nh u t k vng s nhn c trong tng lai s gim. Hai tcng ny u c xu hng lm gim gi ca quyn chn bn. Do gi quyn chn

bn c xu th gim khi li sut phi ri ro trn th trng tng. Vi quyn chn mua,

tc ng u tin c xu th lm tng gi quyn nhng tc ng th hai li c xu th lmgim gi quyn. Tuy nhin tc ng th nht lun ln t tc ng th 2 do khi lisut phi ri ro tng th gi quyn chn bn cng tng.

Cn nhn mnh li nhng tc ng k trn ch c nghin cu trong tnh hungcc yu t khc khng i, iu ny l khng c thc c bit khi mt nhn t quantrng trong nn kinh t l li sut phi ri ro thay i. Thc t cho thy gi c phiu cxu th bin ng ngc chiu vi bin ng ca li li sut phi ri ro. Tc ng cnggp ca li sut v gi c th mang n nhng kt qu rt khc.

C tc

C tc lm cho gi c phiu gim xung trong ngy giao dch khng hng quyn. yl thng tin xu vi gi ca quyn chn mua v l thng tin tt vi gi ca quynchn bn. Nh th gi ca quyn chn mua c tng quan ngc chiu v gi quynchn mua c tng quan cng chiu vi nhng d bo v quy m tr c tc.

2.2 Cc gi nh v k hiu

Vic nghin cu v cc c tnh quyn chn cn c mt s gi nh sau:

1. Khng c chi ph giao dch;

2. Tt c cc li nhun thu v (l thun) t hot ng giao dch u chu cng mtmc thu;

3. C th vay v cho vay ti mc li sut phi ri ro.

Gi nh mi thnh vin tham gia trn th trng u lun sn sng ginh lynhng c hi kinh doanh chnh lch gi nu xut hin. Do bt k c hi no cngs bin mt rt nhanh. Nh vy hon ton c c s gi nh khng c c hi kinhdoanh chnh lch gi no pht sinh trn th trng.Nhng k hiu sau c s dng trong bo co:

c l gi hp ng quyn chn mua kiu Chu u;


c EMISCOM, 4/2006


DHVP - Empirics.net


10/93


C l gi hp ng quyn chn mua kiu M;

p l gi hp ng quyn chn bn kiu Chu u;

P l gi hp ng quyn chn bn kiu M;

X l gi thc hin quyn chn (c mua v bn); v

S l gi c phiu thi im hin ti;

ST l gi c phiu thi im T;

r l li sut phi ri ro trn th trng;

T l thi im o hn;

t l thi im hin ti;

l bt n ca gi c phiu.

Lu : r l li sut danh ngha, khng phi li sut thc. Ta, do , c th gi nhr > 0.

3 Giao dch quyn chn

nh ngha 1 Gi s S l gi tr ca mt ti sn v S dao ng bt nh ph thucvo tc ng ca th trng. T l thi gian o hn. Mt quyn chn l mt hp nggia ngi nm gi v ngi vit, bt u c hiu lc t thi im t = 0, trong ngi nm gi quyn chn c quyn i mt li nhun X ngu nhin no . X phthuc vo s tin trin ca S ti mt thi im trong tng lai, bao gm c thi imT.

Nh vy, quyn chn bn cht l mt v c cc tinh vi. Ta c th c ngay mt skt lun : Th nht, hp ng quyn chn phi c mt gi tr nht nh i vi nmgi n. Ngi vit hp ng c th nh ph rt cao phng v nhm chng li riro chi tr nhiu mt cch thng xuyn. Nhng nu nh vy th ngi vit hp ngdng nh c li hn v th trng s x bn quyn chn ch khng mua. Ngcli, nu ngi bn quyn chn khng a ra mt mc gi cao... Nhng khch hngtham vng s tm c hi mua quyn chn vi s lng ln. C hai trng hp trn cha nhng v d v u c, trong khi nhng nh u t khc trn th trng th umong mun mt c ch xc lp gi cng bng.

Bn cht l mt cng c ti chnh, u im ca quyn chn th hin trong 3 hnhthc giao dch ca 3 nhm ngi trn th trng quyn chn:


c EMISCOM, 4/2006


DHVP - Empirics.net


11/93

3. GIAO DCH QUYN CHN

Ngi phng h. Nhng ngi ny mua quyn chn nh mt dng hp ng bohim trc nhng thay i bt thng ca th trng. Nu mt cng ty c quan hngoi thng th n s mua hp ng quyn chn tin t c chi tr mt khonchc chn khi t gi hi oi tr nn bt li. Theo cch ny, bn c th phng v nhiuhay t ty thuc vo vic bn mua quyn chn tr gi bao nhiu. V d, nu ta munnhp khu 1 t yn hng in t ca Nht trong thi hn 1 nm k t by gi vi t gi200 yn/bng, c th thc hin mt quyn chn cam kt chi tr cho bn 1 t yn saumt nm nu t gi hi oi ch cn 181.23 yn/bng ti bt k thi im no trong 1nm . iu ny c ngha l, khi gi ng yn tng tng i vi ng bng th tan cth thc thi quyn chn v mua hng ha. Cn nu t gi tip tc duy tr mc thpth ta s mt s tin b ra mua quyn chn v s mua hng ti t gi m ta sn sngchi tr. Chi ph ca chin lc phng h ny ch l mua mt quyn chn vi gi tngi r so vi nhng bin ng ln ca th trng tin t.

Nh u c. L nhng ngi nh cc vo s bin ng ca gi cc loi ti sn.H tham gia vo mt v th nht nh th trng ty thuc vo nim tin ca mnh, lhoc li hon ton ngu nhin. H coi chng khon phi sinh nh mt cng c tng gacho hot ng u t ca h. Bi v cc sn phm phi sinh t cc ti sn c s c khnng mang li li nhun nhiu hn chnh cc ti sn c s . V d, bn u t 10.000

bng vo mt c phiu tr gi 10 bng mua 1.000 c phiu . Nu gi c phiu tngln 11 bng trong vng mt nm, bn li c 1.000 bng. Cn nu bn mua mt hpng quyn chn c quyn mua c phiu trn vi gi 10 bng trong mt nm, v

bn phi mt chi ph, gi s, 0.5 bng mt c phiu, bn c th mua c 20.000 nghnc phiu. Nu gi c phiu tng ln 11 bng, bn thc thi quyn chn, mua 20.000 c

phiu vi gi 10 bng v bn li chng trn th trng vi gi 11 bng, bn s li 10.000bng. ng nhin, nu gi c phiu tt xung ch 9.99 bng, bn s mt ton b stin b ra mua quyn chn.

Nhng nh c li phi ri ro. (11) L nhng ngi quan st th trng v c gngtm ra nhng tnh hung thu li phi ri ro. H kt hp vic mua hng ha ti mt thtrng ny v bn li ti mt th trng khc sao cho chnh lch gi m bo mtkhon li. Mt v d n gin l khi mt c phiu c giao dch ti hai mc gi khcnhau trn hai th trng. Nu mt c phiu c giao dch ti London vi gi 100 bng

v 285 mc c ti Frankfurt, trong khi t gi hi oi l 2.82 mc/bng, th c phiu

r hn tng i London. Bn c th mua 1.000 c phiu ti London v bn lichng ti Frankfurt ri i mc c sang bng v thu c mt khon 1063.3 bng mkhng phi chu bt k ri ro no. Nhng c hi nh vy l v cng him v ngay lptc n b chp mt bi nhng ngi sn c hi kim li. Khi mi ngi mua c phiuth gi s tng trn th trng London v khi mi ngi bn c phiu ti Frankfurtth gi y cng s gim i cho n khi no gi hai ni c xc lp cn bng.

(11)Arbitraguer


c EMISCOM, 4/2006


DHVP - Empirics.net


12/93

Chng 2

Cc chin lc kinh doanh hpng quyn chn

1 Trng hp mt quyn chn ca mt c phiuduy nht

C rt nhiu danh mc u t ch gm mt quyn chn trn mt c phiu(1) v chnhc phiu . Li nhun ca nhng chin lc kinh doanh nh vy c minh ha trnhnh 2.1. Nt t biu din mi quan h gia li nhun v gi c phiu trong danh mc,nt lin biu din mi quan h gia li nhun v gi ca chnh danh mc . Hnh 2.1a

m t mt danh mc u t gm mt th trng v (long position(2)

) trn c phiu vmt th on v (short position (3)) trn quyn chn mua chnh c phiu . Ngha l,bn ang nm gi c phiu v bn i mt hp ng quyn chn mua chnh c phiu. Nu gi nh th trng cho php bn khng, danh mc u t c th c xc lp

bng cch bn khng mt quyn chn mua c phiu v dng lun s tin y muac phiu. Khi y chin lc kinh doanh l bn quyn chn khng(4). Trong trnghp khng cho php bn khng, danh mc u t ny tng t vi chin lc kinhdoanh bn quyn chn mua c bo m(5). Bi v trong trng hp ny, th trng

v trn c phiu ng ngha vi vic s hu nhng c phiu v iu ny l t ri rohn rt nhiu so vi vic bun bn khng. N bo v nh u t khng thit hi qunhiu khi gi tr trng ca c phiu tr nn khng nh mong i. Nu gi c phiutng cao, ngi s hu quyn chn mua s thc hin mua c phiu vi gi hi. Nutrc y bn bn khng quyn chn, khng c c phiu trong tay bn s phi chu lln. Nu gi c phiu gim rt thp, ngi s hu quyn chn khng thc hin quynchn na v bn c mt khon b l bng gi quyn chn bn. Hnh 2.1b m tdanh mc u t gm mt th on v trn c phiu v mt th trng v trn mt

(1)Single option on a stock(2)Long position, gi tt l long, tng ng vi vic mua c phiu hoc quyn chn(3)Short position, gi tt l short, tng ng vi vic bn khng c phiu hoc bn/vit quyn chn(4)writing a naked option - m t mt giao dch m ngi bn quyn khng s hu ti sn c s ca

quyn chn.(5)Writing a covered call - nh u t c danh mc u t bao gm mt th trng v ca vi mt ti

sn kt hp vi th on v vi quyn chn mua trn chnh ti sn

12


DHVP - Empirics.net


13/93

1. TRNG HP MT QUYN CHN CA MT C PHIU DUY NHT

quyn chn mua. Trong trng hp ny, danh mc u t tng ng vi mt chinlc kinh doanh ngc vi chin lc k kt quyn chn bo m trn. Hnh 2.1c v2.1d m t cc danh mc gm mt trng v trn c phiu kt hp vi trng v trnquyn chn bn; v mt on v trn c phiu kt hp vi on v trn quyn chn bn.Nhngdanhmcnytngngvichinlckinhdoanhquynchnbnanton(6).

Hnh 2.1: Li nhun t chin lc mua bn lin quan n quyn chn n mt c phiu

(6)Protective put option - Nh u t hin ang nm gi c phiu ng thi mua thm mt quyn chnbn vi chnh loi c phiu .


c EMISCOM, 4/2006


DHVP - Empirics.net


14/93

CHNG 2. CC CHIN LC KINH DOANH HP NG QUYN CHN

H thc cp i mua bn (7) cho bit mi quan h tng quan gia quyn chn bn vmua trn cng mt c phiu gii thch hnh dng ca cc th trn. Cng thc nhsau:

p + S = c + Xer(Tt) + D (1.1)

Trong :

p l gi quyn chn bn kiu Chu u; c l gi quyn chn mua kiu Chu u; S l gi c phiu; X l gi thc thi ca c quyn chn bn v mua;

r l li sut phi ri ro;

T l thi im o hn; v D l gi tr hin ti ca c tc (8).Phng trnh 1.1 cho bit gi tr mt danh mc gm trng v trn quyn chn bn

v trng v trn c phiu tng ng vi mt trng v trn quyn chn mua c phiu v mt lng tin mt l Xer(Tt) + D. iu ny gii thch v sao hnh 2.1c c dngging vi th biu din li nhun ca vic mua quyn chn mua v hnh 2.1a ging

vi th li nhun ca vic bn quyn chn bn. Hnh 2.1d v 2.1b c gii thchngc li.

2 Mua bn song hnh

Chin lc mua bn song hnh l chin lc s hu cng mt v th trn hai quynchn cng loi hoc nhiu hn ca cng mt loi ti sn c s. Ngha l cng mua hoccng bn cc quyn chn mua hoc quyn chn bn trn cng mt loi ti sn.

2.1 Mua bn theo chiu ln(9) Mt trong nhng chin lc mua bn ph bin nht l chin lc mua bn theo

chiu ln. Chin lc ny c thc hin bng cch mua quyn chn mua mt c phiuti mt mc gi thc hin nht nh v bn quyn chn mua chnh loi c phiu timc thc hin cao hn. C hai quyn chn mua ny u c cng ngy o hn. Chinlc ny c minh ha trong hnh 2.2. Li nhun thu c t hai quyn chn muac biu din bi ng nt t.

Li nhun tng hp khi thc hin chin lc c biu din bng ng nt lin.V gi mt quyn chn lun gim khi gi thc hin tng, nn gi tr ca quyn chn bn i lun nh hn gi ca quyn chn c mua vo. Nh vy chin lc mua bn

(7)Put - Call parity

(8)D l gi tr chiu khu v hin ti ca tt c cc dng c tc trn c phiu xut hin trong tng lai.(9)Bull Spreads


c EMISCOM, 4/2006


DHVP - Empirics.net


15/93

2. MUA BN SONG HNH

Hnh 2.2: Mua bn chiu ln vi quyn chn mua

Bng 2.1: Li nhun t chin lc mua bn theo chiu lnKhong gi Li nhun t trng v Li nhun t on v Tng

c phiu trong quyn chn mua trong quyn chn mua li nhunST X2 STX1 X2 ST X2 X1

X1 < ST < X2 STX1 0 STX1ST X1 0 0 0

theo chiu ln cn phi c u t ban u.

Gi s rng X1 l gi thc hin ca quyn chn mua c mua vo, X2 l gi thchin ca quyn chn mua bn ra, v ST l gi c phiu vo ngy o hn ca quynchn. Bng 2.5 cho thy tng ton b li nhun thu c t chin lc mua bn theochiu ln trong cc tnh hung khc nhau.

Chin lc mua bn theo chiu ln hn ch c kh nng thng ln cng nh thua trngca nh u t. C th m t chin lc ny ging nh nh u t c c mt quynchn mua vi gi thc hin l

X1v quyt nh t b tim nng thng ln bng cch

bn quyn chn mua c gi thc hin l X2 (X2 > X1). i li, nh u t gimbt c s tin thua l ban u bng vi mc gi ca quyn chn mua c gi thc hinl X2. C 3 loi chin lc mua bn theo chiu ln khc nhau:

1. C hai quyn chn ban u trng thi l - out of the money(10)

2. Mt quyn chn lc u trng thi l - out of the money), quyn chn kia lcu trng thi li - in the money(11)

(10)out of the money l trng hp: vi quyn chn bn l gi thc hin thp hn gi th trng ca cphiu; vi quyn chn mua l gi thc hin cao hn gi th trng ca c phiu.

(11)in the money l trng hp: vi quyn chn bn l gi thc hin cao hn gi th trng ca c phiu;vi quyn chn mua l gi thc hin thp hn gi th trng ca c phiu.


c EMISCOM, 4/2006


DHVP - Empirics.net


16/93


3. C hai quyn chn lc u trng thi li - in the money)

Chin lc mo him nht l chin lc u tin. Chi ph thc hin chin lcny rt thp, xc sut c c li nhun (= X2

X1) kh thp. Chin lc loi 2 v

loi 3 l nhng chin lc thn trng hn.

Chin lc mua bn theo chiu ln cng c th c thc hin bng cch mua quynchn bn vi gi thc hin thp v bn quyn chn bn vi gi thc hin cao (xem hnh2.3). Khc vi chin lc mua bn s dng quyn chn mua, chin lc mua bn sdng quyn chn bn c li ngay t u. Li nhun c c t chin lc s dngquyn chn bn cng t hn so vi s dng quyn chn mua.

Hnh 2.3: Mua bn chiu ln vi quyn chn bn

2.2 Mua bn theo chiu xung

Ngc vi mua bn theo chiu ln, nh u t thc hin mua bn theo chiu xung(12)

vi hy vng rng gi c phiu s gim. Chin lc mua bn theo chiu xung cng

c thc hin bng cch mua v bn hai quyn chn mua vi gi thc hin khc nhau.Trong trng hp mua bn theo chiu xung, gi thc hin ca quyn chn mua vocao hn gi thc hin ca quyn chn bn ra. iu ny c minh ha trong hnh 2.4,trong li nhun c biu din bi ng nt lin. Chin lc mua bn theo chiuxung s dng quyn chn mua s c li ngay t u v gi ca quyn chn c bn racao hn gi ca quyn chn c mua vo.

Gi s rng gi thc hin l X1 v X2 vi X1 < X2. Bng 2.2 cho thy li nhun thuc t chin lc mua bn theo chiu xung trong cc tnh hung khc nhau. Lu

(12)Bear Spreads


c EMISCOM, 4/2006


DHVP - Empirics.net


17/93

2. MUA BN SONG HNH

Hnh 2.4: Mua bn chiu xung vi quyn chn bn

Bng 2.2: Li nhun t chin lc mua bn theo chiu xungKhong gi Li nhun t trng v Li nhun t on v Tng

c phiu quyn chn mua quyn chn mua li nhunST X2 STX2 X1 ST (X2 X1)

X1 < ST < X2 0 X1 ST (STX1)ST X1 0 0 0


c EMISCOM, 4/2006


DHVP - Empirics.net


18/93


trong trng hp ny, phn li ban u c tnh gp vo li nhun.

Ging nh chin lc mua bn theo chiu ln, chin lc mua bn theo chiu xunghn ch c c hi c li ln cng nh ri ro chu thit hi ln. Chin lc mua bn theochiu xung c th c thc hin bng cch mua bn quyn chn bn. Nh u tmua quyn chn bn c gi thc hin cao v bn quyn chn bn c gi thc hin thp(xem hnh 2.5). Chin lc mua bn theo chiu xung s dng cc quyn chn bn sc chi ph u t ban u. Thc cht l nh u t mua mt quyn chn bn vi githc hin xc nh v t b li nhun tim nng khi bn quyn chn bn khc vi githc hin thp hn. i li, nh u t phi b tin ra b vo gi chnh lch giahai quyn chn.

Hnh 2.5: Mua bn chiu xung vi quyn chn mua

2.3 Mua bn quyn chn lin hp

Chin lc mua bn quyn chn lin hp(13) l khi thc hin mua bn cc quyn chnvi ba mc gi thc hin khc nhau. C th thc hin chin lc ny bng cch muamt quyn chn mua vi gi thc hin X1 thp; ng thi mua mt quyn chn mua vigi thc hin X3 cao; v bn hai quyn chn mua vi gi thc hin X2 trong khong tX1 n X3. Nhn chung, c th chn X2 gn bng gi c phiu hin ti. Dng li nhunc c t chin lc ny c biu din trong hnh 2.6. Chin lc mua bn quynchn lin hp c th sinh ra li nhun nu gi c phiu ng mc gn X2, nhng sgy thit hi nu gi c phiu tng hay gim ng k. Do y l mt chin lc thchhp cho nh u t nu gi c phiu khng c xu hng thay i ng k. Chin lcny cng i hi u t ban u. Li nhun c c t chin lc ny c m t trong

bng 2.3.

Chin lc mua bn quyn chn lin hp cng c th thc hin vi quyn chn bn.Nh u t mua quyn chn bn vi gi thc hin thp, mua thm mt quyn chn bn

(13)Butterfly Spreads


c EMISCOM, 4/2006


DHVP - Empirics.net


19/93

2. MUA BN SONG HNH

Hnh 2.6: Mua bn lin hp vi quyn chn mua

Bng 2.3: Li nhun t chin lc mua bn lin hpKhong gi Li nhun t Li nhun t Li nhun t Tng

c phiu trng v trng v on v li nhun(14)

quyn chn mua quyn chn mua quyn chn muath nht th hai

ST X1 0 0 0 0X1 < ST X2 STX1 0 0 STX1X2 < ST X3 STX1 0 2(STX2) X3 ST

ST > X3 STX1 STX3 2(STX2) 0


c EMISCOM, 4/2006


DHVP - Empirics.net
http://-/?-http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://-/?-


20/93


vi gi thc hin cao, v bn hai quyn chn bn vi gi thc hin trung bnh. iu nyc m t trong hnh 2.7.

Hnh 2.7: Mua bn lin hp vi quyn chn bn

Chin lc mua bn lin hp cng c th c thc hin theo kiu ngc li. Nhu t bn quyn chn mua vi gi thc hin X1 v X3, v mua hai quyn chn vigi thc hin X2 nm trong khong X1, X3. Chin lc ny s mang li mt khon li

nhun khim tn nu gi c phiu thay i ng k.

2.4 Mua bn song hnh theo lch

Trong cc chin lc mua bn trc, tt c cc quyn chn u c cng thi im ohn. Trong chin lc mua bn song hnh theo lch(15), cc quyn chn c cng mcgi thc hin nhng o hn nhng thi im khc nhau.

Chin lc mua bn song hnh theo lch c th c thc hin bng cch bn mtquyn chn mua vi mt gi thc hin nht nh v mua mt quyn chn mua khc vicng gi thc hin nhng c thi im o hn lu hn. Thi im o hn cng luth gi ca quyn chn cng cao. Do chin lc ny cn phi u t ban u. Gi srng quyn chn o hn mun hn c bn vo thi im o hn quyn chn ohn sm hn, li nhun c c t chin lc ny c minh ha trong hnh 2.8. Hnhny trng gn ging nh hnh 2.6 biu din li nhun ca chin lc mua bn quynchn lin hp. Nh u t c li nhun nu gi c phiu thi im o hn ca quynchn o hn sm hn gn bng gi thc hin ca quyn chn ny. Ngc li nh ut s b l nu gi c phiu cao hay thp hn gi thc hin.

c th hiu c c cu li nhun t chin lc mua bn song hnh theo lch,u tin xem xt trng hp gi c phiu thp vo thi im o hn ca quyn chn

(15)Calendar Spreads


c EMISCOM, 4/2006


DHVP - Empirics.net


21/93

2. MUA BN SONG HNH

Hnh 2.8: Mua bn theo lch vi hai quyn chn mua

o hn sm hn. Lc ny quyn chn ny v gi tr v quyn chn o hn lu hn cgi tr gn bng 0. Do , nh u t chu l mt khon t hn khon u t ban u

mt cht. Tip tc xem xt trng hp nu gi c phiu ST cao vo thi im o hnca quyn chn o hn sm hn. Chi ph ca quyn chn o hn sm m nh ut phi chu l ST X v gi tr ca quyn chn o hn mun cao hn ST X mtcht (X l gi thc hin ca quyn chn). Nh vy nh u t li phi chu mt tn thtrng thp hn chi ph u t ban u mt cht. Nu ST gn bng X, chi ph ca quynchn o hn sm i vi nh u t hoc l rt t, hoc bng khng. Trong khi gitr ca quyn chn o hn mun li kh cao. Trong trng hp ny nh u t c linhun rng ng k.

Trong mt chin lc mua bn song hnh trung lp (16), nh u t chn gi thc

hin gn bng gi c phiu. Chin lc mua bn song hnh theo chiu ln(17)

c githc hin cao hn v chin lc mua bn song hnh theo chiu xung (18) c gi thchin thp hn.

Chin lc mua bn song hnh theo lch cng c th c thc hin vi quyn chnbn. Nh u t mua quyn chn bn o hn lu hn v bn quyn chn bn o hnsm hn. Hnh 2.9 cho thy dng li nhun ca chin lc ny gn ging chin lc sdng quyn chn mua.

(16)neutral calendar spread

(17)bullish calendar spread(18)bearish calendar spread


c EMISCOM, 4/2006


DHVP - Empirics.net


22/93


Hnh 2.9: Mua bn theo lch vi hai quyn chn bn

Chin lc mua bn theo lch ngc (19) c m t ngc li vi hnh 2.8 v hnh2.9. Nh u t mua mt quyn chn o hn sm v bn mt quyn chn o hnmun. iu ny s mang li cho nh u t mt khon li nhun nh vo ngy o hn

ca quyn chn o hn sm nu gi c phiu kh cao hoc kh thp hn gi thc hinca quyn chn. Ngc li, nh u t s thit hi nu gi c phiu gn vi gi thchin.

2.5 Mua bn theo t l

Chin lc mua bn theo t l (20) gn tng t nh mua bn c bo m (21). Chin lcmua bn theo t l ny thng c coi l chin lc trung ho, nhng vic thay i slng nhng quyn chn th on v s lm thay i bn cht ca chin lc. Chinlc mua bn theo t l chung nht c hiu s(22) gia hai v th bng 0. Khi thay i s

lng quyn chn th on v s lm thay i hiu s ny. Gi s nh u t munmua bn theo t l. Ch cn gim i 1 quyn chn th on v, chin lc ny chuynthnh chin lc mua bn theo chiu ln. Ngc li, nu bn nhiu quyn chn hn,lm cho hiu s chuyn t 0 sang m, th chin lc chuyn thnh chin lc mua bntheo chiu xung.

Nhn chung, thc hin chin lc ny c ngha nh u t phi to lp mt v thtrung ho hiu s. Khi nh u t mun thc hin mua bn theo t l, tm hiu s gia

(19)reverse calendar spread(20)ratio spread

(21)covered write(22)delta


c EMISCOM, 4/2006


DHVP - Empirics.net


23/93

3. CHIN LC KINH DOANH KT HP

hai v th xem liu v th cui cng l trng v hay on v, v liu v th c phhp vi quan im hay chin lc th trng ca nh u t hay khng.

Chin lc mua bn theo t l c coi l mt chin lc trung ho, v trng hpmang li li nhun ti a nm trong khong gi thc hin (23) chn. Trn thc t,nh u t mong mun gi chng khon n nh khi thc hin chin lc mua bn theot l. Tuy nhin, lu rng khi gi ti sn c s vn nm trong khong gi thc hin,nh u t c li nhiu t quyn chn on v hn l t quyn chn trng v.

Mt trong nhng c im quan trng ca chin lc mua bn theo t l l chinlc ny ch l khi gi thay i mt chiu. Nh u t ch mt tin khi gi thay i theochiu hng gi thc hin quyn chn th on v.

Li nhun ti a bng s quyn chn mua hoc bn th trng v nhn vi khonggi im, tr i (cng vo) phn c (n) ban u.

Vi chin lc mua bn quyn chn mua theo t l, gi tr ti im ho vn (24) theochiu ln bng gi thc hin cao nht cng vi thng s ca php chia li nhun tia cho s lng quyn chn khng.

Vi chin lc mua bn quyn chn bn theo t l, gi tr ti im ho vn theo chiuxung bng gi thc hin thp nht tr i thng s ca php chia li nhun ti a chos lng quyn chn khng.

2.6 Chin lc mua bn chnh lch theo ng cho

Trong chin lc mua bn theo chiu ln, theo chiu xung hay theo lch u s dngs chnh lch v cc tham s gia cc quyn chn c mua v bn. Trong trng hpmua bn theo chiu ln v xung, cc quyn chn c cng mt ngy o hn v chnhlch v gi thc hin. Trong trng hp mua bn theo lch, cc quyn chn c cng mtgi thc hin v khc ngy o hn. Vi chin lc mua bn chnh lch theo ngcho(25), tt c cc tham s nh gi thc hin v ngy o hn ca cc quyn chn ukhc nhau. C mt s cch khc nhau thc hin chin lc ny. Li nhun thu cthng thay i ty theo dng chin lc p dng tng t kiu mua bn theo chiuln hay theo chiu xung.

3 Chin lc kinh doanh kt hp

Chin lc kinh doanh kt hp l chin lc mua bn c quyn chn mua v bn cngmt loi chng khon c s.

(23)strike price

(24)break-even point(25)Diagonal Spreads


c EMISCOM, 4/2006


DHVP - Empirics.net


24/93


Hnh 2.10: Mua bn chnh lch theo ng cho

Bng 2.4: Li nhun t chin lc mua hng haiKhong gi Li nhun t Li nhun t Tng

c phiu quyn chn mua quyn chn bn li nhunST X 0 X ST X STST > X STX 0 STX

3.1 Chin lc mua hng haiMt trong nhng cch kt hp ph bin l chin lc mua hng hai(26). Chin lc nythc hin bng cch mua c quyn chn mua v bn vi cng mt gi thc hin v ngyo hn. Li nhun c biu din trn hnh 2.10,vigithchinlX.Nugichngkhon cng gn vi gi thc hin ti thi im o hn th chin lc ny s dn tithit hi. Song nu gi chng khon tng gim ng k th s c li nhun. Li nhunt chin lc c lit k trong bng 2.4.

Chin lc mua hng hai ph hp khi nh u t nhn thy gi c phiu s bin ngmnh song khng chc chn s bin ng theo hng no.

Chin lc mua hng hai thch hp vi c phiu ca cng ty chun b c tip qun.Nu qu trnh tip qun thnh cng, gi c phiu c th tng t bin. Ngc li nukhng thnh cng, gi c phiu c th gim nhanh chng. Trong thc t kh m kimtin d dng nh vy. Gi ca quyn chn vi cc c phiu c gi dao ng mnh nh

vy thng l cao so vi cc c phiu c gi d on khng bin ng.

Chin lc mua hng hai trong hnh 2.10 i khi cn c gi l bottom straddlehaystraddle purchase. Ngc li l chin lc top straddle haystraddle write. Chin

(26)Straddle


c EMISCOM, 4/2006


DHVP - Empirics.net


25/93

3. CHIN LC KINH DOANH KT HP

lc ny thc hin bng cch bn quyn chn mua v bn vi cng mt gi thc hin vngy o hn. y l mt chin lc c ri ro cao. Nu gi c phiu vo thi imo hn gn vi gi thc hin th s c li nhun ng k. Song nu gi c phiu chnhlch ng k v c 2 pha th thit hi s kh ln.

3.2 Chin lc Strips v Straps

Chin lc strip bao gm mt th trng v trong mt quyn chn mua v hai quynchn bn vi cng mt gi thc hin v ngy o hn. Chin lc strap bao gm mtth trng v trong hai quyn chn mua v mt quyn chn bn vi cng mt gi thchin v ngy o hn. M hnh li nhun ca hai chin lc ny c m t trong hnh2.11. Trong chin lc strip, nh u t t cc vo s tng gi ng k ca c phiu,trong khi kh nng gim gi ln hn kh nng tng gi. Trong chin lc strap, nhu t cng t cc vo s tng gi ng k ca c phiu. Song trong trng hp ny,

kh nng tng gi c phiu ln hn kh nng gim gi.

Hnh 2.11: Li nhun t chin lc Strips v Straps

3.3 Chin lc mua bn hn hpTrong chin lc mua bn hn hp(27), i khi cn gi chin lc mua bn kt hpthng ng t y (28), mt nh u t mua mt quyn chn bn v mt quyn chnmua vi cng mt ngy o hn nhng gi thc hin khc nhau. M hnh li nhunc m t trong hnh 2.12. Gi thc hin quyn chn mua X2 cao hn gi thc hinquyn chn bn X1. Hm li nhun ca chin lc mua bn hn hp ny c chotrong bng ??.

(27)Strangles(28)bottom vertical combination


c EMISCOM, 4/2006


DHVP - Empirics.net


26/93


Hnh 2.12: Li nhun t chin lc mua bn hn hp

Bng 2.5: Li nhun t chin lc mua bn theo hn hpKhong gi Li nhun t Li nhun t Tng

c phiu quyn chn mua quyn chn bn li nhunST X 0 X1 ST X1 ST

X1 < ST < X2 0 0 0ST X2 STX2 0 STX2

Chin lc mua bn hn hp gn tng t nh chin lc mua hng hai. Nh u

t t cc vo s tng gi ng k nhng khng chc chn c c phiu s tng haygim gi. So snh hnh 2.12 v hnh 2.10, c th thy cho nh u t c li nhunth gi c phiu trong chin lc mua bn hn hp phi tng mnh hn trong chinlc mua hng hai. Tuy nhin trong trng hp gi c phiu khng tng ng k th

vi cng mt gi c phiu, nh u t thc hin chin lc mua bn hn hp s chu lt hn chin lc mua hng hai.

M hnh li nhun ca chin lc mua bn hn hp ph thuc vo khong cch giahai gi thc hin. Khong cch ny cng ln th ri ro cng t v c li nhun th gic phiu cng phi tng nhiu hn.

Vic kinh doanh chin lc mua bn hn hp i khi cn c gi l chin lcmua bn kt hp thng ng t nh (29). Chin lc ny thch hp vi nh u t cphn on gi c phiu s gim. Du sao, ging nh kinh doanh mua hng hai, y lmt chin lc mo him v kh nng l ca nh u t l khng gii hn.

(29)top vertical combination


c EMISCOM, 4/2006


DHVP - Empirics.net


27/93

Chng 3

nh gi quyn chn

Vic ng dng ton hc vo trong ti chnh bt u c tip cn t th k 19. Mu bng pht hin ca Bachelier rng gi chng khon c dao ng gn ging vichuyn ng Brown trong vt l. ng cng gi rng vi mt cht chnh sa, chuynng Brown c th m hnh ha kh chnh xc dao ng gi chng khon. Tuy nhin,

y khng phi l mt m hnh ph hp hon chnh v n cho php gi chng khonnhn gi tr m. n nhng cui nhng nm 1965, khi Samuelson a ra kin rng cth dng chuyn ng Brown ly tha hoc hnh hc th m hnh s ph hp hn. K ty, lch s ngnh ton hc ti chnh chnh thc bt u. Cng vo nm ny, McKean,nh xc sut hc ni ting, a ra phng n nh gi quyn chn mua kiu M datrn l thuyt ton hc. ng xem xt vn nh gi nh mt kiu vn Dirichlet,mt lp vn ni ting trong l thuyt vt l thng k. Nhng quan st ny vn cnnh hng ln cho n nay. y cng l im khi u cho cc cng trnh nghin cuca Black - Scholes v nhng nh khoa hc khc sau ny.

Bi bo u tin v cng trnh nghin cu ca Black - Scholes b t chi ng tirt nhiu tp ch. Ngi ta khng nhn ra gi tr thc ca n ch v mt l do rtc in: n i trc thi i. Phi n nm 1973, ngi ta mi l gii c cng thctrong bi bo , khi p dng nh gi quyn chn kiu chu u trong mi trngton hc n gin. Cng thc ny by gi c bit n nh cng thc nh gi caBlack - Scholes. Khng lu sau , Merton c cng trnh nghin cu m rng ktqu trn. Cng trnh nghin cu ca c ba nh khoa hc ny xy dng y mtc ch ngu nhin nh gi quyn chn. Gii Nobel Kinh t nm 1997 c trao

cho Scholes v Merton v thnh tu ny. Tic rng, Black cht trc v khngth c tn vinh nh vy.

27


DHVP - Empirics.net


28/93

CHNG 3. NH GI QUYN CHN

1 Mt s tnh cht c bn ca hp ng quyn chnc phiu

1.1 Cc gii hn trnTrn th trng, d trong tnh hung no th gi quyn chn cng khng th vt quagi c phiu. Do , chng ta c:

c S v C S; p X v P X (1.1)

Chng minh: Gi sc > S, khi chng ta c th tn dng c hi kinh doanhchnh lch gi bng cch mua khng mt c phiu v bn quyn chn mua trn chnhc phiu . V thng tin trn th trng s nhanh chng c tn dng, v c hi kinhdoanh c li nh trn s khng tn ti c lu.

Ngoi ra, i vi quyn chn bn kiu Chu u, ti thi im o hn T khng thc gi tr ln X nn gi quyn chn ny cng khng th c gi tr ln hn gi tr hin tica X, PV(X). Theo :

P Xer(Tt)

Chng minh: Nu gi thit trn khng c tha mn, ta c th tn dng c libng cch bn khng mt quyn chn kiu Chu u ly P v cho vay P vi li sut phiri ro trn th trng. n thi im o hn, thc thi quyn chn vi gi X v nhnc phn li vn cng vi li sut thu c trn khon cho vay.

1.2 Gii hn di ca quyn chn khng tr c tc

1. i vi quyn chn mua kiu Chu u

c > SXer(Tt) (PV(X)) (1.2)

Chng minh: Lp hai danh mc u t A v B nh sau:

A gm 1 quyn chn mua v mt khon tin tr gi Xer(Tt)

B gm 1 c phiuGi t l mt thi im bt k no trong k hn ca quyn chn; v T l thiim o hn ca quyn chn y, ta c:

Danh mc Gi tr ti t Gi tr ti TST < X ST > X

A c + Xer(Tt) 0 + X STB S ST ST

Ti T, gi tr A gi tr B. Nn ti t gi tr A > B. D dng chng minhc + Xer(Tt) > ST.


c EMISCOM, 4/2006


DHVP - Empirics.net


29/93

1. MT S TNH CHT C BN CA HP NG QUYN CHN C PHIU

2. i vi quyn chn bn kiu Chu u

Gii hn di ca quyn chn bn kiu Chu u khng chi tr c tc l:

P > Xer(Tt) (1.3)

Bng cch lp hai danh mc tng t nh trn vi quyn chn bn, ta c th ddng chng minh c iu ny.

3. i vi quyn chn mua kiu M

i vi quyn chn mua kiu M khng nn thc hin sm, v thc hin smkhng ti u.

Chng minh: Thit lp 2 danh mc u t

A gm 1 quyn chn mua kiu M v 1 khon tin Xer(Tt); B gm 1 c phiu

Gi s ti thi im t

< T no ngi nm gia quyn chn mua thc thi quynchn vi iu kin gi c phiu ln hn gi thc thi, St > X. Ta c:

Danh mc Gi tr ti t Gi tr ti t

Gi tr ti T

A C+ Xer(Tt) (St

X) + Xer(Tt

) Max (ST, X)B S St ST

So snh Gi tr B > gi tr A Gi tr A gi tr B

Cho d ti t

gi c phiu c vt qu gi thc hin quyn chn mua, cng khngnn thc hin sm. V gi tr ca danh mc B vn ln hn danh mc A. Nu cthc hin, nn thc hin ti thi im o hn. Nh vy, gi ca quyn chn muakiu Chu u v quyn chn mua kiu M l nh nhau. HayC = c. Theo , giihn di ca quyn chn mua kiu M khng tr c tc s l:

C > S

Xer(Tt) (PV(X)) (1.4)

4. i vi quyn chn bn kiu M

Gii hn di l:P SX (1.5)

Chng minh: Bng cch lp 2 danh mc u t A v B

A gm 1 quyn chn bn kiu M v 1 c phiu; B gm 1 khon tin Xer(Tt).

Tnh ton tng t ta chng minh c P > SXer(T

t)

. Khi t tin n T thP > SX.


c EMISCOM, 4/2006


DHVP - Empirics.net


30/93


1.3 Gii hn di ca quyn chn tr c tc

1. i vi quyn chn mua kiu Chu uGi D l gi tr hin ti ca khon c tc phi tr. D thy gii hn di ca gi

quyn chn ch thay i: c > SD Xer(T

t)

.2. i vi quyn chn bn kiu Chu u

p > D + Xer(Tt) S.3. i vi quyn chn mua kiu M: trong trng hp c tr c tc th quyn chn

bn kiu M c th c thc hin trc thi hn v khi tr c tc, gi s gim.

4. i vi quyn chn bn kiu M: cc bt ng thc trn khng cn ng na.

1.4 Mi quan h gia quyn chn mua v quyn chn bn

i vi nhng cp quyn chn mua v quyn chn bn trn cng mt loi c phiu vc cng thi gian o hn s c nhng h thc lin h gi ca chng. Cc quyn chnkiu Chu u do thi im thc hin l xc nh nn tn ti cc ng thc cho phpta tnh ton gi ca quyn chn mua thng qua gi quyn chn bn hoc ngc li. Cni vi nhng cp quyn chn kiu M, ch tn ti nhng bt ng thc cho php xcnh mi quan h m thi.

H thc cp i mua bn vi quyn chn kiu Chu u

Trong trng hp khng c c tc

c + Xer(Tt) = p + S (1.6)Nh vy, h thc trn cho php tnh ton gi mt quyn chn mua nu bit gi quynchn bn trn cng mt loi c phiu (hay c th m rng cho cng mt loi ti sn cs) vi cng mt thi gian o hn.

chng minh h thc ny, ta tnh ton tng t nh trn vi gi tr ca 2 danhmc u t tng ng A v B:

A gm 1 quyn chn bn v 1 khon tin Xer(Tt);

B gm 1 quyn chn mua v 1 c phiu.

Trong trng hp tr c tcH thc cp i mua bn tr thnh:

c + Xer(Tt) + D = p + S (1.7)

Cc bt ng thc lin quan n quyn chn kiu M

Trong trng hp tr c tc

SXer(Tt) > C P > SX (1.8)Trong trng hp tr c tc

SD X < C P < SXer(Tt) (1.9)


c EMISCOM, 4/2006


DHVP - Empirics.net


31/93

2. NH GI QUYN CHN

2 nh gi quyn chn

2.1 nh gi quyn chn cy nh phn

Mt k thut nh gi chng khon hay cc cng c phi sinh rt hu hiu v ph binl cy nh phn.

M hnh quyn chn cy nh phn mt bc

Gi s gi c phiu hin ti l $20 v sau 3 thng c th l $22 v $18. Gi thit rng cphiu khng tr c tc v nh gi mt quyn chn chu u mua c phiu ny vi gi$21 vi thi gian o hn l 3 thng. Quyn chn ny s c mt trong hai gi tr sau 3thng na. Nu gi c phiu tng ln $22 th gi ca quyn chn s l $1; ngc li nugi c phiu gim xung $18 th gi ca quyn chn bng khng. iu ny c minhha trong hnh 3.1.

Hnh 3.1: Minh ho bng s thay i gi c phiu

Lun c nh gi quyn chn ny khng phc tp, gi nh rng nh u t khngc c hi kinh doanh da vo chnh lch gi. Chng ta lp mt danh mc u t cac phiu v quyn chn sao cho gi danh mc u t sau 3 thng na c xc nh cth. V danh mc u t khng c ri ro, cho nn li nhun thu c phi bng t l lisut phi ri ro. iu ny gip gim chi ph lp danh mc u t v do gim c gi

ca quyn chn. V ch c hai loi chng khon (l c phiu v quyn chn) v ch chai h qu, nn c th a ra mt danh mc u t phi ri ro.

Hy xem xt mt danh mc u t bao gm mt th trng v trong c phiu vmt th on v trong mt quyn chn mua. Tnh c gi ca cho danh mc ut ny l phi ri ro. Nu gi c phiu tng t 20 n 22, th gi ton b c phiu l 22

v gi ca quyn chn l 1, do vy tng gi tr ca danh mc u t l 22 1. Nu gica c phiu gim t 20 xung 18 th gi ca ton b c phiu l 18 v gi ca quynchn l 0, do tng gi tr ca danh mc u t l 18. Danh mc u t l phi riro nu gi tr ca c chn sao cho tng gi tr ca danh mc u t khng i bt

k gi c phiu thay i th no, c ngha l:


c EMISCOM, 4/2006


DHVP - Empirics.net


32/93


22 1 = 18hay:

= 0.25

Do , mt danh mc u t phi ri ro l:

Th trng v: 0.25 c phiu

Th on v: 1 quyn chn

Nu gi c phiu ln ti 22, gi tr ca danh mc u t l:

22 0.25 1 = 4.5Nu gi c phiu gim xung 18, gi tr ca danh mc u t l:

18 0.25 = 4.5Nh vy l d gi c phiu tng hay gim, gi tr ca danh mc u t lun l 4.5 vothi im o hn.

Trong trng hp khng c c hi kinh doanh da vo chnh lch t gi th danhmc u t phi ri ro phi c li sut phi ri ro. Gi thit trong trng hp ny li sutphi ri ro l 12% mt nm. C ngha l gi tr hin ti ca danh mc u t tng ng

vi gi tr 4.5 sau 3 thng l:

4.5e0.120.25 = 4.367

Gi tr ca c phiu ti thi im hin ti l 20. Gi s gi c phiu c th hinbng f. Do , gi tr ca danh mc u t hin ti l:

20 0.25 f = 5 fsuy ra:

f = 0.633

iu ny chng t rng nu khng c c hi kinh doanh da trn chnh lch v tgi th gi tr hin ti ca quyn chn phi l $0.633. Nu gi tr ca quyn chn lnhn $0.633, chi ph lp danh mc u t nh hn $4.367 v s c li cao hn li sut

phi ri ro. Nu gi tr ca quyn chn nh hn $0.633, bn khng danh mc u t lcch vay mt khon tin vi li sut thp hn li sut phi ri ro.


c EMISCOM, 4/2006


DHVP - Empirics.net


33/93

2. NH GI QUYN CHN

Tng qut ha C th tng qut ha quan im trn bng cch xem xt mt c phiukhng tr c tc, gi c phiu l S v mt cng c phi sinh vi c phiu c gi hinthi l f . Thi im hin ti l mc thi gian. Gi thit rng cng c phi sinh cho linhun vo thi im T , v rng trong thi gian tn ti cng c phi sinh, gi c phiuc th tng t S ln Su hoc gim t S xung Sd (u > 1; d < 1). Gi c phiu tng t lthun khi xu hng i ln l u - 1; gi gim t l thun khi i xung l 1 - d . Nu gi cphiu tng ln Su , gi thit rng li nhun thu c t cng c phi sinh l fu; nu gic phiu gim xung Sd , gi thit rng li nhun thu c t cng c phi sinh l fd.Tnh hung ny c m t trong hnh 3.2.

Hnh 3.2: Gi c phiu v cng c phi sinh trong cy nh phn mt bc

Vn nh trn, xem xt mt danh mc u t bao gm mt th trng v vi cphiu v mt th on v vi mt cng c phi sinh. Tnh ton gi tr ca sao chodanh mc u t l phi ri ro. Nu gi c phiu tng th gi tr ca danh mc u t

vo thi im o hn ca cng c phi sinh l:

Su fu

Nu gi c phiu gim th gi tr ny tr thnh:

Sd fdt hai i lng ny bng nhau:

Su fu = Sd fdhay:

= fu fdSu Sd (2.10)


c EMISCOM, 4/2006


DHVP - Empirics.net


34/93


Trong trng hp ny danh mc u t l phi ri ro v phi c li sut phi ri ro.Cng thc 2.10 cho thy l t l thay i trong gi cng c phi sinh so vi gi cachng khon khi thay i t nt ny sang nt kia ti thi im T.

t r biu din t l li sut phi ri ro, gi tr hin ti ca danh mc u t l:

(Su fu)erTGi tr lp danh mc u t l:

S fKt qu l:

(Su fu)erT = S fThay t phng trnh 2.10 v n gin ha, cn li

f = erT[pfu + (1 p)fd] (2.11)Trong

p =erT du d (2.12)

Cng thc 2.11 v 2.12 gip nh gi mt cng c phi sinh s dng m hnh cy nhphn mt bc.

Xt li v d vi s c th xem xt trn, vi u = 1.1, d = 0.9, r = 0.12, T =0.25, fu = 0. T cng thc 2.12:

p = e0.030.91.10.9 = 0.6523

v t cng thc 2.11

f = e0.03[0.6523 1 + 0.3477 0] = 0.633Kt qu ny cng trng vi kt qu tnh phn trc.

S khng thch hp trong cch tnh li nhun k vng ca c phiu Cngthc nh gi cng c phi sinh 2.11 khng tnh n kh nng gi c phiu tng haygim. V d, theo cng thc ny th khi xc sut gi c phiu tng l 0.5 hay 0.9 s vntnh ra cng mt gi quyn chn chu u. iu ny tht khng hp l. Gi nh rngkhi gi c phiu tng th ng nhin gi tr ca quyn chn mua c phiu tng vgi tr quyn chn bn gim.

L do ch yu l chng ta khng nh gi quyn chn theo nh ngha tuyt i.Chng ta tnh ton gi tr ca n da trn gi ca chng khon c s. Kh nng gi tnghay gim c xem xt da trn gi c phiu. iu c ngha l chng ta khng

cn xem xt n thay i gi ca quyn chn khi nh gi quyn chn da trn gic phiu.


c EMISCOM, 4/2006


DHVP - Empirics.net


35/93

2. NH GI QUYN CHN

nh gi trung lp ri ro

(1) Mc d khng cn phi gi nh v xc sut tng hay gim gi rt ra c cngthc 2.11 song cng c th coi bin p trong cng thc 2.11 l xc sut gi c phiu tng.

Do bin 1 - p l xc sut gi c phiu gim v cng thc

pfu + (1 p)fdl li nhun k vng t cng c phi sinh. Theo cch hiu bin p nh vy, cng thc2.11 cho thy gi tr ca cng c phi sinh thi im hin ti chnh l gi tr k vngtng lai khu tr li phi ri ro.

Chng ta li xem xt s tin thu vo k vng t c phiu khi xc sut gi c phiutng l p. Gi c phiu k vng ti thi im T, E(ST) c tnh bng:

E(ST) = pSu + (1 p)Sdhoc

E(ST) = pS(u d) + SdThay p t cng thc 2.12 vo s c

E(ST) = SerT (2.13)

cho thy gi c phiu tng trung bnh ti li sut phi ri ro. Nh vy gi nh xc sutgi c phiu tng bng p tng ng vi gi nh li sut ca c phiu bng li sutphi ri ro.

Chng ta s xem xt mt mi trng m mi ngi u khng b cc ri ro nhhng n, gi tn l mi trng trung lp cc ri ro (2). Trong mi trng cc nhu t khng phi bi thng ri ro, v li sut k vng ca tt c mi chng khon ul li sut phi ri ro. Cng thc 2.13 cho thy gi thit gi c phiu tng vi xc sut lp. Cng thc 2.11 cho thy gi tr ca cng c phi sinh l li nhun k vng trong mtmi trng trung lp cc ri ro khu tr li phi ri ro.

Kt qu ny l mt v d minh ho cho mt nguyn tc chung ca nh gi quynchn, gi l nguyn tc nh gi trung lp ri ro.

Xem xt li v d v cy nh phn mt bc minh ha r hn nguyn tcnh gi trung lp ri ro, hy xem xt li v d c m t trong hnh 3.1. Gi ca cphiu hin ti l $20 v s c th tng ln $22 hoc gim xung $18 sau thi hn 3thng. Cng c phi sinh c xem xt y l quyn chn mua chu u vi gi thchin l $21 v thi gian o hn l 3 thng. Li sut phi ri ro l 12%/nm.

(1)Risk-Neutral Valuation(2)risk-neutral world


c EMISCOM, 4/2006


DHVP - Empirics.net


36/93


Chng ta biu din xc sut gi c phiu tng trong mi trng trung lp ri ro l p.Trong mi trng ny t sut li nhun k vng ca c phiu phi bng li sut phi riro, 12%. iu ny c ngha l p tha mn

22p + 18(1p) = 20e0.120.25hoc

4p = 20e0.120.25 18Khi , p phi bng 0.6523.

Sau 3 thng, xc sut quyn chn mua tng gi ln 1 l 0.6523 v xc sut gimgi xung 0 l 0.3477. Gi tr k vng ca quyn chn mua ny l

0.65231 + 0.3477 0 = $0.6523Khu tr vi li sut phi ri ro th gi tr ca quyn chn hin ti l

0.6523e0.120.25

hay bng $0.633. Gi tr ny bng gi tr tnh ra lc trc, biu th rng gi thitkhng kinh doanh da trn chnh lch v t gi v nh gi trung lp ri ro c cng mtkt qu.

Cy nh phn hai bc

Chng ta c th m rng phn tch cho m hnh cy nh phn hai bc nh trong hnh3.3. y gi c phiu hin ti l $20 v ti mi bc gi c th tng hay gim 10%.Gi s rng di ca mt bc l 3 thng v li sut phi ri ro l 12%/nm. Cng nhtrn, xem xt mt quyn chn mua vi gi thc hin l $21.

Mc tiu ca phn tch ny l tnh ton gi quyn chn ti nt u ca cy. iuny c th c thc hin bng cch p dng lin tip cc nguyn tc c thit lp pha trn. Hnh 3.4 m t hnh cy ging hnh 3.3, vi gi c phiu pha trn v giquyn chn pha di mi nt. D tnh c gi quyn chn ti nt cui cng ca cy.N chnh bng li nhun c c t quyn chn. nt D gi c phiu l 24.2 v gi

quyn chn l 24.2 - 21 = 3.2; ti nt E v F, quyn chn l out of the money v gi trca quyn chn ny bng 0.

Ti nt C gi ca quyn chn bng 0, v nt C dn ti nt E hoc nt F, v gi quynchn ti hai nt ny u bng 0. Tnh ton gi quyn chn ti nt B bng cch ch n nhnh ny ca cy trong hnh 3.5. S dng nhng gi thit trn, vi u = 1.1, d =0.9, r = 0.12, T = 0.25, v p = 0.6523, thay vo cng thc 2.11 c gi tr ca quynchn ti nt B. e0.120.25(0.6523 3.2 + 0.3477 0) = 2.0257

tnh ton gi quyn chn ti nt A ban u, tp trung vo bc u tin ca cy.

Gi tr ca quyn chn ti nt B l 2.0257 v ti nt C l 0. Do , cng thc 3.2 tnhc gi tr ca nt A l


c EMISCOM, 4/2006


DHVP - Empirics.net


37/93

2. NH GI QUYN CHN

Hnh 3.3: Gi c phiu trong cy nh phn hai bc

Hnh 3.4: Gi c phiu v cng c phi sinh trong cy nh phn hai bc

(3)


c EMISCOM, 4/2006


DHVP - Empirics.net


38/93


e0.120.25(0.65232.0257 + 0.3477 0) = 1.2823Gi ca quyn chn l $1.2823.

Lu rng v d ny c xy dng vi u v d (t l tng v gim gi) l nh nhauti mi nt ca cy v vi khong thi gian t nt ny ti nt kia l nh nhau. Gi thitny dn n xc sut trung lp ri ro p, c tnh bng cng thc 2.12, l nh nhau choton b cc nt.

Tng qut ha Tng qut ha trng hp hai bc bng cch xem xt tnh hungtrong hnh 3.6. Gi c phiu lc u l S. Sau mi khong thi gian, gi c th tng uln hoc gim d ln gi gc. Gi ca cng c phi sinh c ghi ch trn cy. Gi srng li sut phi li nhun l r v khong thi gian t nt ny ti nt kia l t nm.

ng dng cng thc 2.11

fu = ert[pfuu + (1 p)fud] (2.14)

fd = ert[pfud + (1 p)fdd] (2.15)

f = ert[pfu + (1 p)fd] (2.16)Thay cng thc 2.14 v 2.15 vo 2.16

f = e2rt

[p2

fuu + 2p(1 p)fud + (1 p)2

fud] (2.17)

iu ny ph hp vi nguyn l nh gi trung lp ri ro c cp trn y. Ccbin p2, 2p(1 p), v(1 p)2 l xc sut t ti cc nt cao, trung bnh v thp. Gi cacng c phi sinh bng vi gi li nhun k vng trong mt mi trng khng b ri rotc ng n.

Hnh 3.5: nh gi c phiu ti nt B


c EMISCOM, 4/2006


DHVP - Empirics.net


39/93

2. NH GI QUYN CHN

Nu tng qut ha vic s dng cy nh phn bng cch thm cc bc th nguyntc nh gi trung lp ri ro vn p dng c. Gi ca cng c phi sinh lun bng vigi li nhun k vng trong mt mi trng khng b ri ro tc ng n, tr i li phiri ro.

V d vi quyn chn bn

Nguyn l trn c th p dng nh gi cho bt k cng c phi sinh no ph thucvo c phiu c gi thay i theo kiu nh phn. Hy xem xt trng hp mt quynchn bn chu u vi thi hn 2 nm, gi thc hin l 52, chng khon c s c gihin thi l 50. Gi thit rng c hai thi k trong mt nm v mi thi k gi c phiuc th tng vi t l 20% hoc gim vi t l 20%, li sut phi ri ro l 5%.

S hnh cy c biu din trong hnh 3.7. Gi tr ca xc sut trung lp ri ro p

c tnh bng

p = e0.0510.81.20.8 = 0.6282

Gi c phiu cui cng c th t ti l 72, 48 v 32. Trong trng hpfuu = 0, fud = 4, fdd = 20, vt = 1. S dng cng thc 2.17 tnh c

f = e20.051(0.62822 0 + 2 0.6282 0.3718 4 + 0.37182 20) = 4.1923Gi tr ca quyn chn bn l $4.1923. Cng c th tnh c kt qu ny bng cch

s dng cng thc 2.11 v ln ngc li cy theo mi thi k. Hnh 3.7 biu din gi

quyn chn mua trung gian c tnh ton.

Hnh 3.6: Gi c phiu v cng c phi sinh trong cy nh phn hai bc


c EMISCOM, 4/2006


DHVP - Empirics.net


40/93


Quyn chn mua kiu M

Ngoi quyn chn mua kiu chu u, phng php cy nh phn cn c dng nh gi quyn chn mua kiu M. Quy trnh tnh ton l i t ngn n gc cy, kim

tra ti mi nt xem liu vic thc hin trc c ti u khng. Gi tr ca quyn chnti nt cui cng bng gi tr quyn chn kiu chu u. nhng nt pha trn gi trca quyn chn l gi tr cao nht trong hai gi tr sau

1. Gi tr tnh theo cng thc 2.11.

2. Li nhun t vic thc hin trc.

minh ha, xem xt hnh 3.7 thay i ra sao khi quyn chn l kiu M ch khngphi kiu chu u. Gi c phiu v xc sut thay i gi vn nh trc. Gi tr caquyn chn ti nt cui cng khng thay i. nt B, cng thc 2.11 cho gi tr quyn

chn l 1.4147, trong khi li nhun t vic thc hin trc l m (= -8). R rng l victhc hin trc khng ti u nt B v gi tr ca quyn chn ti nt ny l 1.4147. Tint C, cng thc 2.11 cho gi tr quyn chn l 9.4636, trong khi li nhun t vic thchin trc l 12.0. Trong trng hp ny vic thc hin trc l ti u v gi tr caquyn chn l 12.0. nt ban u A, gi tr tnh c theo cng thc 2.11 le0.051(0.6282 1.4147 + 0.3718 12.0) = 5.0894trong khi li nhun thu c t vic thc hin trc l 2.0. Trong trng hp ny, victhc hin trc khng ti u. Do , gi tr ca quyn chn l $5.0894. Hnh 3.8 mt nhng gi tr ca cy nh phn tng ng.

Hnh 3.7: S dng cy nh phn hai bc nh gi quyn chn mua kiu Chu u

(4)


c EMISCOM, 4/2006


DHVP - Empirics.net


41/93

2. NH GI QUYN CHN

2.2 M hnh Black-Scholes

Gi nh v s bin ng ca gi c phiu

Mi m hnh nh gi quyn chn u cn t ra mt s gi nh v s bin ng ca gic phiu theo thi gian. Gi nh ny cho php ngi tnh ton c th c nh hng

v bin ng ca gi quyn chn c phiu sau mt giai on nht nh.

Vi m hnh Black-Scholes, gi nh c bn c t ra l gi chng khon binng ngu nhin lin tc. Gi nh ny c ngha: mi iu chnh ca gi c phiutrong mt khong thi gian ngn s tun theo quy lut phn phi chun.

t:: T sut li nhun k vng ca c phiu.: bt n ca gi c phiu.

Gi tr trung bnh ca cc bin ng trong khong thi gian t l t. lch chunca cc bin ng nyn l

t. Gi nh ca m hnh Black-Scholes c vit li nh

sau:

S

S (t,

t) (2.18)

trong S l bin ng ca ca S trong khong thi gian t v (m, s) th hinmt phn phi chun vi gi tr trung bnh m v lch chun s.

Phn phi L-ga chun

Gi nh bin ng ngu nhin lin tc ca gi c phiu nh nu trn a chngta n kt lun gi c phiu ti bt k thi im no trong tng lai s c phn phil-ga chun. Ta c th thy dng tng qut ca mt phn phi l-ga chun hnh 3.9,

Hnh 3.8: S dng cy nh phn hai bc nh gi quyn chn bn kiu M

(5)


c EMISCOM, 4/2006


DHVP - Empirics.net


42/93


phn phi loi ny ch nhn gi tr khng m, trong khi vi gi tr phn phi chunnh hnh 3.10 th c th nhn gi tr m. Bn cnh cng c th thy mt phn phichun c dng i xng qua im gi tr 0 cn phn phi l-ga chun li lch, gi trtrung bnh, trung v v mod u khc nhau.

Hnh 3.9: Phn phi L-ga chun

Hnh 3.10: Phn phi chun

Bin c phn phi l-ga chun c c im l cc gi tr l-ga-rt t nhin ca nc phn phi chun. Do , t gi nh ca m hnh Blacks-Scholes ta c ln ST phnphi chun, trong ST l gi c phiu thi im T trong tng lai. Gi tr trung bnh

v lch chun ca ln ST c vit nh sau:

ln S+ ( 2

2)T

v

T

S l gi c phiu thi im hin ti. Ta c th vit li:


c EMISCOM, 4/2006


DHVP - Empirics.net


43/93

2. NH GI QUYN CHN

ln ST

ln S+

(

2

2

)T,

T

(2.19)

Gi tr k vng hay gi tr trung bnh E(ST) ca ST l:E(ST) = Se

T (2.20)

Kt qu ny ph hp vi nh ngha l t sut li nhun k vng ca c phiu.Phng sai ca var(ST) c tnh nh sau:

var(ST) = S2e2T(e

2T 1) lm r nhng cng thc trn, ta kho st qua v d di y:

V d 2.1 Xt mt c phiu vi gi ban u l 40$, t sut li tc k vng l

16%/nm, bt n l 20%/nm. T cng thc 2.19, ta c th m t phn phi gic phiu trong 6 thng u nh sau:

ln ST

ln 40 +

(0.16 0.2

2

2

)0.5, 0.2

0.5

hayln ST (3.759, 0.141)

C 95% kh nng mt bin phn phi chun nhn gi tr trong khong 2 mc bin lch chun so vi gi tr trung bnh. Vi lch chun l 1.96 v 95% m bo ta c:

3.759 1.96 0.141 < ln ST < 3.759 + 1.96 0.141tng ng

e3.477 < ln ST < e4.041

hay

32.26 < ST < 56.88

Nh vy c 95% kh nng gi c phiu trong 6 thng s nm trong khong 32.36 v56.88. Gi tr trung bnh v phng sai ca ST l :

40e0.16

0.5

= 43.33v

402e20.160.5(e0.20.20.5 1) = 37.93

T cng thc 2.19 ta c th suy ra:

lnSTS

(

2

2

)T,

T

(2.21)

Vi T = 1 biu thc ln STS

l mc li nhun tnh gp lin tc ca c phiu trong 1 nm.

Gi tr trung bnh v lch chun ca li nhun tnh gp lin tc trong 1 nm ln ltl 2/2 v .


c EMISCOM, 4/2006


DHVP - Empirics.net


44/93


Li nhun k vng

Li nhun k vng m nh u t yu cu t mt loi c phiu ph thuc vo riro ca c phiu . Ri ro cng cao th li nhun k vng cng ln. Ngoi ra, li nhun

k vng cng ph thuc vo li sut trong nn kinh t. Li sut phi ri ro cng cao thli nhun k vng cng s cng cao. Tuy nhin, trong phm v nghin cu quyn chnc phiu, ta khng nht thit phi i su nghin cu cc c tnh ca . Nghin cucho thy gi tr ca quyn chn c phiu, khi c th hin qua gi tr ca c phiu cs, khng h ph thuc vo .Gi tr trung bnh ca cc t sut li nhun thu c trong nhiu nm khng nht thitphi bng vi li nhun bnh qun nm trong giai on , tr khi tt c cc nm uc t sut li nhun bng nhau. C th thy rt r iu ny, qua v d: Gi s ta u t100$ trong 5 nm, t sut li nhun mi nm l 15%, 20%, 30%, -20%, 25%. Trung

bnh s hc ca cc mc t sut li nhun ny l 14% (tnh bng cch ly tng nm gi

tr chia cho 5). Li nhun tnh gp lin tc sau 5 nm s l:100 1.145 = 192.54U SD.

Tuy nhin gi tr thc t thu v sau 5 nm l100 1.15 1.20 1.30 0.80 1.25 = 179.40U SD

tng ng vi 1.79401/5 1 = 0.124 tc l 12.4%

R rng c lch nht nh gia li nhun bnh qun trong giai on v bnh qunli nhun cc nm.

bt n

bt n ca c phiu, , l thc o mc khng chc chn v li nhun s thuc t c phiu. c gi tr nh hn 1 v thng th hin theo ga tr phn trm.T cng thc 2.21, ta c th a ra nh ngha tng i chnh xc v bt n nhsau:

bt n ca gi c phiu l lch chun ca li nhun thu c t c phiu trongvng mt nm vi li nhun c tnh gp lin tc.

T l s xp x gn ng lch chun ca bin ng gi chng khon trong khongthi gian T. Nh th bt n ca gi chng khon s tng tng ng vi cn bc 2ca khong thi gian xem xt ch khng tng tuyn tnh.

c lng bt n t d liu qu kh

bt n ca gi c phiu c th c lng bng cch s dng d liu bin ng gitrong qu kh. Gi c phiu thng c quan st trong nhng khong thi gian cnh (chng hn hng ngy, hng tun, hoc hng thng).t:

n + 1 s quan stSi gi c phiu cui giai on quan st th i (i=0,1,. . . ,n)

di ca khong thi gian quan st tnh theo nmv t:


c EMISCOM, 4/2006


DHVP - Empirics.net


45/93

2. NH GI QUYN CHN

ui = ln

(Si

Si1

)

lch chun s ca cc ui c tnh theo cng thc:

s =

1n1

ni=1(ui u)2

hay

s =

1

n1n

i=1 ui2 1

n1

(ni=1 ui

)2

vi u l gi tr trung bnh ca cc ui.T cng thc 2.21 ta c lch chun ca ui l

. Do bin s l gi tr c lng

ca . c th c c lng theo vi: = s

Sai s chun ca php c lng ny c th coi xp x

2n chn c mt gi tr ph hp cho n khng d. Thng thng cng nhiu d liuthng k th kt qu tnh ton cng chnh xc, tuy nhin c gi tr thay i theo thigian. Do d liu qu c c th khng thch hp n kt qu d bo tng lai. gii quyt vn ny, vic tnh ton cc nc Chu u v M thng s dng ging ca hng ngy trong vng 90 hoc 180 ngy gn nht. Bn cnh , vic tnh

ton thng k cng gp phi vn v vic la chn tnh v s dng tham s v btn theo lch thng hay theo s ngy giao dch.

V d 2.2 c tnh bt n

Bng 3.1 m t d liu giao dch c phiu trong 21 ngy lin tip. Trong v d ny:ui = 0.09531 v

ui

2 = 0.00333

ta cng c tnh c lch chun ca li nhun ngy l:

0.0033319

0.95312

380= 0.0123

Gi nh mt nm c 252 ngy giao dch, = 1/252, d liu cho php c lng btn bnh qun nm l 0.0123

252 = 0.195. Nh vy bt n c tnh l 19.5% mt

nm. Sai s chun c tnh nh sau:

0.195220 = 0.031

tc 3% mt nm.Nhng phn tch m t trn u c thc hin vi gi thit c phiu c xemxt khng tr c tc. Vic phn tch c th iu chnh tng thch trong trng hp

c phiu c tr c tc. Li nhun ui thu c trong khong thi gian theo di c ngytr c tc l:


c EMISCOM, 4/2006


DHVP - Empirics.net


46/93


Bng 3.1: Tnh ton bt n

Gi ng ca Tng quan gi Li nhun ngyNgy ($) Si/Si

1 ui = ln

SiSi1

0 201 201

8

2 1978

0.98758 -0.012503 20 1.00629 0.006274 201

21.02500 0.02469

5 2014

0.98781 -0.012276 207

81.03086 0.03040

7 2078

1.00000 0.000008 207

81.00000 0.00000

9 2034

0.99401 -0.00601

10 2034 1.00000 0.0000011 21 1.01205 0.0119812 211

81.00595 0.00593

13 2078

0.98817 -0.0119014 207

81.00000 0.00000

15 2114

1.01796 0.0178016 213

81.00588 0.00587

17 2138

1.00000 0.0000018 211

40.99415 -0.00587

19 2134

1.02353 0.02326

20 22 1.01149 0.01143


c EMISCOM, 4/2006


DHVP - Empirics.net


47/93

2. NH GI QUYN CHN

ui = lnSi+DSi1

trong D l lng c tc thanh ton. Li nhun thu c trong nhng khong thigian theo di khc s vn l

ui = lnSi

Si1

Thu l mt yu t quan trng cn xem xt trong xc nh li nhun thu c t cphiu xung quanh ngy giao dch khng hng c tc. Do vy, s tt hn nu ta loiring ra d liu trong nhng khong quan st c ngy giao dch khng hng c tc.

Gi nh c bn ca m hnh Black-Scholes

Black v Scholes khi xy dng m hnh nh gi quyn chn a ra nhng gi nh

sau:1. Gi c phiu s bin ng theo th l-ga chun vi cc hng s v nh

trnh by phn trn;

2. Mi giao dch s b qua chi ph v thu. Gi ca tt c cc chng khon u cth c chia nh v hn;

3. C phiu s khng tr c tc trong thi gian quyn chn c hiu lc;

4. Khng tn ti c hi kinh doanh chnh lch gi phi ri ro;

5. Hot ng giao dch chng khon din ra lin tc;6. Nh u t c th vay hoc cho vay ti cng mt mc li sut phi ri ro;

7. Li sut phi ri ro trong ngn hn, r, l hng s.

Trn c s m hnh ca Black v Scholes, nhiu nh nghin cu phn tch v gimnh dn rng buc ca mt s gi nh. Chng hn, mt m hnh bin i t m hnhBlack-Scholes cho php tnh vi r v l cc hm ph thuc vo thi gian, mt mhnh bin i khc cng cho php tnh c trong trng hp c phiu c tr c tctrong gian on quyn chn cn hiu lc (m hnh ny s c nghin cu phn tip

theo).

Phn tch Black-Scholes/Merton

Phn tch Black-Scholes/Merton tng t vi phn tch trong trng hp khng ckinh doanh chnh lch gi nh gi quyn chn khi gi c phiu bin i theo mhnh cy nh phn. Ngi ta xy dng mt danh mc u t phi ri ro bao gm c mtquyn chn (vi v th nht nh) v mt c phiu c s. Khi khng tn ti c hi kinhdoanh chnh lch gi, li nhun thu c t danh mc u t ny s tng ng vili sut phi ri ro r. Khi quyn chn phi p ng mt phng trnh vi phn iukin.

C s lp mt danh mc u t phi ri ro l ngun gc chung v tnh bt n nhhng n gi c phiu v gi quyn chn - l bin ng gi c phiu. Trong


c EMISCOM, 4/2006


DHVP - Empirics.net


48/93


khong thi gian rt ngn, gi ca mt quyn chn mua c tng quan dng honho (tuyt i) vi bin ng ca gi c phiu c s; gi ca quyn chn bn s ctng quan m hon ho (tuyt i). Trong c hai trng hp, khi c th xy dngc mt danh mc u t hp l bao gm quyn chn v c phiu c s ca quynchn , li hay l t c phiu s b p li hay l t quyn chn, do gi tr cadanh mc u t vo cui giai on s c th c d bo trc mt cch chc chn.Gi s ti mt thi im bt k mi tng quan gia mc iu chnh S rt nh ca gic phiu v mc iu chnh cng gp c rt nh trong gi mt quyn chn mua Chu

u c xc nh theo cng thc:

c = 0.4S

iu ny c ngha l dc ca ng thng th hin mi tng quan gia c v S l0.4 (xem hnh 3.11). Danh mc u t phi ri ro s bao gm:

1. 0.4 c phiu th trng v;

2. Mt quyn chn mua th on v (bn quyn chn mua) .

Hnh 3.11: Tng quan gia c v S

im khc bit c bn gia phn tch Black-Scholes/Merton vi phn tch theo mhnh cy nh phn l tnh phi ri ro ca v th c xc lp ch ng trong khong thigian rt ngn. (Trn l thuyt, tnh phi ri ro ch xut hin trong 1 khong thi gianmang tnh thi im.) duy tr tnh phi ri ro cn lin tc iu chnh v ti cn bngdanh mc u t. Chng hn mi tng quan gia c v Sc th thay i tc = 0.4Sthnh c = 0.5S trong 2 tun na. Nh th s cn phi c 0.5 c phiu bn miquyn chn bn. Tuy nhin li nhun thu c t danh mc u t phi ri ro mi

thi im s vn bng vi li sut phi ri ro. y l c s cho lp lunBlack-Scholes/Merton v a n m hnh nh gi ca h.


c EMISCOM, 4/2006


DHVP - Empirics.net


49/93

2. NH GI QUYN CHN

M hnh nh gi

Cng thc tnh gi quyn chn mua v bn kiu Chu u ca Black-Scholes p dngvi nhng c phiu khng tr c tc nh sau:

c = SN(d1)XerTN(d2) (2.22)

p = XerTN(d2) SN(d1)trong :

d1 =ln(S/X)+(r+2/2)T

T

d2 =ln(S/X)+(r2/2)T

T

= d1

T

Hm N(x) l hm xc sut tch ly cho mt bin phn phi chun ha. Ni cch khcn th hin xc sut mt bin phn phi chun (0, 1) c gi tr nh hn x (hnh 3.12).Cc bin khc trong cng thc 2.22 v 2.23 l: c v p gi quyn chn bn v quynchn mua kiu Chu u, S l gi c phiu, X l gi thc hin, r l li sut phi ri ro, Tl thi gian cn li cho n thi im thc thi quyn v l bt n ca gi c phiu.Do gi quyn chn mua kiu MC bng gi quyn chn mua kiu Chu u c i vi cphiu khng tr c tc nn cng thc 2.22 cng c dng tnh gi ca mt quynchn kiu M.

Hnh 3.12: Khong mu xm th hin N(x)

Trn l thuyt, cc cng thc Black-Scholes ch ng nu li sut trong ngn hn r lmt hng s. Trn thc t cng thc ny thng dng li sut r bng vi li sut phiri ro t hot ng u t thc hin trong khong thi gian T.

c im ca cc cng thc Black-Scholes

Ta xem xt c tnh ca cc cng thc Black-Scholes bng cch xem xt khi cho ccbin trong cng thc n cc tr.


c EMISCOM, 4/2006


DHVP - Empirics.net


50/93


Khi gi c phiu S ln rt cao, kh nng quyn chn mua c thc hin s hu nhchc chn. Quyn chn khi s ging vi mt hp ng k hn vi gi giao l X. Tcng thc nh gi hp ng k hn:

f = SKerT(6)Khi gi ca hp ng quyn chn mua s l:

SXerT

y chnh l gi quyn chn mua c c t phng trnh 2.22: khi St gi tr rtln th c d1 v d2 u s c gi tr rt ln, khi N(d1) v N(d2) s c gi tr gn n 1.Khi gi c phiu Stng ln rt cao, gi ca mt quyn chn bn kiu Chu u p s timcn dn n 0. Din gii ny ph hp vi phng trnh 2.23 v N(d1) v N(d2)cng tim cn dn v 0.

Khi gi c phiu h xung rt thp, c d1 v d2 s rt ln v m. N(d1) v N(d2) khi s cng tim cn v 0 v gi quyn chn mua kiu Chu u cho bi phng trnh 2.22s tim cn dn v 0. ng thi N(d1) v N(d2) c gi tr dn n 1, do gi caquyn chn bn tnh qua phng trnh 2.23 s c gi tr gn n XerT S.

Hm phn phi chun tch ly

Trong phng trnh 2.22 v 2.23, vic tnh ton vi hm phn phi chun tch lyN lcng on phc tp nht. Bng gi tr ca N c trong phn ph lc ca bo co. Hmny cng c th c tnh bng php tnh xp x a thc. Gi tr xp x c th tnh quamy tnh theo cng thc:

N(x) = 1 (a1k + a1k2 + a1k3)N(x) vi: x 0N(x) = 1N(x) vi: x < 0

trong

k = 11+x

= 0.33267

1 = 0.4361836

2 = 0.12016763 = 0.9372980

v

N(x) = 12

ex2/2

Cng thc ny cho php ta tnh gi tr ca N(x) chnh xc n 0.0002.

V d 2.3 V dMt c phiu c gi 42USD vo thi im 6 thng trc khi quyn chn ht hiu lc,gi thc hin ca quyn l 40USD, li sut phi ri ro l 10% mt nm v bt n l20% mt nm. Ta c S = 42, X = 40, r = 0.1, = 0.2, T = 0.5:

(6)ta chp nhn cng thc tnh gi tr hp ng k hn trong f l gi tr hp ng, S l gi ti sn vK l gi giao ti sn tha thun


c EMISCOM, 4/2006


DHVP - Empirics.net
http://-/?-http://-/?-http://-/?-http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://www.emiscom.com/http://-/?-http://-/?-http://-/?-


51/93

2. NH GI QUYN CHN

d1 =ln(42/40)+(0.1+0.22/2)0.5

0.20.5

= 0.7693

d2 =ln(42/40)+(0.1

0.22/2)

0.5

0.20.5 = 0.6278. v

XerT = 40e0.1 0.5 = 38.049

Do nu quyn chn l quyn chn mua kiu Chu u, gi trc ca n s l:

42N(0.7693) 38.049N(0.6278)Nu l quyn chn bn kiu Chu u, gi p l:

p = 38.049N(

0.6278)

42N(

0.7693)

S dng phng php xp x a thc trn hoc tra bng ta c:

N(0.7693) = 0.7791 N(0.7693) = 0.2209N(0.6278) = 0.7349 N(0.6278) = 0.2651

t :

c = 4.76, p = 0.81

Gi ca c phiu s phi tng thm 2.76 USD quyn chn mua c th ha vn.

Tng t gi c phiu phi gim 2.81 USD quyn chn bn c th ha vn.

nh gi trung lp ri ro

C mt kt qu quan trng rt ra t vic nh gi cc hp ng phi sinh, cc nhnghin cu thng gi l nh gi trung lp ri ro. Nguyn l c bn ca kt lun nyl:

Bt k chng khon no ph thuc vo mt loi chng khon c giaodch khc u c th c nh gi trn c s p dng gi nh nh u tl trung lp ri ro.

Cn lu l ch vi nh gi cc chng khon phi sinh mi a vo p dng gi nhnh u t trung lp ri ro. Gi nh ny c ngha l nhng hnh thc ri ro lin quann nh u t s khng c nh hng n gi tr ca mt quyn chn c phiu nugi tr c vit di dng mt hm vi bin l gi ca c phiu c s. iu ny giithch v sao trong phng trnh 2.22 v 2.23 khng c bin .nh gi trung lp ri ro l mt cng c rt quan trng v trong mt mi trng ri rotrung lp ta c hai kt qu sau:

1. Li nhun k vng t tt c cc chng khon chnh l mc li sut phi ri ro.

2. Li sut phi ri ro cng l t sut chit khu c th p dng ph hp cho midng tin d kin trong tng lai.


c EMISCOM, 4/2006


DHVP - Empirics.net


52/93


Quyn chn v cc hp ng phi sinh khc c kh nng thanh ton vo mt thi imnht nh trong tng lai c th c nh gi s dng k thut nh gi trung lp riro. Quy trnh nh gi theo cc bc sau:

1. Gi nh t sut li nhun k vng ca ti sn c s bng li sut phi ri ro (tc lr = ).

2. Tnh ton khon tin thanh ton k vng t quyn chn ti thi im thc hin.

3. Chit khu khon thanh ton k vng bng li sut phi ri ro.

bt n

Trong m hnh nh gi Black-Scholes, tham s khng th c ghi nhn trc tip l bt n ca gi c phiu. phn trc gii thiu cch c lng bt n t dliu qu kh.Ngoi phng php gii thiu trn, ngi ta thng da trn bt n ca ccquyn chn ht hiu lc c lin quan (cng mt loi ti sn c s chng hn) clng ra bt n ca mt quyn chn. bt n ca nhng quyn chn ht hiulc c c lng ngc li trn c s gi ti sn c s, gi thc hin, gi quyn chnli sut. Sau khi c lng bt n ca mt s hp ng quyn chn (phi sinh nichung) c lin quan, ngi ta gn cho mi gi tr tm c mt trng s v ly bnhqun trng s ca cc gi tr ny. Cch gn trng s c tm hiu trong nhiunghin cu ca [?][Manaster], [?][Lantane], [?][Whaley].Xem xt v nguyn nhn gy ra bt n ca quyn chn. Mt s nh nghin cu cho

rng bt n ca quyn chn bt ngun duy nht t nhng thng tin pht sinh ngunhin v thu nhp trong tng lai t c phiu. Nhng nh phn tch khc li gi kincho rng ngun gc gy bt n ch yu l do hot ng giao dch. Do nhiungi t ra cu hi liu bt n ca chng khon khi s giao dch m ca c ginguyn ngay c khi n ng ca.[?][Fama] v [?][French] tin hnh kim nh thng k i vi cu hi ny. H tinhnh thu thp s liu thu thp v gi ng ca mi sau mi ngy giao dch trong mtkhong thi gian di v tin hnh tnh:

1. sai lch gia li nhun c phiu thu c t lc ng ca ca mt phin vi

mc li nhun t c phiu thi im ng ca phin tip theo vi iu kinkhng c ngy ngh giao dch xem gia.

2. sai lch gia thu nhp t c phiu khi ng ca phin giao dch ngy th 6 vkhi ng ca ngy th 2.

Nu s ngy giao dch v s ngy khng giao dch bng nhau th sai lch trong tnhhung th 2 phi ln gp khong 3 ln so vi tnh hung th nht. Fama nhn thycon s ny ch l 22%. French cng tm ra mt con s tng t, ng tnh c sai lchtrong tnh hung th 2 ln hn tnh hung th nht 19%.Kt qu trn ch ra rng bt n ca gi c phiu trong nhng ngy c giao dch ln

hn nhiu so vi khi khng giao dch. Nh th gi nh truyn thng v ngun gc ca bt n xut hin ch t thng tin mi c th s phi iu chnh thnh nhng thng


quyỀn chỌn vÀ quyỀn chỌn thỰc Ứng dỤng trÊn thỊ trƯỜng tÀi chÍnh viỆt nam

Documents