Risk/arbitrage strategies: an application to stock option portfolio

47 Pages·2015·2.42 MB·English

egartibrA/ksiR :seigetartS An noitacilppA ot
kcotS noitpO oiloftroP tnemeganaM
oznecniV ,oihccihcoB Niklaus ,nnamlhüB enahpetS donuJ dna oderF-snaH tsiL
ssiwS ecnarusnieR ynapmoC
iauqnehtyM 50/60, CH-8022 hciruZ
:enohpeleT [phone]
:elimiscaF [phone]
Mark .A.H sivaD
Tokyo-Mitsubishi International plc
6 ,etagdaorB nodnoL EC2M AA2
:enohpeleT [phone]
:elimiscaF [phone]
.tcartsbA ytilibaiL/tessA ,tnemeganam lamitpo dnuf ngised dna lamitpo oiloftrop
noitceles evah neeb yek seussi fo tseretni ot eht ecnarusni)er( dna tnemtsevni gniknab
,seitinummoc ,ylevitcepser rof emos sraey - yllaicepse ni eht ngised fo decnavda -ksir
refsnart snoitulos rof stneilc ni eht enutroF 500 puorg fo .seinapmoc ,yltneceR eht
noitazitiruces fo ecnarusni)er( smialc soiloftrop sah osla detcartta elbaredisnoc
noitnetta gnoma ecnarusni)er( seinapmoc dna rieht .stneilc tI snrut tuo taht eht wen
tpecnoc fo detimil ksir egartibra )ARL( tnemtsevni tnemeganam ni a noisuffid epyt
,seitilibail seitiruces dna sevitavired tekram decudortni ni our srepap enilesaB rof
egnahcxE etaR – sksiR fo na lanoitanretnI ,rerusnieR RIFA 1996, .loV ,I .p 395, dna
egartibrA/ksiR :seigetartS A weN tpecnoC rof ytilibaiL/tessA ,tnemeganaM lamitpO
dnuF ngiseD dna lamitpO oiloftroP noitceleS ni a ,cimanyD emiT-suounitnoC
krowemarF traP :I seitiruceS stekraM dna traP :II seitiruceS dna sevitavireD ,stekraM
RIFA 1997, .loV ,II .p 543, si yletaidemmi elbacilppa ot all fo eht evoba denoitnem
lacitcarp .smelborp ehT evititepmoc egatnavda fo gniylppa ARL seigetarts ni eht
ngised fo decnavda ksir refsnart snoitulos rof enutroF 500 stneilc seil ni eht tcaf taht
eseht seuqinhcet eveihca na tneiciffe noitacolla fo ksir ni na llarevo oiloftrop txetnoc
rehtar naht gnitanimile (at a hgih )ecirp sevitavired ksir erusopxe no a -elgnis
tnemurtsni sisab yb noitacilper )gnigdeh( htiw gniylrednu .seitiruces ehT niam
seititnauq fo lacitcarp tseretni ,.e.i( eht lamitpo ARL tessa ,noitacolla ).cte nac eb
devired yb gnivlos a )-isauq( raenil laitrap laitnereffid noitauqe fo eht dnoces redro
,.g.e( yb gnisu a etinif ecnereffid noitamixorppa htiw yllacol mrofinu ecnegrevnoc
,seitreporp ees traP :III A egartibrA/ksiR gnicirP )yroehT ro ni( our erom
detacitsihpos esulpmi lortnoc ,hcaorppa ees traP :VI nA eslupmI lortnoC hcaorppA ot
detimiL ksiR )egartibrA yb gnisu na tneiciffe vokraM niahc noitamixorppa emehcs
,.e.i[ yllaitnesse eht emas )lamrof( etinif ecnereffid seuqinhcet htiw( kaew ecnegrevnoc
.])seitreporp ,revewoH ni ynam lacitcarp snoitacilppa ereht era hcum relpmis
laciremun noitulos ,seuqinhcet ees traP :V A ediuG ot tneiciffE laciremuN
.snoitatnemelpmI eW tneserp ereh hcus na evitanretla derab-ecittal snoitpo oiloftrop
25
management methodology which swolla the determination of the main ARL
quantities by simply solving a linear program at each lattice node.
yeK sdroW dna .sesarhP egartibrA/ksiR ,mroftalp cimanyd gnimmargorp ,erudecorp
tnegnitnoc mialc ytivitisnes/ecirp ,tsacerof ARL noitazimitpo ,margorp etats tnedneped
raenil .noitazimitpo
Contents.
1. noitcudortnI 3
-
s-siwS eR deretsigeR erahS ledoM 3
- - eerf-ksiR tseretnI etaR 3
-
yt-ilitaloV 3
- - dnediviD dleiY 3
- - naeporuE Call snoitpO 5
- - naeporuE tuP snoitpO 8
- - enO doireP ARL seigetartS 11
- - esaB eulaV oiranecS 11
- -muminiM muimerP oiranecS 21
- - mumixaM muimerP oiranecS 23
2. ARL noitpO seigetartS 25
3. ”noitpO-retiebratiM“ gnidarT 36
- esaB eulaV oiranecS 37
- muminiM muimerP oiranecS 43
-
mumixaM muimerP oiranecS 45
:xidneppA secnerefeR 47
1. noitcudortnI
nI redro ot niag a tsrif thgisni otni woh detimil ksir egartibra )ARL( gnidart dna
oiloftrop tnemeganam seigetarts krow ni ecitcarp dna nac eb yllufsseccus desu ni
nredom ecnarusni)er( dna etaroproc dna tnemtsevni gniknab ,snoitacilppa ew redisnoc
detad-gnol naeporuE llac dna tup snoitpo no eht ssiwS eR deretsiger erahs )NKUR(
htiw a tnerruc tekram eulav fo FHC 1218.00 sa( fo 18 rebotcO 1995, ees osla
,nnamlhüB sivaD dna tsiL [1], [2] dna [3]).
ssiwS eR deretsigeR erahS .ledoM nI a tsrif ,noitamixorppa eht ssiwS eR deretsiger
erahs nac eb demussa ot wollof na otI ssecorp
26
ksir esreva- noitulove
lartuen-ksir noitulove
dradnats nainworB snoitom
htiw tnatsnoc detcepxe etar fo nruter µ = 17% dna tnatsnoc ytilitalov s cirtemoeg(
nainworB .)noitom ehT eerf-ksir etar fo tseretni r dna eht dnedivid dleiy y nac osla eb
demussa ot eb tnatsnoc revo eht 5 raey noitpo ytirutam .noziroh
eerf-ksiR tseretnI .etaR ehT eerf-ksir etar fo tseretni elbacilppa gnirud eht 5 raey noitpo
ytirutam doirep si detamitse ot eb 4% .a.p ylsuounitnoc( .)dednuopmoc ehT ytivitisnes
fo eht naeporuE llac dna tup noitpo scitsiretcarahc htiw tcepser ot segnahc ni eht -ksir
eerf tseretni etar si revewoh denimaxe rof a etar noitairav egnar morf 3% ot 5% .).a.p(
.ytilitaloV ehT ytilitalov fo eht ssiwS eR deretsiger erahs elbacilppa gnirud eht 5 raey
noitpo ytirutam doirep si detamitse ot eb 22.5% ;.a.p eht ytivitisnes fo eht naeporuE
llac dna tup noitpo scitsiretcarahc htiw tcepser ot segnahc ni NKUR ecirp ytilitalov si
revewoh denimaxe rof a ytilitalov noitairav egnar morf 20% ot 25% .).ap(
dnediviD .dleiY ehT dnedivid dleiy fo eht ssiwS eR deretsiger erahs elbacilppa gnirud
eht 5 raey noitpo ytirutam doirep si detaluclac sa :swollof
tnerruC dnediviD eulaV (18 rebotcO 1995):
FHC 15.00
tnerruC erahS eulaV (18 rebotcO 1995):
FHC 1218.00
tneceR dnediviD htworG etaR setamitsE (18 rebotcO 1995):
SBU 13.3% .ap
CBS grubraW 26.0% a.p
semaJ lepaC 21.6% ap
egarevA 20.3% a.p
dnediviD :dleiY
27
dnedivid ni raey i
serutuf ecirp fo deretsiger erahs ni raey i
esaercni ni erahs noitisop ni raey i
tnemtsevnier( fo )sdnedivid
noitauqe rof dnedivid dleiy y
etoN taht siht noitauqe si deifilpmis rof esae fo .noitaluclac A erom etarucca dna( erom
)detacilpmoc noisserpxe dluow eb
ehT stceffe fo siht noitacifilpmis era detasnepmoc rof ni eht eciohc fo eht dnedivid
dleiy noitairav egnar deniltuo .woleb
laciremuN noitaulavE :)scitamehtaM(
htiW eht laitini seulav D0 = 15.00 dna S0 = 1218.00 acitamehtaM setaluclac eht
deilpmi dnedivid sdleiy rof eht evoba tseretni etar dna dnedivid htworg etar soiranecs
sa :swollof
=g 13% a.p
r = 3% a.p 4% a.p 5% a.p
y = 1.66% a.p 1.60% a.p 1.55% a.p
g = 20% a.p
r= 3% a.p 4% a.p 5% a.p
y = 2.02% a.p 1.96% a.p 1.89% a.p
g = 26% a.p
r = 3% a.p 4% a.p 5% a.p
y = 2.39% a.p 2.31% a.p 2.23% a.p
ehT dnedivid dleiy fo eht ssiwS eR deretsiger erahs elbacilppa gnirud eht 5 raey noitpo
ytirutam doirep si erofereht nekat ot eb 2% .a.p ylsuounitnoc( .)dednuopmoc ehT
ytivitisnes fo eht naeporuE llac dna tup noitpo scitsiretcarahc htiw tcepser ot segnahc
ni dnedivid dleiy si revewoh denimaxe rof a dleiy noitairav egnar morf 1.6% ot 2.4%
.).a.p(
naeporuE Call .snoitpO htiW eht evoba (Black & )selohcS kcots ecirp ledom serutuf
secirp fo eht ssiwS eR deretsiger erahs )NKUR( dna eht seulav fo gnidnopserroc
naeporuE llac snoitpo nac eb yllacitylana detaluclac sa :swollof
28
:serutuF
T serutuf ytirutam
naeporuE :llaC
T noitpo ytirutam
X noitpo ekirts
N[ ] dradnats lamron noitubirtsid
,yllacificepS we redisnoc the llac snoitpo ekirts( )eludehcs
naeporuE llaC noitpO noitpO ecirP
esicrexE ecirP Base eulaV muminiM muimerP muimerP mumixaM
1218.0000 265.0653 204.7840 326.4088
1268.0000 246.1182 186.7104 307.1242
1318.0000 228.4387 170.1043 288.9330
1368.0000 211.9629 154.8749 271.7880
1418.0000 196.6260 140.9314 255.6410
1468.0000 182.3631 128.1841 240.4437
1518.0000 169.1102 116.5454 226.1481
1568.0000 156.8048 105.9308 212.7071
1618.0000 145.3866 96.2598 200.0744
1668.0000 134.7972 87.4559 188.2053
1718.0000 124.9809 79.4474 177.0566
Base eulaV muminiM :muimerP mumixaM :muimerP
ytilitalov = 22.5% ytilitalov = 20% ytilitalov = 25%
dnedivid dleiy = 2% dnedivid dleiy = 2.4% dnedivid dleiy = 1.6%
tseretni rate = 4% tseretni rate = 3% tseretni rate = 5%
or ni lacihparg mrof
29
ehT detaicossa noitpo ksir sretemarap era
30
eton( the ylevitaler tsedom tsrif dna dnoces order ksir erusopxe htiw respect ot segnahc
ni the eulav of the gniylrednu ssiwS Re deretsiger share, )NKUR
31
as a noitcnuf of the esicrexe or ekirts .ecirp elihW the llac s’noitpo tsrif dna dnoces
order ksir erusopxe htiw respect ot segnahc ni the eulav of the gniylrednu ssiwS Re
deretsiger share atled( dna )ammag si ylevitaler ,tsedom sti ytilitalov ,)agev( tseretni
rate (rho rate) dna dnedivid dleiy (rho )dleiy ksir serusopxe are etiuq .tnacifingis
naeporuE tuP .snoitpO ehT ecirp of a naeporuE tup noitpo si ylralimis
ekiL ,evoba we redisnoc the tup snoitpo ekirts( )eludehcs
naeporuE tuP noitpO noitpO ecirP
esicrexE ecirP Base eulaV muime rmPumixaM muminiM muimerP
1218.0000 160.0896 172.8269 150.4712
1268.0000 182.0700 197.7817 170.1159
1318.0000 205.3181 224.2039 190.8541
1368.0000 229.7699 252.0029 212.6385
1418.0000 255.3606 281.0876 235.4209
1468.0000 282.0253 311.3687 259.1529
1518.0000 309.6999 342.7583 283.7867
1568.0000 338.3221 375.1721 309.2750
1618.0000 367.8314 408.5293 335.5717
1668.0000 398.1696 442.7538 362.6320
1718.0000 429.2809 477.7736 390.4127
Base :eulaV mumixaM :muimerP muminiM :muimerP
ytilitalov = 22.5% ytilitalov 20% = ytilitalov = 25%
dnedivid dleiy = 2% dnedivid dleiy = 2.4% dnedivid dleiy = 1.6%
tseretni rate = 4% tseretni rate = 3% tseretni rate = 5%
or ni lacihparg mrof
32
eton( taht fo esruoc won eht mumixam dna eht muminim muimerp soiranecs evah eht
etisoppo .)sgninaem ehT detaicossa noitpo ksir sretemarap era
33
eton( niaga eht ylevitaler tsedom tsrif dna dnoces redro ksir erusopxe htiw tcepser ot
segnahc ni eht eulav fo eht gniylrednu ssiwS eR deretsiger ,erahs )NKUR
34