A N N A L E S
8 1 , 9 ( 5 6 , 7$7 , 6 0 $ 5 , $ ( & 8 5 , ( 6 . à 2 ' 2 : 6 . $ /8%/,1±32/21,$
92/;/9,, 6(&7,2+
8QLZHUV\WHW0LNRáDMD.RSHUQLNDZ7RUXQLX.DWHGUD(NRQRPHWULLL6WDW\VW\NL
(:$'=,$:*2
:Sá\ZF]DVXZ\JDĞQLĊFLDQDZáDVQRĞFLK\EU\GRZHMRSFMLFROODU
7KHLQIOXHQFHRIWLPHWRH[SLUDWLRQRQSURSHUWLHVRIK\EULGFROODURSWLRQV
6áRZDNOXF]RZH RSFMDRSFMDNXSQD .H\ZRUGV RSWLRQFDOORSWLRQ
:VWĊS
:]URVW]PLHQQRĞFLZDUXQNyZU\QNRZ\FKMHVWSU]\F]\QąSRV]XNLZDQLDQRZ\FK
UR]ZLą]DĔLLQVWUXPHQWyZNWyU\FK]DVWRVRZDQLHXPRĪOLZLáRE\VNXWHF]QLHMV]H]DU]ą- G]DQLHU\]\NLHP2SFMHQDOHĪąGRNODV\QLHV\PHWU\F]Q\FKLQVWUXPHQWyZSRFKRG- Q\FKFRR]QDF]DĪHMHGQD]HVWURQPDSUDZRDOHQLHRERZLą]HNUHDOL]DFMLXPRZ\
'ODWHJR RSFMH Vą Z\MąWNRZ\P LQVWUXPHQWHP ]DU]ąG]DQLD U\]\NLHP >-DMXJD
V 7DUF]\ĔVNL +XOO V @ 1DE\ZFD RSFML PD ]DJZDUDQWRZDQą
FHQĊSRNWyUHMZSU]\V]áRĞFLEĊG]LHPyJáNXSLü RSFMDNXSQD OXEVSU]HGDü RSFMD
VSU]HGDĪ\ LQVWUXPHQWED]RZ\5\]\NRQDE\ZF\RSFMLMHVWRJUDQLF]RQHGRZ\VR- NRĞFL]DSáDFRQHMSUHPLL
: ]DU]ąG]DQLX U\]\NLHP Z NV]WDáWRZDQLX QRZ\FK SURILOL GRFKRGX NOXF]RZH
]QDF]HQLHPDWZRU]HQLHQRZ\FKLQVWUXPHQWyZILQDQVRZ\FKOXEWHĪNRQVWUXRZDQLH
QRZ\FKVWUDWHJLL]LVWQLHMąF\FKLQVWUXPHQWyZ']LĊNLLQQRZDF\MQ\PLQVWUXPHQWRP
ILQDQVRZ\PLVWQLHMHPRĪOLZRĞüGRVWRVRZ\ZDQLDZ\SáDW\]W\FKLQVWUXPHQWyZGR
LVWQLHMąF\FKSRWU]HELQZHVW\F\MQ\FK:]URVW]DSRWU]HERZDQLDQDQRZHWHFKQLNL]DU]ą-
2SFMHILQDQVRZHZ\VWDZLDVLĊQDDNFMHZDOXW\LQGHNV\HNRQRPLF]QHVWRSĊSURFHQWRZą,QVWUXPHQWDPL
ED]RZ\PLRSFMLWRZDURZ\FKVąQSPHWDOHV]ODFKHWQH]ERĪDVXURZFH
(:$'=,$:*2
G]DQLDU\]\NLHPSRZVWDZDQLHPRGHOLWHRUHW\F]Q\FKRSLVXMąF\FKSURFHV\L]MDZLVND
ILQDQVRZH]DVWRVRZDQLHWHRULLDQDOL]\VWRFKDVW\F]QHMRUD]DQDOL]\PDWHPDW\F]QHM
GRUR]ZLą]\ZDQLDSUREOHPyZ]DU]ąG]DQLDU\]\NLHPMDNUyZQLHĪUR]ZyMWHFKQRORJLL
NRPSXWHURZHMVąJáyZQ\PLSU]\F]\QDPLUR]ZRMXLQĪ\QLHULLILQDQVRZHM>-RH
7XIDQR )LQQHJDQ 0LOOHU 7DUF]\ĔVNL=ZRODQNRZVNL V
3LDVHFNL@:JUXSLHLQQRZDF\MQ\FKLQVWUXPHQWyZLQĪ\QLHULLILQDQVRZHMV]F]H- JyOQHPLHMVFH]DMPXMąLQVWUXPHQW\K\EU\GRZHNWyUHáąF]ąFHFK\FRQDMPQLHMGZyFK
JUXSLQVWUXPHQWyZILQDQVRZ\FK+\EU\GRZDRSFMDW\SXFROODUMHVWNRPELQDFMąRSFML
VWDQGDUGRZ\FKRUD]NRQWUDNWXIRUZDUG
:DUW\NXOHRSLVDQR]DJDGQLHQLD]ZLą]DQH]K\EU\GRZąRSFMąW\SXFROODU FKD- UDNWHU\VW\NDLQVWUXPHQWXPRGHOZ\FHQ\RSFMLZáDVQRĞFLJUHFNLFKZVSyáF]\QQLNyZ
&HOHPDUW\NXáXMHVWSU]HGVWDZLHQLHZSá\ZXF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ
FHQ\RUD]ZDUWRĞFLJUHFNLFKZVSyáF]\QQLNyZK\EU\GRZHMRSFMLW\SXFROODU,OXVWUD- FMDHPSLU\F]QD]DZDUWDZDUW\NXOH]RVWDáDSU]HSURZDG]RQDQDSRGVWDZLHV\PXODFML
Z\FHQ\RSFMLZDOXWRZ\FKZ\VWDZLRQ\FKQD(853/1
+\EU\GRZDRSFMDW\SXFROODU±FKDUDNWHU\VW\NDLQVWUXPHQWX
)XQNFMDZ\SáDW\K\EU\GRZHMRSFMLFROODUMHVWSRVWDFL>=KDQJV @
w PLQ>PD[ ST K K@ JG]LH
w±IXQNFMDZ\SáDW\RSFMLFROODUST±FHQDLQVWUXPHQWXED]RZHJRZFKZLOLT
T ± F]DV Z\JDĞQLĊFLD RSFML K ± QLĪV]D FHQD Z\NRQDQLD RSFML K ± Z\ĪV]D FHQD
Z\NRQDQLDRSFML
:\SáDWD]K\EU\GRZHMRSFMLFROODUZ\QRVL
KMHĞOLFHQDLQVWUXPHQWXED]RZHJRVSHáQLDQLHUyZQRĞüSTK
STZSU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJRVSHáQLDQLHUyZQRĞüK < ST < K KMHĞOLFHQDLQVWUXPHQWXED]RZHJRVSHáQLDQLHUyZQRĞüKST
=DQDOL]\ZDUWRĞFLIXQNFMLZ\SáDW\Z\QLNDĪHK\EU\GRZDRSFMDW\SXFROODUMHVW
SDNLHWHPVNáDGDMąF\PVLĊ]GáXJLHMRSFMLNXSQD]FHQąZ\NRQDQLDKNUyWNLHMRSFML
NXSQD]FHQąZ\NRQDQLDKRUD]NRQWUDNWXIRUZDUG GáXJDSR]\FMD ]FHQąKeíU 7íW
SU]\F]\PK < K:\SáDWD]K\EU\GRZHMRSFMLFROODU]DZLHUDVLĊZSU]HG]LDOH>K K@
+\EU\GRZDRSFMDW\SXFROODUMHVWQD]\ZDQDÄRSFMą]NRáQLHU]HP´&HQ\Z\NRQDQLD
VWDQGDUGRZ\FK RSFML WZRU]ą W]Z SU]HG]LDá NRáQLHU]D SU]\ F]\P FHQD Z\NRQDQLD
GáXJLHMRSFMLNXSQDVWDQRZLSRF]ąWHNSU]HG]LDáXDFHQDZ\NRQDQLDNUyWNLHMRSFML
NXSQD±NRQLHFZ\]QDF]RQHJRSU]HG]LDáX
&HQDK\EU\GRZHMRSFMLFROODURSLVDQDMHVWUyZQDQLHP
2SUDFRZDQLHZáDVQH>QDSRGVWDZLH =KDQJV@
:3à<:&=$68:<*$ĝ1,ĉ&,$1$:à$612ĝ&,+<%5<'2:(-23&-,&2//$5
( ) ( ) ( )
1 1 1 2 2 2 1
( ( ) ( )) ( ( ( ) ( ))
q T t r T t r T t
t t
c =e− − S N d −N d −e− − K N d −K N d +e− − K JG]LH
Ft±FHQDK\EU\GRZHMRSFMLW\SXFROODU
St±FHQDLQVWUXPHQWXED]RZHJRZFKZLOLt
T±F]DVZ\JDĞQLĊFLDRSFMLt > T@
N G ±G\VWU\EXDQWDUR]NáDGXQRUPDOQHJR
( )
( )
2
1
1 2 1
2
2
1 2 1
ln 0,5 ( )
, ,
ln 0,5 ( )
, ,
t
t
S r q T t
d K d d T t
T t
S r q T t
d K d d T t
T t σ σ σ
σ σ σ
⎛ ⎞+ − + −
⎜ ⎟
⎝ ⎠
= = − −
−
⎛ ⎞+ − + −
⎜ ⎟
⎝ ⎠
= = − −
−
ı±]PLHQQRĞüFHQ\LQVWUXPHQWXED]RZHJR
r±VWRSDSURFHQWRZDDNW\ZyZZROQ\FKRGU\]\ND
q±VWRSDG\ZLGHQG\SR]RVWDáHR]QDF]HQLDVąWDNLHVDPHMDNZHZ]RU]H 5R]ZDĪDQLDGRW\F]ąZSá\ZXF]DVXZ\JDĞQLĊFLDQDFHQĊK\EU\GRZHMRSFMLW\SXFROODU
6\PXODFMDZ\FHQ\]RVWDáDSU]HSURZDG]RQDGODRSFMLZDOXWRZ\FKZ\VWDZLRQ\FKQD(85
3/1LGRW\F]\RNUHVXVW\F]QLD±PDUFDU1DU\VXQNXSU]HVWDZLRQRNV]WDá- WRZDQLHVLĊFHQ\GZyFKK\EU\GRZ\FKRSFMLFROODUNWyUHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
7HUPLQZ\JDĞQLĊFLDMHGQHMRSFMLZ\QRVLPLHVLąFHDGUXJLHMPLHVLĊF\&HQDZ\NRQDQLD
GáXJLHMRSFMLNXSQDMHVWUyZQDK ]áQDWRPLDVWFHQDZ\NRQDQLDNUyWNLHMRSFML
NXSQDWRK ]á&HQ\Z\NRQDQLDRSFMLVWDQGDUGRZ\FKWZRU]ąSU]HG]LDáK\EU\GRZHM
RSFMLFROODUSRVWDFL> @1DU\VXQNX]DSUH]HQWRZDQRZSá\ZFHQ\LQVWUXPHQWX
ED]RZHJRRUD]F]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊFHQ\K\EU\GRZHMRSFMLFROODU
3,9 4 4,1 4,2 4,3 4,4 4,5
02.01 09.01 13.01 19.01 25.01 31.01 06.02 10.02 16.02 22.02 28.02 05.03 09.03 15.03 21.03 27.03 data
cena [PLN]
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN.V]WDáWRZDQLHVLĊFHQ\K\EU\GRZHMRSFMLW\SXFROODU
2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
ħUyGáR RSUDFRZDQLHZáDVQH
(:$'=,$:*2
3,9 4 4,1 4,2 4,3 4,4 4,5
K1 K2
cena instrumentu bazowego
cena opcji [PLN]
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLD
QDFHQĊK\EU\GRZHMRSFMLW\SXFROODU ħUyGáR RSUDFRZDQLHZáDVQH
1DSRF]ąWNXUR]SDWU\ZDQHJRRNUHVXFHQDLQVWUXPHQWXED]RZHJRNV]WDáWRZDáD
VLĊZSREOLĪXSXQNWXNRĔFRZHJRZ\]QDF]RQHJRSU]HG]LDáX-HĞOLFHQDLQVWUXPHQ- WX ED]RZHJR ]EOLĪD VLĊ GR NRĔFD SU]HG]LDáX WR Z\VWĊSXMH Z]URVW UyĪQLF\ PLĊG]\
FHQąK\EU\GRZHMRSFMLFROODU]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLDDFHQąRSFMLFROODU
]NUyWV]\PWHUPLQHPZ\JDĞQLĊFLD:SU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJR
NV]WDáWXMH VLĊ Z SREOLĪX SXQNWX SRF]ąWNRZHJR SU]HG]LDáX ]PQLHMV]D VLĊ UyĪQLFD
PLĊG]\FHQąRSFML]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLDDFHQąRSFMLFROODU]NUyWV]\P
WHUPLQHPZ\JDĞQLĊFLD3RGNRQLHFDQDOL]RZDQHJRRNUHVXFHQDLQVWUXPHQWXED]RZHJR
]EOLĪDáDVLĊGRSRF]ąWNXZ\]QDF]RQHJRSU]HG]LDáX>K K@
+\EU\GRZDRSFMDFROODU]NUyWV]\PWHUPLQHPZ\JDĞQLĊFLDMHVWGURĪV]DRGRSFML
FROODU]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLD:]URVWVSDGHNFHQ\LQVWUXPHQWXED]RZHJR
ZSá\ZDQDZ]URVWVSDGHNFHQ\K\EU\GRZHMRSFMLFROODU
:Sá\ZWHUPLQXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊZDUWRĞFL
JUHFNLFKZVSyáF]\QQLNyZK\EU\GRZHMRSFMLFROODU±LOXVWUDFMDHPSLU\F]QD
*UHFNLHZVSyáF]\QQLNLVąPLDUDPLZUDĪOLZRĞFLFHQ\RSFMLNWyUHZVND]XMąMDN
]PLHQL VLĊ FHQD RSFML SRG ZSá\ZHP ]PLDQ\ ZDUWRĞFL F]\QQLND U\]\ND 'R PLDU
ZUDĪOLZRĞFL NRQWUDNWyZ RSF\MQ\FK QDOHĪą ZVSyáF]\QQLNL GHOWD JDPPD YHJD
WKHWDRUD]UKR>']LDZJRV@5R]ZDĪDQLDSU]HSURZDG]RQHZQLQLHMV]\P
SXQNFLH GRW\F]ą ZSá\ZX WHUPLQX Z\JDĞQLĊFLD QD NV]WDáWRZDQLH VLĊ ZDUWRĞFL JUH- FNLFKZVSyáF]\QQLNyZK\EU\GRZ\FKRSFMLW\SXFROODU,OXVWUDFMDHPSLU\F]QD]RVWDáD
SU]HSURZDG]RQDGODRSFMLDQDOL]RZDQ\FKZSRSU]HGQLPUR]G]LDOH
:VSyáF]\QQLNGHOWDRNUHĞODRLOH]PLHQLVLĊFHQDRSFMLJG\FHQDLQVWUXPHQWX
ED]RZHJR]PLHQLVLĊRMHGQRVWNĊ
1D U\VXQNX SU]HGVWDZLRQR NV]WDáWRZDQLH VLĊ ZDUWRĞFL ZVSyáF]\QQLND GHOWD
UR]SDWU\ZDQ\FKK\EU\GRZ\FKRSFMLFROODU5\VXQHNMHVWLOXVWUDFMąZSá\ZXELHĪąFHM
:3à<:&=$68:<*$ĝ1,ĉ&,$1$:à$612ĝ&,+<%5<'2:(-23&-,&2//$5
FHQ\LQVWUXPHQWXED]RZHJRRUD]WHUPLQXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊZDUWRĞFL
ZVSyáF]\QQLNDGHOWDK\EU\GRZHMRSFMLW\SXFROODU
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
02.01 10.01 17.01 24.01 31.01 07.02 14.02 21.02 28.02 06.03 13.03 20.03 27.03 data
delta
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDGHOWDK\EU\GRZHMRSFMLW\SXFROODU
2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
ħUyGáR RSUDFRZDQLHZáDVQH
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8
K1 K2
cena instrumentu bazowego
delta
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ
ZDUWRĞFLZVSyáF]\QQLNDGHOWDK\EU\GRZHMRSFMLW\SXFROODU ħUyGáR RSUDFRZDQLHZáDVQH
:VSyáF]\QQLNGHOWDK\EU\GRZHMRSFMLW\SXFROODUMHVWGRGDWQLLSU]\MPXMHZDUWRĞFL
]SU]HG]LDáX> @'RGDWQLDZDUWRĞüZVSyáF]\QQLNDGHOWDR]QDF]DĪHZ]URVWVSDGHN
FHQ\LQVWUXPHQWXED]RZHJRZSá\ZDQDZ]URVWVSDGHNFHQ\RSFML.UyWV]\WHUPLQ
Z\JDĞQLĊFLDZSá\ZDQDZ]URVWZDUWRĞFLZVSyáF]\QQLNDGHOWDK\EU\GRZHMRSFMLW\SX
FROODUSU]\F]\PPQLHMV]DUyĪQLFDPLĊG]\ZDUWRĞFLDPLZVSyáF]\QQLNDGHOWD]D]QDF]D
VLĊZSU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRSRF]ąWNXZ\]QD- F]RQHJRSU]HG]LDáX>K K@-HĞOLFHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRSXQNWyZ
NUDĔFRZ\FK SU]HG]LDáX WR Z\VWĊSXMH VSDGHN ZDUWRĞFL ZVSyáF]\QQLND GHOWD SU]\
(:$'=,$:*2
F]\PZLĊNV]\VSDGHNZDUWRĞFLZVSyáF]\QQLNDGHOWD]D]QDF]DVLĊZSU]\SDGNXNLHG\
FHQDLQVWUXPHQWXED]RZHJRNV]WDáWXMHVLĊZSREOLĪXNRĔFDZ\]QDF]RQHJRSU]HG]LDáX
:yZF]DVFHQDK\EU\GRZHMRSFMLFROODUFKDUDNWHU\]XMHVLĊPQLHMV]ąZUDĪOLZRĞFLąQD
]PLDQĊFHQ\LQVWUXPHQWXED]RZHJR1DMZLĊNV]DZUDĪOLZRĞüFHQ\RSFMLQD]PLDQĊ
FHQ\LQVWUXPHQWXED]RZHJRZ\VWĊSXMHZSU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]R- ZHJRRVF\OXMHZRNyáĞURGNDZ\]QDF]RQHJRSU]HG]LDáX>K K@
:VSyáF]\QQLNJDPPDZVND]XMHRLOH]PLHQLVLĊZDUWRĞüZVSyáF]\QQLNDGHOWD
MHĞOLFHQDLQVWUXPHQWXED]RZHJR]PLHQLVLĊRMHGQRVWNĊ
5\VXQHNSU]HGVWDZLDNV]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDJDPPDDQDOL- ]RZDQ\FKK\EU\GRZ\FKRSFMLW\SXFROODU1DU\VXQNX]LOXVWURZDQRZSá\ZELHĪąFHM
FHQ\LQVWUXPHQWXED]RZHJRRUD]WHUPLQXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊZDUWRĞFL
ZVSyáF]\QQLNDJDPPDK\EU\GRZHMRSFMLW\SXFROODU
-0,03 -0,02 -0,01 0 0,01 0,02 0,03
02.01 10.01 17.01 24.01 31.01 07.02 14.02 21.02 28.02 06.03 13.03 20.03 27.03 data
gamma
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDJDPPDK\EU\GRZHMRSFMLW\SXFROODU
2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
ħUyGáR RSUDFRZDQLHZáDVQH
-0,03 -0,02 -0,01 0 0,01 0,02 0,03
K1 K2
cena instrumentu bazowego
gamma
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ
ZDUWRĞFLZVSyáF]\QQLNDJDPPDK\EU\GRZHMRSFMLW\SXFROODU ħUyGáR RSUDFRZDQLHZáDVQH
:3à<:&=$68:<*$ĝ1,ĉ&,$1$:à$612ĝ&,+<%5<'2:(-23&-,&2//$5
:DUWRĞFLZVSyáF]\QQLNDJDPPDK\EU\GRZHMRSFMLW\SXFROODUXOHJDMą]QDF]Q\P
ZDKDQLRP3RQDGWRZVSyáF]\QQLNJDPPDRSFMLFROODUPRĪHSU]\MPRZDü]DUyZQR
ZDUWRĞFLGRGDWQLHMDNLXMHPQH'RGDWQLDZDUWRĞüZVSyáF]\QQLNDJDPPDZVND]X- MH QD WR ĪH Z]URVWVSDGHN FHQ\ LQVWUXPHQWX ED]RZHJR ZSá\ZD QD Z]URVWVSDGHN
ZDUWRĞFLZVSyáF]\QQLNDGHOWD'RGDWQLDZDUWRĞüZVSyáF]\QQLNDJDPPDZ\VWĊSXMH
ZSU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRSRF]ąWNXZ\]QDF]R- QHJRSU]HG]LDáX8MHPQDZDUWRĞüZVSyáF]\QQLNDJDPPDR]QDF]DĪHZ]URVWVSDGHN
FHQ\LQVWUXPHQWXED]RZHJRSRZRGXMHVSDGHNZ]URVWZDUWRĞFLZVSyáF]\QQLNDGHOWD
-HĞOLFHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRNRĔFDZ\]QDF]RQHJRSU]HG]LDáXWR
ZDUWRĞFLZVSyáF]\QQLNDJDPPDK\EU\GRZHMRSFMLFROODUVąXMHPQH:\ĪV]DZDUWRĞü
EH]Z]JOĊGQDZVSyáF]\QQLNDJDPPDĞZLDGF]\RZLĊNV]HMZUDĪOLZRĞFLZVSyáF]\Q- QLND GHOWD QD ]PLDQĊ FHQ\ LQVWUXPHQWX ED]RZHJR :\ĪV]D ZDUWRĞü EH]Z]JOĊGQD
ZVSyáF]\QQLNDJDPPDZ\VWĊSXMHZSU]\SDGNXK\EU\GRZHMRSFMLFROODUNWyUDFKD- UDNWHU\]XMHVLĊNUyWV]\PWHUPLQHPZ\JDĞQLĊFLD
.ROHMQąPLDUąZUDĪOLZRĞFLMHVWZVSyáF]\QQLNYHJDNWyU\ZVND]XMHMDN]PLHQL
VLĊFHQDRSFMLJG\]PLHQQRĞüFHQ\LQVWUXPHQWXED]RZHJR]PLHQLVLĊRMHGQRVWNĊ 1D U\VXQNX SU]HGVWDZLRQR NV]WDáWRZDQLH VLĊ ZDUWRĞFL ZVSyáF]\QQLND YHJD
DQDOL]RZDQ\FKK\EU\GRZ\FKRSFMLFROODU5\VXQHNMHVWLOXVWUDFMąZSá\ZXELHĪąFHM
FHQ\LQVWUXPHQWXED]RZHJRRUD]WHUPLQXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊZDUWRĞFL
ZVSyáF]\QQLNDYHJDK\EU\GRZHMRSFMLW\SXFROODU
-0,015 -0,01 -0,005 0 0,005 0,01
02.01 10.01 17.01 24.01 31.01 07.02 14.02 21.02 28.02 06.03 13.03 20.03 27.03 data
vega
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDYHJDK\EU\GRZHMRSFMLW\SXFROODU
2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
ħUyGáR RSUDFRZDQLHZáDVQH
=PLHQQRĞüFHQ\LQVWUXPHQWXED]RZHJRMHVWPLHU]RQDRGFK\OHQLHPVWDQGDUGRZ\P
(:$'=,$:*2
-0,015 -0,01 -0,005 0 0,005 0,01
K1 K2
cena instrumentu bazowego
vega
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ
ZDUWRĞFLZVSyáF]\QQLNDYHJDK\EU\GRZHMRSFMLW\SXFROODU ħUyGáR RSUDFRZDQLHZáDVQH
:]URVWVSDGHNFHQ\LQVWUXPHQWXED]RZHJRZSá\ZDQDVSDGHNZ]URVWZDUWRĞFL
ZVSyáF]\QQLND YHJD :DUWRĞFL ZVSyáF]\QQLND YHJD K\EU\GRZHM RSFML W\SX FROODU
XOHJDMą ]QDF]Q\P ZDKDQLRP 'RGDWQLH ZDUWRĞFL ZVSyáF]\QQLND YHJD K\EU\GRZHM
RSFMLFROODUZ\VWĊSXMąZV\WXDFML]EOLĪDQLDVLĊFHQ\LQVWUXPHQWXED]RZHJRGRSXQNWX
SRF]ąWNRZHJRZ\]QDF]RQHJRSU]HG]LDáX>K K@:yZF]DVZ]URVWVSDGHN]PLHQQRĞFL
FHQ\LQVWUXPHQWXED]RZHJRZSá\ZDQDZ]URVWVSDGHNFHQ\K\EU\GRZHMRSFMLFROODU
-HĞOLFHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRNRĔFDSU]HG]LDáX>K K@WRZDUWRĞFL
ZVSyáF]\QQLNDYHJDVąXMHPQH:W\PSU]\SDGNXZ]URVWVSDGHN]PLHQQRĞFLFHQ\
LQVWUXPHQWX ED]RZHJR SU]\F]\QLD VLĊ GR VSDGNXZ]URVWX FHQ\ K\EU\GRZHM RSFML
FROODU :\ĪV]D ZDUWRĞü EH]Z]JOĊGQD ZVSyáF]\QQLND YHJD ĞZLDGF]\ R ZLĊNV]HM
ZUDĪOLZRĞFLFHQ\RSFMLQDZDKDQLD]PLHQQRĞFL-HĪHOLFHQDLQVWUXPHQWXED]RZHJR
NV]WDáWXMH VLĊ Z SREOLĪX SXQNWX SRF]ąWNRZHJR SU]HG]LDáX >K K@ WR K\EU\GRZD
RSFMD FROODU ] NUyWV]\P WHUPLQHP Z\JDĞQLĊFLD RG]QDF]D VLĊ ZLĊNV]ą ZDUWRĞFLą
ZVSyáF]\QQLNDYHJD:]ZLą]NX]W\PFHQDRSFML]NUyWV]\PWHUPLQHPZ\JDĞQLĊFLD
MHVWZyZF]DVEDUG]LHMZUDĪOLZDQDZDKDQLD]PLHQQRĞFLFHQ\LQVWUXPHQWXED]RZHJR
:SU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRNRĔFDZ\]QDF]RQHJR
SU]HG]LDáX ZLĊNV]ą ZDUWRĞFLą EH]Z]JOĊGQą ZVSyáF]\QQLND YHJD FKDUDNWHU\]XMH
VLĊRSFMD]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLD:WHMV\WXDFMLFHQDRSFML]GáXĪV]\P
WHUPLQHPZ\JDĞQLĊFLDRG]QDF]DVLĊZLĊNV]ąZUDĪOLZRĞFLąQDZDKDQLD]PLHQQRĞFL
FHQ\LQVWUXPHQWXED]RZHJR
:VSyáF]\QQLNWKHWDRNUHĞOD]PLDQĊZDUWRĞFLRSFMLJG\GáXJRĞüRNUHVXGRWHUPLQX
Z\JDĞQLĊFLDVSDGQLHRMHGQRVWNĊ
1D U\VXQNX SU]HGVWDZLRQR NV]WDáWRZDQLH VLĊ ZDUWRĞFL ZVSyáF]\QQLND WKHWD
DQDOL]RZDQ\FKK\EU\GRZ\FKRSFMLW\SXFROODU5\VXQHNLOXVWUXMHZSá\ZELHĪąFHM
FHQ\LQVWUXPHQWXED]RZHJRRUD]WHUPLQXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊZDUWRĞFL
ZVSyáF]\QQLNDWKHWDK\EU\GRZHMRSFMLW\SXFROODU
:3à<:&=$68:<*$ĝ1,ĉ&,$1$:à$612ĝ&,+<%5<'2:(-23&-,&2//$5
0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035
02.01 10.01 17.01 24.01 31.01 07.02 14.02 21.02 28.02 06.03 13.03 20.03 27.03 data
theta
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN .V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDWKHWDK\EU\GRZHMRSFMLW\SXFROODU
2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
ħUyGáR RSUDFRZDQLHZáDVQH
0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035
K1 K2
cena instrumentu bazowego
theta
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ
ZDUWRĞFLZVSyáF]\QQLNDWKHWDK\EU\GRZHMRSFMLW\SXFROODU ħUyGáR RSUDFRZDQLHZáDVQH
:VSyáF]\QQLN WKHWD K\EU\GRZHM RSFML FROODU SU]\MPXMH ZDUWRĞFL GRGDWQLH FR
R]QDF]D ĪH RSFMD ] GáXĪV]\P WHUPLQHP Z\JDĞQLĊFLD MHVW WDĔV]D :]URVWVSDGHN
FHQ\LQVWUXPHQWXED]RZHJRZSá\ZDQDZ]URVWVSDGHNZDUWRĞFLZVSyáF]\QQLNDWKHWD
K\EU\GRZHMRSFMLFROODU-HĞOLFHQDLQVWUXPHQWXED]RZHJRNV]WDáWXMHVLĊZSREOLĪX
NRĔFD SU]HG]LDáX >K K@ WR K\EU\GRZD RSFMD ] GáXĪV]\P WHUPLQHP Z\JDĞQLĊFLD
FKDUDNWHU\]XMH VLĊ PQLHMV]ą ZDUWRĞFLą ZVSyáF]\QQLND WKHWD :yZF]DV FHQD WDNLHM
RSFML RG]QDF]D VLĊ PQLHMV]ą ZUDĪOLZRĞFLą QD XSá\ZDMąF\ F]DV = NROHL MHĞOL FHQD
LQVWUXPHQWX ED]RZHJR ]EOLĪD VLĊ GR SXQNWX SRF]ąWNRZHJR SU]HG]LDáX >K K@ WR
(:$'=,$:*2
ZLĊNV]HZDUWRĞFLZVSyáF]\QQLNDWKHWDZ\VWĊSXMąZSU]\SDGNXK\EU\GRZHMRSFMLFROODU
]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLD:WHMV\WXDFMLFHQDRSFML]GáXĪV]\PWHUPLQHP
Z\JDĞQLĊFLDMHVWEDUG]LHMZUDĪOLZDQDVNUDFDQLHVLĊRNUHVXGRWHUPLQXZ\JDĞQLĊFLD
:VSyáF]\QQLNUKRMHVWPLDUąZUDĪOLZRĞFLRNUHĞODMąFąZSá\Z]PLDQ\VWRS\SUR- FHQWRZHMDNW\ZyZZROQ\FKRGU\]\NDQDFHQĊRSFML
5\VXQHNSU]HGVWDZLDNV]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDUKRUR]SDWU\- ZDQ\FKK\EU\GRZ\FKRSFMLW\SXFROODU1DU\VXQNX]LOXVWURZDQRZSá\ZELHĪąFHM
FHQ\LQVWUXPHQWXED]RZHJRRUD]WHUPLQXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊZDUWRĞFL
ZVSyáF]\QQLNDUKRK\EU\GRZHMRSFMLFROODU
:DUWRĞFLZVSyáF]\QQLNDUKRK\EU\GRZHMRSFMLFROODUVąXMHPQH2]QDF]DWRĪH
Z]URVWVSDGHNVWRS\SURFHQWRZHMDNW\ZyZZROQ\FKRGU\]\NDZSá\ZDQDVSDGHN
Z]URVWZDUWRĞFLRSFMLFROODU
-0,014 -0,012 -0,01 -0,008 -0,006 -0,004 -0,002 0
02.01 10.01 17.01 24.01 31.01 07.02 14.02 21.02 28.02 06.03 13.03 20.03 27.03 data
rho
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDUKRK\EU\GRZHMRSFMLW\SXFROODU
2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD
ħUyGáR RSUDFRZDQLHZáDVQH
-0,014 -0,012 -0,01 -0,008 -0,006 -0,004 -0,002 0
K1 K2
cena instrumentu bazowego
rho
collar [T= 6 mies.] collar [T= 3 mies.]
5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ
ZDUWRĞFLZVSyáF]\QQLNDUKRK\EU\GRZHMRSFMLW\SXFROODU ħUyGáR RSUDFRZDQLHZáDVQH
:3à<:&=$68:<*$ĝ1,ĉ&,$1$:à$612ĝ&,+<%5<'2:(-23&-,&2//$5
:DUWRĞFL ZVSyáF]\QQLND UKR K\EU\GRZHM RSFML FROODU ] GáXĪV]\P WHUPLQHP
Z\JDĞQLĊFLDFKDUDNWHU\]XMąVLĊZLĊNV]ąZDUWRĞFLąEH]Z]JOĊGQąZVSyáF]\QQLNDUKR
&HQDRSFML]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLDRG]QDF]DVLĊZLĊNV]ąZUDĪOLZRĞFLąQD
]PLDQĊVWRS\SURFHQWRZHM:SU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJR]EOLĪD
VLĊ GR SXQNWyZ NUDĔFRZ\FK Z\]QDF]RQHJR SU]HG]LDáX >K K@ Z\VWĊSXMH VSDGHN
ZDUWRĞFL ZVSyáF]\QQLND UKR 1DMPQLHMV]D ZDUWRĞü ZVSyáF]\QQLND UKR PD PLHMVFH
ZV\WXDFMLNLHG\FHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRNRĔFDSU]HG]LDáX-HĞOL
FHQD LQVWUXPHQWX ED]RZHJR RVF\OXMH ZRNyá ĞURGND Z\]QDF]RQHJR SU]HG]LDáX WR
QDVWĊSXMHZ]URVWZDUWRĞFLZVSyáF]\QQLNDUKR:yZF]DVFHQDK\EU\GRZHMRSFMLW\SX
FROODUFKDUDNWHU\]XMHVLĊQDMPQLHMV]ąZUDĪOLZRĞFLąQDZDKDQLDVWRS\SURFHQWRZHM
=DNRĔF]HQLH
+\EU\GRZDRSFMDFROODUXPRĪOLZLDRWU]\PDQLHZ\SáDW\PLHV]F]ąFHMVLĊZZ\- ]QDF]RQ\PSU]HG]LDOH>K K@:]URVWVSDGHNFHQ\LQVWUXPHQWXED]RZHJRZSá\ZD
QDZ]URVWVSDGHNFHQ\K\EU\GRZHMRSFMLFROODU:Z\]QDF]RQ\PSU]HG]LDOH>K K@
K\EU\GRZD RSFMD FROODU ]DEH]SLHF]D U\]\NR ZDKDĔ FHQ\ LQVWUXPHQWX ED]RZHJR
: ]ZLą]NX ] W\P RSFMD WHJR W\SX PRĪH E\ü VWRVRZDQD Z SURGXNWDFK VWUXNWXU\- ]RZDQ\FK4 7HUPLQ Z\JDĞQLĊFLD MHVW LVWRWQ\P F]\QQLNLHP ZSá\ZDMąF\P ]DUyZQR
QDFHQĊRSFMLMDNLQDZUDĪOLZRĞüWHMFHQ\QD]PLDQĊFHQ\LQVWUXPHQWXED]RZHJR
ZDKDQLD]PLHQQRĞFL]PLDQĊVWRS\SURFHQWRZHMF]\WHĪXSá\ZDMąF\F]DV:]DOHĪ- QRĞFLRGRF]HNLZDĔ]ZLą]DQ\FK]NV]WDáWRZDQLHPVLĊFHQ\LQVWUXPHQWXED]RZHJR
ZSU]\V]áRĞFLZ\EyUK\EU\GRZHMRSFMLFROODU]RGSRZLHGQLąGáXJRĞFLąSU]HG]LDáXRUD]
WHUPLQHPZ\JDĞQLĊFLDXPRĪOLZLDNV]WDáWRZDQLHSURILOLGRFKRGX]Z\EUDQHMRSFML
+\EU\GRZDRSFMDW\SXFROODU]NUyWV]\PWHUPLQHPZ\JDĞQLĊFLDMHVWGURĪV]DRGRSFML
FROODU]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLD2SFMD]NUyWV]\PWHUPLQHPZ\JDĞQLĊFLD
MHVWEDUG]LHMZUDĪOLZDQD]PLDQĊFHQ\LQVWUXPHQWXED]RZHJR1DMZLĊNV]DZUDĪOLZRĞü
FHQ\ RSFML FROODU QD ]PLDQĊ FHQ\ LQVWUXPHQWX ED]RZHJR Z\VWĊSXMH Z SU]\SDGNX
NLHG\FHQDLQVWUXPHQWXED]RZHJRRVF\OXMHZRNyáĞURGNDZ\]QDF]RQHJRSU]HG]LDáX
>K K@-HĞOLFHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRNRĔFDSU]HG]LDáX>K K@WR
RSFMDRG]QDF]DVLĊQDMPQLHMV]ąZUDĪOLZRĞFLąQD]PLDQĊFHQ\LQVWUXPHQWXED]RZHJR
:V\WXDFMLNLHG\FHQDLQVWUXPHQWXED]RZHJR]EOLĪDVLĊGRSRF]ąWNXSU]HG]LDáX
>K K@ZLĊNV]HZDUWRĞFLZVSyáF]\QQLNDYHJDZ\VWĊSXMąZSU]\SDGNXRSFML]NUyW- V]\PWHUPLQHPZ\JDĞQLĊFLD2]QDF]DWRĪHFHQDK\EU\GRZHMRSFMLFROODU]NUyWV]\P
WHUPLQHPZ\JDĞQLĊFLDMHVWZyZF]DVEDUG]LHMZUDĪOLZDQDZDKDQLD]PLHQQRĞFLFHQ\
LQVWUXPHQWXED]RZHJR-HĪHOLFHQDLQVWUXPHQWXED]RZHJRNV]WDáWXMHVLĊZSREOLĪX
NRĔFD SU]HG]LDáX >K K@ WR ZLĊNV]H ZDUWRĞFL EH]Z]JOĊGQH ZVSyáF]\QQLND YHJD
Z\VWĊSXMąZSU]\SDGNXRSFMLFKDUDNWHU\]XMąFHMVLĊGáXĪV]\PWHUPLQHPZ\JDĞQLĊ-
4 3URGXNWVWUXNWXU\]RZDQ\MHVWSDNLHWHPLQVWUXPHQWyZZROQ\FKRGU\]\NDRUD]LQVWUXPHQWyZU\]\NRZQ\FK
>0RNURJXOVNL6HSLHODN@
(:$'=,$:*2
FLD:WHMV\WXDFMLFHQDK\EU\GRZHMRSFMLFROODU]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLD
RG]QDF]DVLĊZLĊNV]ąZUDĪOLZRĞFLąQD]PLDQĊFHQ\LQVWUXPHQWXED]RZHJR
:SU]\SDGNX]EOLĪDQLDVLĊFHQ\LQVWUXPHQWXED]RZHJRGRSXQNWXSRF]ąWNRZHJR
SU]HG]LDáX>K K@FHQDK\EU\GRZHMRSFMLFROODU]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLD
FKDUDNWHU\]XMH VLĊ ZLĊNV]ą ZUDĪOLZRĞFLą QD VNUDFDQLH VLĊ RNUHVX GR WHUPLQX Z\- JDĞQLĊFLD=NROHLMHĞOLFHQDLQVWUXPHQWXED]RZHJRNV]WDáWXMHVLĊZSREOLĪXNRĔFD
SU]HG]LDáX >K K@ WR FHQD RSFML ] NUyWV]\P WHUPLQHP Z\JDĞQLĊFLD MHVW EDUG]LHM
ZUDĪOLZDQDXSá\ZDMąF\F]DV
:DUWRĞFLZVSyáF]\QQLNDUKRRSFML]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLDVąZ\ĪV]H
RGZDUWRĞFLZVSyáF]\QQLNDUKRRSFML]NUyWV]\PWHUPLQHPZ\JDĞQLĊFLD:]ZLą]NX
]W\PFHQDK\EU\GRZHMRSFMLW\SXFROODU]GáXĪV]\PWHUPLQHPZ\JDĞQLĊFLDRG]QDF]D
VLĊZLĊNV]ąZUDĪOLZRĞFLąQDZDKDQLDVWRS\SURFHQWRZHMDNW\ZyZZROQ\FKRGU\]\ND
SU]\F]\PZLĊNV]DZUDĪOLZRĞüFHQ\RSFMLZ\VWĊSXMHZSU]\SDGNX]EOLĪDQLDVLĊFHQ\
LQVWUXPHQWXED]RZHJRGRSXQNWyZNUDĔFRZ\FKZ\]QDF]RQHJRSU]HG]LDáX>K K@
=QDF]QHZDKDQLDZDUWRĞFLJUHFNLFKZVSyáF]\QQLNyZĞZLDGF]ąRGXĪHMZUDĪOLZRĞFL
FHQ\K\EU\GRZHMRSFMLFROODUQD]PLDQĊF]\QQLNyZU\]\NDFR]ZLĊNV]DDWUDNF\MQRĞü
WHJRLQVWUXPHQWXZWUDQVDNFMDFKVSHNXODF\MQ\FK
%LEOLRJUDILD
']LDZJR(:SURZDG]HQLHGRVWUDWHJLLRSF\MQ\FK:\GDZQLFWZR1DXNRZH80.7RUXĔ
)LQQHJDQ-:KDWLV)LQDQFLDO(QJLQHHULQJ"³)LQDQFLDO(QJLQHHULQJ1HZV´QU
+XOO-&2SWLRQV)XWXUHVDQGRWKHU'HULYDWLYHV3UHQWLFH+DOO,QWHUQDWLRQDO,QF1HZ-HUVH\
-DMXJD.=DU]ąG]DQLHU\]\NLHP:\GDZQLFWZR1DXNRZH3:1:DUV]DZD
-RH*'HILQLQJ)LQDQFLDO(QJLQHHULQJ³)LQDQFLDO(QJLQHHULQJ1HZV´ QU
0LOOHU0+)LQDQFLDO,QQRYDWLRQ $FKLHYHPHQWVDQG3URVSHFWV³-RXUQDORI$SSOLHG&RUSRUDWH
)LQDQFH´ QU
0RNURJXOVNL06HSLHODN33URGXNW\VWUXNWXU\]RZDQHZ3ROVFHZODWDFK±.RPLVMD
1DG]RUX)LQDQVRZHJR:DUV]DZD
3LDVHFNL.0RGHOHPDWHPDW\NLILQDQVRZHM,QVWUXPHQW\SRGVWDZRZH:\GDZQLFWZR1DXNRZH
3:1:DUV]DZD
7DUF]\ĔVNL:,QVWUXPHQW\SRFKRGQHQDU\QNXNDSLWDáRZ\P3:(:DUV]DZD
7DUF]\ĔVNL:=ZRODQNRZVNL0,QĪ\QLHULDILQDQVRZD,QVWUXPHQWDULXPVWUDWHJLH]DU]ąG]DQLH
U\]\NLHP$JHQFMD:\GDZQLF]D3ODFHW:DUV]DZD
7XIDQR3+RZILQDQFLDOHQJLQHHULQJFDQDGYDQFHFRUSRUDWHVWUDWHJ\³+DUYDUG%XVLQHVV5HYLHZ´
QU
=KDQJ3*([RWLF2SWLRQV$*XLGHWR6HFRQG*HQHUDWLRQ2SWLRQV:RUG6FLHQWLILF6LQJDSRUH
7KHLQIOXHQFHRIWLPHWRH[SLUDWLRQRQSURSHUWLHVRIK\EULGFROODURSWLRQV
7KHDLPRIWKHSDSHULVWRSUHVHQWWKHLQIOXHQFHRIWLPHWRPDWXULW\RQWKHSURSHUWLHVRIK\EULG
FROODURSWLRQV7KHDUWLFOHSUHVHQWV FKDUDFWHULVWLFRIFROODURSWLRQVWKHSD\RIIIXQFWLRQWKHLQIOXHQFH
RI VHOHFWHG IDFWRUV WKH SULFH RI WKH XQGHUO\LQJ LQVWUXPHQW DQG WKH RSWLRQ¶V WLPH WR PDWXULW\ RQ WKH
:3à<:&=$68:<*$ĝ1,ĉ&,$1$:à$612ĝ&,+<%5<'2:(-23&-,&2//$5
SULFH DQG RQ WKH YDOXH *UHHN FRHIILFLHQWV GHOWD JDPPD YHJDWKHWD DQG UKR RI WKRVH RSWLRQV 7KH
HPSLULFDOLOOXVWUDWLRQLQFOXGHGLQWKHDUWLFOHDUHFRQFHUQHGZLWKWKHSULFLQJVLPXODWLRQVRIWKHFXUUHQF\
RSWLRQVRQ(853/1
