Wpływ czasu wygaśnięcia na własności hybrydowej opcji collar

(:$'=,$:*2

:Sá\ZF]DVXZ\JDĞQLĊFLDQDZáDVQRĞFLK\EU\GRZHMRSFMLFROODU

7KHLQIOXHQFHRIWLPHWRH[SLUDWLRQRQSURSHUWLHVRIK\EULGFROODURSWLRQV 6áRZDNOXF]RZHRSFMDRSFMDNXSQD .H\ZRUGVRSWLRQFDOORSWLRQ :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]LHPyJáNXSLüRSFMDNXSQDOXEVSU]HGDüRSFMD 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

UMCS

 (:$'=,$:*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)LQQHJDQ0LOOHU7DUF]\ĔVNL=ZRODQNRZVNLV 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\SXFROODUFKD-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[S_TK_௘K_@  JG]LH w±IXQNFMDZ\SáDW\RSFMLFROODUS_T±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 K_MHĞOLFHQDLQVWUXPHQWXED]RZHJRVSHáQLDQLHUyZQRĞüS_T”K_ S_TZSU]\SDGNXNLHG\FHQDLQVWUXPHQWXED]RZHJRVSHáQLDQLHUyZQRĞüK_ < S_T < K_ K_MHĞOLFHQDLQVWUXPHQWXED]RZHJRVSHáQLDQLHUyZQRĞüK_”S_T =DQDOL]\ZDUWRĞFLIXQNFMLZ\SáDW\Z\QLNDĪHK\EU\GRZDRSFMDW\SXFROODUMHVW SDNLHWHPVNáDGDMąF\PVLĊ]GáXJLHMRSFMLNXSQD]FHQąZ\NRQDQLDK_NUyWNLHMRSFML NXSQD]FHQąZ\NRQDQLDK_RUD]NRQWUDNWXIRUZDUGGáXJDSR]\FMD]FHQąK_eíU7íW_ 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 F_t±FHQDK\EU\GRZHMRSFMLW\SXFROODU S_t±FHQDLQVWUXPHQWXED]RZHJRZFKZLOLt T±F]DVZ\JDĞQLĊFLDRSFMLt >T@ NG±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 K d d d T t T t S r q T t K d 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

ħUyGáRRSUDFRZDQLHZáDVQH

 (:$'=,$:*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

ħUyGáRRSUDFRZDQLHZáDVQH

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 ħUyGáRRSUDFRZDQLHZáDVQH 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 ħUyGáRRSUDFRZDQLHZáDVQH :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 ħUyGáRRSUDFRZDQLHZáDVQH -0,03 -0,02 -0,01 0 0,01 0,02 0,03 K1 K2

cena instrumentu bazowego

ga

mma

collar [T= 6 mies.] collar [T= 3 mies.]

5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ ZDUWRĞFLZVSyáF]\QQLNDJDPPDK\EU\GRZHMRSFMLW\SXFROODU

ħUyGáRRSUDFRZDQLHZáDVQH



: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 ve ga

collar [T= 6 mies.] collar [T= 3 mies.]

5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDYHJDK\EU\GRZHMRSFMLW\SXFROODU 2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD

ħUyGáRRSUDFRZDQLHZáDVQH

_{ =PLHQQRĞüFHQ\LQVWUXPHQWXED]RZHJRMHVWPLHU]RQDRGFK\OHQLHPVWDQGDUGRZ\P}

 (:$'=,$:*2 -0,015 -0,01 -0,005 0 0,005 0,01 K1 K2

cena instrumentu bazowego

ve

ga

collar [T= 6 mies.] collar [T= 3 mies.]

5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ ZDUWRĞFLZVSyáF]\QQLNDYHJDK\EU\GRZHMRSFMLW\SXFROODU

ħUyGáRRSUDFRZDQLHZáDVQH

:]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 th et a

collar [T= 6 mies.] collar [T= 3 mies.]

5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDWKHWDK\EU\GRZHMRSFMLW\SXFROODU 2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD ħUyGáRRSUDFRZDQLHZáDVQH 0 0,0005 0,001 0,0015 0,002 0,0025 0,003 0,0035 K1 K2

cena instrumentu bazowego

th

et

a

collar [T= 6 mies.] collar [T= 3 mies.]

5\VXQHN:Sá\ZFHQ\LQVWUXPHQWXED]RZHJRLF]DVXZ\JDĞQLĊFLDQDNV]WDáWRZDQLHVLĊ ZDUWRĞFLZVSyáF]\QQLNDWKHWDK\EU\GRZHMRSFMLW\SXFROODU

ħUyGáRRSUDFRZDQLHZáDVQH

: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 rh o

collar [T= 6 mies.] collar [T= 3 mies.]

5\VXQHN.V]WDáWRZDQLHVLĊZDUWRĞFLZVSyáF]\QQLNDUKRK\EU\GRZHMRSFMLW\SXFROODU 2SFMHUyĪQLąVLĊWHUPLQHPZ\JDĞQLĊFLD ħUyGáRRSUDFRZDQLHZáDVQH -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

ħUyGáRRSUDFRZDQLHZáDVQH



: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 FROODURSWLRQV7KHDUWLFOHSUHVHQWVFKDUDFWHULVWLFRIFROODURSWLRQVWKHSD\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

UMCS