)UHVQHO7HUP$SSUR[LPDWLRQVIRU0HWDOV
/iV]Oy6]LUPD\.DORV
,VWYiQ/D]iQ\L
%XGDSHVW8QLYHUVLW\RI7HFKQRORJ\
0DJ\DU7XGyVRN.UW
+%XGDSHVW+XQJDU\
%XGDSHVW8QLYHUVLW\RI7HFKQRORJ\
0DJ\DU7XGyVRN.UW
+%XGDSHVW+XQJDU\
LOD]DQ\L#IUHHPDLOKX
V]LUPD\#LLWEPHKX
$%675$&7
&RORUHGUHIOHFWLRQVDUHJRYHUQHGE\WKH)UHVQHOWHUPZKLFKFDQEHH[SUHVVHGIURPWKHUHIUDFWLRQLQGH[RIWKH
PDWHULDO 7KLV IXQFWLRQ HVSHFLDOO\ IRU PHWDOV ZKHUH WKH UHIUDFWLRQ LQGH[ EHFRPHV D FRPSOH[ QXPEHU LV UDWKHU
FRPSXWDWLRQ LQWHQVLYH 7KLV SDSHU SUHVHQWV DQ DFFXUDWH VLPSOLILFDWLRQ ZKLFK FDQ DOVR FRSH ZLWK FRPSOH[
UHIUDFWLRQLQGLFHV,QRUGHUWRHVWDEOLVKWKHDSSUR[LPDWLRQ6FKOLFN¶VIRUPXODLVUHVFDOHGDQGWKHUHVLGXDOHUURULV
FRPSHQVDWHGE\DVLPSOHUDWLRQDODSSUR[LPDWLRQ7KHUHVXOWLQJIRUPXODFDQSUHVHQWUHDOLVWLFPHWDOVDQGLVVLPSOH
HQRXJKWREHLPSOHPHQWHGRQWKHYHUWH[RUSL[HOVKDGHUDQGXVHGLQJDPHV
.H\ZRUGV%5'))UHVQHOWHUP6FKOLFN¶VDSSUR[LPDWLRQ
,1752'8&7,21
LOOXPLQDWLRQWRWKHYLHZLQJGLUHFWLRQ
0DWHULDOPRGHOVDUHXVXDOO\GHILQHGE\%LGLUHFWLRQDO
5HIOHFWDQFH 'LVWULEXWLRQ )XQFWLRQV %5')V WKDW
GHVFULEHWKHFKDQFHRIUHIOHFWLRQIRUGLIIHUHQWSDLUVRI
LQFRPLQJ
DQG
RXWJRLQJ OLJKW GLUHFWLRQV
3URJUDPPDEOH YHUWH[ DQG SL[HO VKDGHUV DOORZ
VRSKLVWLFDWHG PDWHULDO PRGHOV LQVWHDG RI WKH VLPSOH
3KRQJ%OLQQ UHIOHFWLRQ PRGHO 8QOLNH WKH 3KRQJ
%OLQQ PRGHO WKHVH VRSKLVWLFDWHG PRGHOV FDQ EH
SK\VLFDOO\SODXVLEOHWKDWLVWKH\GRQRWYLRODWHEDVLF
UXOHV RI RSWLFV LQFOXGLQJ WKH +HOPKROW] V\PPHWU\
DQGHQHUJ\FRQVHUYDWLRQ
3+<6,&$//<3/$86,%/(%5')
02'(/6
$ PLFURIDFHW EDVHG VSHFXODU %5') PRGHO XVXDOO\
KDVWKHIROORZLQJSURGXFWIRUP>&RRN+H@
& &
& & &
& &
3 1 ˜ + ˜ * / 1 9 ˜ ) / ˜ + O &
1 LVWKHVXUIDFH
ZKHUHOLVWKHZDYHOHQJWKRIOLJKW
&
&
QRUPDO / LV WKH LOOXPLQDWLRQ
GLUHFWLRQ 9 LV WKH
&
YLHZLQJ GLUHFWLRQ DQG + LV WKH KDOIZD\ YHFWRU
EHWZHHQWKHLOOXPLQDWLRQDQGYLHZLQJGLUHFWLRQV
& &
0LFURIDFHWGLVWULEXWLRQ 31 ˜ + GHILQHVWKHURXJKQHVV
RI WKH VXUIDFH E\ GHVFULELQJ WKH GHQVLW\ RI
PLFURIDFHWV WKDW FDQ LGHDOO\ UHIOHFW IURP WKH
3HUPLVVLRQ WR PDNH GLJLWDO RU KDUG FRSLHV RI DOORUSDUWRI
WKLVZRUNIRUSHUVRQDORUFODVVURRPXVHLVJUDQWHGZLWKRXW
IHH SURYLGHG WKDW FRSLHV DUH QRW PDGH RU GLVWULEXWHG IRU
SURILW RU FRPPHUFLDO DGYDQWDJH DQG WKDW FRSLHV EHDU WKLV
QRWLFH DQG WKH IXOO FLWDWLRQ RQ WKH ILUVW SDJH 7R FRS\
RWKHUZLVHRUUHSXEOLVKWRSRVWRQVHUYHUVRUWRUHGLVWULEXWH
WROLVWVUHTXLUHVSULRUVSHFLILFSHUPLVVLRQDQGRUDIHH
6+257SDSHUVSURFHHGLQJV,6%1
:6&*¶-DQXDU\)HEUXDU\
3O]HQ&]HFK5HSXEOLF
&RS\ULJKW81,21$JHQF\±6FLHQFH3UHVV
& & &
*HRPHWULFWHUP * / 1 9 VKRZVKRZPXFKRIWKHVH
LGHDO UHIOHFWLRQV FDQ DFWXDOO\ RFFXU DQG LV QRW
EORFNHG E\ DQRWKHU PLFURIDFHW FDOOHG PDVNLQJ RU
VHOIVKDGRZLQJ 7KH JHRPHWULF WHUP LV LQGHSHQGHQW
RI WKH PDWHULDO SURSHUWLHV DQG LW FDXVHV D JHQHUDO
UHGXFWLRQRIWKHVSHFXODUWHUPIRUFHUWDLQLOOXPLQDWLRQ
DQG YLHZLQJ GLUHFWLRQV 6XFK UHGXFWLRQ VKRXOG EH
FRPSHQVDWHG LQ WKH GLIIXVH UHIOHFWLRQ VLQFH ZH FDQ
DVVXPH WKDW SKRWRQV UHIOHFWHG RQ WKH PLFURIDFHWV E\
PXOWLSOH WLPHV FRQWULEXWH WR WKH GLIIXVH DOVR FDOOHG
PDWWHSDUW,WDOVRPHDQVWKDWWKHPDWWHDQGVSHFXODU
SDUWVDUHQRWLQGHSHQGHQWDVDVVXPHGE\PRVWRIWKH
%5') PRGHOV EXW DUH FRXSOHG E\ DQ DSSURSULDWH
ZHLJKWLQJ ZKLFK GHSHQGV RQ WKH YLHZLQJ GLUHFWLRQ
>$VKLN.HOH@
)UHVQHOWHUP
& &
)LQDOO\ )UHVQHO WHUP ) / ˜ + O HTXDOV WR WKH
SUREDELOLW\ WKDW D SKRWRQ LV UHIOHFWHG IURP WKH
PLFURIDFHW FRQVLGHUHG DV DQ LGHDO PLUURU $FFRUGLQJ
WR WKH ODZ RI LGHDO UHIOHFWLRQ WKH QRUPDO RI WKRVH
PLFURIDFHWV
& WKDW FDQ UHIOHFW IURP
& LOOXPLQDWLRQ
GLUHFWLRQ / WR &YLHZLQJ
GLUHFWLRQ
9
& &
& & LV H[DFWO\ WKH
KDOIZD\YHFWRU + 9 / _ 9 / _7KLVLVZK\ZH
LQFOXGHGWKHDQJOHRIWKHKDOIZD\YHFWRUDQGWKHOLJKW
GLUHFWLRQ LQ WKH )UHVQHO IXQFWLRQ ZKLFK GHSHQGV RQ
WKH DQJOH RI OLJKW LQFLGHQFH7KH )UHVQHO WHUP LV WKH
RQO\IDFWRUWKDWLVZDYHOHQJWKGHSHQGHQWWKXVLWLVWKH
SULPDU\VRXUFHRIFRORULQJ7KDWLVZK\WKHDFFXUDWH
FRPSXWDWLRQ RI WKH )UHVQHO WHUP LV VR LPSRUWDQW WR
SUHVHQWUHDOLVWLFORRNIRUPDWHULDOV
7KH )UHVQHO WHUP FDQ EH REWDLQHG DV WKH VROXWLRQ RI
WKH 0D[ZHOO HTXDWLRQV DVVXPLQJ DQ LGHDO SODQDU
VXUIDFH7KHIRUPXODRIDQDUELWUDU\SRODUL]DWLRQFDQ
EH H[SUHVVHG IURP WZR EDVLF VROXWLRQV ZKHQ WKH
RVFLOODWLRQLVSDUDOOHORUSHUSHQGLFXODUWRWKHVXUIDFH
,Q WKH ILQDO UHVXOW IRU WKHVH FDVHV WKH FRPSOH[
UHIUDFWLRQLQGH[ Q N M DOVRSOD\VDFUXFLDOUROH
)S
T
FRVT
FRV
Tc
Q N M FRVT c
Q N M FRV
)
V
FRVT c Q N M FRVT
FRVT c Q N M FRVT
,QWKHVHIRUPXODH T LVWKHDQJOHRILQFLGHQFHDQG T c LV WKH DQJOH RI UHIUDFWLRQ $VVXPLQJ WKDW WKH OLJKW LV
QRW SRODUL]HG WKH UDWLR RI WKH UHIOHFWHG DQG LQFLGHQW
UDGLDQFH FDQ EH H[SUHVVHG E\ WKH 3\WKDJRUDV
)V ) S
WKHRUHP )
8VLQJ 6QHOO¶V ODZ WKH DQJOH RI UHIUDFWLRQ FDQ EH
HOLPLQDWHG IURP WKH IRUPXOD WKXV WKH )UHVQHO WHUP
GHSHQGVRQWKUHHDUJXPHQWVQDQGNDUHWKHUHDODQG
LPDJLQDU\ SDUWV RI WKH UHIUDFWLRQ LQGH[ UHVSHFWLYHO\
DQG LV WKH DQJOH RI LQFLGHQFH IRU WKH JLYHQ
PLFURIDFHW ([SUHVVLQJ WKH DEVROXWH YDOXH RI WKH
FRPSOH[ QXPEHUV WKH IROORZLQJ IRUP RI WKH )UHVQHO
IRUPXODFDQEHREWDLQHG>*ODVV@
)V
)S
)V
)LJXUH&RPSOH[UHIUDFWLRQLQGLFHVIRUGLIIHUHQW
PHWDOVIRUGLIIHUHQWZDYHOHQJWKV QP
)RU FRPSOH[UHIUDFWLRQLQGLFHVWKH)UHVQHOWHUPFDQ
KDYH YDULRXV FKDUDFWHULVWLFV )LJXUH )RU VPDOO
H[WLQFWLRQFRHIILFLHQWVIRUH[DPSOHWKH)UHVQHOWHUP
LV D PRQRWRQRXV IXQFWLRQ RI FRVT ZLWK LQFUHDVLQJ
YDOXHVDWFRVT ZKHQNLVLQFUHDVLQJ)XUWKHUPRUH
IRUODUJHUNYDOXHVWKHUHH[LVWVDORFDOPLQLPXP
D E D FRVT FRV T D E D FRV T FRV T
D E D VLQ T WDQ T VLQ T WDQ T D E D VLQ T WDQ T VLQ T WDQ T
ZKHUHDDQGEDUHGHILQHGE\WKHIROORZLQJHTXDWLRQV
D
Q
N VLQ T QN Q N VLQ T E
Q
N VLQ T QN Q N VLQ T 7KH FRPSXWDWLRQ RI WKH H[DFW )UHVQHO LV TXLWH
H[SHQVLYHHYHQRQWKHJUDSKLFVKDUGZDUH,QUHDOWLPH
DSSOLFDWLRQV ZH QHHG LWV DSSUR[LPDWLRQ ZKLFK LV
PXFKFKHDSHUWRHYDOXDWHEXWLVDFFXUDWHHQRXJKQRW
WRGHVWUR\LPDJHTXDOLW\>19@7KHPDLQREMHFWLYH
RI WKLV SDSHU LV WR SURSRVH VXFK )UHVQHO
DSSUR[LPDWLRQV
)LJXUH7KH)UHVQHOIXQFWLRQQ N ,I ZH DSSO\ 6FKOLFN¶V IRUPXOD IRU PHWDOV WKH UHVXOW
ZLOO EH HUURQHRXV ZLWK D VLJQLILFDQWO\ ODUJH HUURU DW
FRVT )LJXUHDQG)LJXUH
,Q WKH IROORZLQJV ZH SURSRVH WZR LPSURYHPHQWV WR
VLJQLILFDQWO\UHGXFHWKHHUURURIWKHRULJLQDO6FKOLFN¶V
DSSUR[LPDWLRQ
35(9,286:25.21)5(61(/
7(50$3352;,0$7,21
)RU PDQ\ QRQPHWDOOLF PDWHULDOV WKH H[WLQFWLRQ
FRHIILFLHQW N LVTXLWHVPDOOZKLFKDOORZVXVWRLJQRUH
WKHLPDJLQDU\SDUWDOWRJHWKHU7KHDVVXPSWLRQRIWKH
H[WLQFWLRQFRHIILFLHQWEHLQJ]HURKDVDOVREHHQPDGH
E\ 6FKOLFN ZKR KDV IRXQG WKH IROORZLQJ VLPSOH
UDWLRQDODSSUR[LPDWLRQIRUWKH)UHVQHOWHUP>6FKO@
)LJXUH$FRSSHUULQJUHQGHUHGZLWKWKHRULJLQDO
)UHVQHOWHUPDQGZLWK6FKOLFN¶VDSSUR[LPDWLRQ
+LED
Q Q FRVT Q 7KLVIRUPXODSURYLGHVDIDLUO\JRRGDSSUR[LPDWLRQLI
WKHH[WLQFWLRQFRHIILFLHQWLVUHDOO\]HURN DQGQLV
LQ WKH UDQJH RXWVLGH WKLV UDQJH WKH UHODWLYH
HUURULQFUHDVHVVKDUSO\VHH)LJXUH
)6FKOLFN Q FRVT 1RZ OHW XV FRQFHQWUDWH RQ PHWDOV RU RWKHU PDWHULDOV
KDYLQJFRPSOH[UHIUDFWLRQLQGH[N!)LJXUH
)LJXUH7KH)UHVQHOWHUP6FKOLFN¶VIRUPXODDQG
RXUQHZDSSUR[LPDWLRQIRUQ N 7+(1(:)5(61(/7(50
$3352;,0$7,21)250(7$/6
(UURUFRPSHQVDWLRQ
6LQFHRXUDSSUR[LPDWLRQLVXQDEOHWRIROORZWKHORFDO
PLQLPXPRIWKHRULJLQDO)UHVQHOIXQFWLRQPHWDOVZLWK
ODUJH Q N YDOXHV HJ DOXPLQXP PD\ KDYH D
QRWLFHDEOH HUURU 7R LPSURYH RXU DSSUR[LPDWLRQ ZH
VKDOO FRPSHQVDWH WKH HUURU WHUP ± WKH GLIIHUHQFH
EHWZHHQWKHRULJLQDO)UHVQHOIXQFWLRQDQGWKHUHVFDOHG
6FKOLFN¶V IRUPXOD ± ZLWK D UDWLRQDO DSSUR[LPDWLRQ
WKDWLVVLPSOHHQRXJKWRHQDEOHIDVWFDOFXODWLRQDQGLWV
VKDSH LV FORVH WR WKH VKDSH RI WKH HUURU IXQFWLRQ
)LJXUH $IWHU H[DPLQLQJ WKH HUURU WHUP ZH FKRVH
WKHIROORZLQJDSSUR[LPDWLRQ
5HVFDOLQJWKH6FKOLFN¶VIXQFWLRQ
7R UHGXFH WKH HUURU RI WKH DSSUR[LPDWLRQ ZH VKDOO
UHVFDOH 6FKOLFN¶V IRUPXOD VR WKDW LW ZLOO REH\ WKH
YDOXHRIWKHRULJLQDOIXQFWLRQQRWRQO\DWFRVT EXW
DWFRVT DVZHOO)LJXUH
7R DFKLHYH WKLV ZH FRPSXWH WKH H[DFW DQG
DSSUR[LPDWHGIXQFWLRQYDOXHVDWFRVT DVIROORZV
) )UHVQHO Q N FRVT
6 )6FKOLFN Q FRVT
Q
Q N Q Q 7KXVWKHVFDOLQJIDFWRULV )
6
Q
Q D [ [ ZKHUH [ FRVT 7KH GHULYDWLYH RI WKLV H[SUHVVLRQ DW
[ DQG HTXDOV WR D DQG UHVSHFWLYHO\ 7KH
H[SUHVVLRQKDVDORFDOPLQLPXPDW [ Q Q N 1RZ WKH PRGLILHG UHVFDOHG 6FKOLFN¶V IRUPXOD FDQ
EHH[SUHVVHGDVIROORZV
) Q N FRVT )
6
)6FKOLFN Q FRVT )LJXUH(UURUWHUPIRUQ N DQGDUDWLRQDO
DSSUR[LPDWLRQZLWKSDUDPHWHUVD DQG FRVT Q Q FRVT N
N Q N
7KH UHVXOWLQJ IRUPXOD LV DEOH WR GHDO ZLWK FRPSOH[
UHIUDFWLRQ LQGLFHV DQG LV VLPSOH HQRXJK IRU SUDFWLFDO
DSSOLFDWLRQV
Q
Q
) Q N FRVT 7RGHWHUPLQHWKHSDUDPHWHUV D DQG ZHZLOOKDYHWR
VHWXSWZRFRQVWUDLQWV
Q Q FRVT N Q N $IWHU H[DPLQLQJ WKH UHODWLYH HUURU RI WKH PRGLILHG
DSSUR[LPDWLRQ )LJXUH ZH FDQ FRQFOXGH WKDW WKLV
VLPSOHPRGLILFDWLRQHQDEOHVXVWRH[WHQGWKHRULJLQDO
6FKOLFN¶V IRUPXOD WR FRPSOH[ UHIUDFWLRQ LQGLFHV
ZLWKRXW VLJQLILFDQW LQFUHDVH RI WKH UHODWLYH HUURU
FRPSDUH HUURU IRU N DQG N! 1RWH WKDW IRU N ZHJHWEDFN6FKOLFN¶VRULJLQDOIRUPXOD
8QIRUWXQDWHO\ ZH FDQQRW HDVLO\ UHSURGXFH WKH ORFDO
PLQLPXPRIWKHHUURUWHUP+RZHYHUIRUPRVWQN
YDOXHVWKHORFDOPLQLPXPRIWKHHUURUWHUPLVORFDWHG
VRPHZKHUH LQ WKH UDQJH RI 7KH RQO\
H[FHSWLRQV DUH WKRVH Q N SDLUV ZKHUH ERWKQDQGN
DUHVPDOOEXWLQWKHVHFDVHV±DVZHKDYHVHHQHDUOLHU
± WKH HUURU WHUP LV QHJOLJLEOH 6R WKH UDWLRQDO
DSSUR[LPDWLRQ VKRXOG REH\ WKH YDOXH RI WKH RULJLQDO
HUURUIXQFWLRQDW [ FRVT ZKLFKLVFORVHWRLWV
ORFDOPLQLPXP
2XU VHFRQG FRQVWUDLQW ZLOO EH WKH HTXDOLW\ RI WKH
GHULYDWLYHVDW[ )RUODUJHNYDOXHV±WKDWLVZKHUH
HUURUFRPSHQVDWLRQEHFRPHVQHFHVVDU\±ZHFDQXVH
WKHIROORZLQJDSSUR[LPDWLRQ D Q ZKHUHYDOXH
Q LVDTXLWHJRRGDSSUR[LPDWLRQIRUWKHGHULYDWLYH
RIWKHRULJLQDO)UHVQHOWHUPDW[ 7KHGHULYDWLYHRI
WKH PRGLILHG 6FKOLFN¶V IRUPXOD LV DVVXPHG WR EH
]HUR $V VKRZQ EHORZ WKH UHODWLYH HUURU FDQ EH
UHGXFHG EHORZ HYHQ ZLWK WKLV DVVXPSWLRQ VR
WKHUH LV QR QHHG WR FDOFXODWH WKH H[DFW GHULYDWLYH
1RWHWKHGUDPDWLFLPSURYHPHQWLQFDVHRIDOXPLQXP
UHODWLYH
)LJXUH5HODWLYHHUURURIWKHUHVFDOHG6FKOLFN¶V
IRUPXODIRUGLIIHUHQWQDQGNYDOXHV
HUURU
UHVFDOLQ
DSSUR[
H[DFW
IRU
JRQO\
GHULYDWLYH
GHULYDWLYH
FRSSHU
JROG
VLOYHU
DOX
9DOXHV D DQG VKRXOG EH UHJDUGHG DV GHULYHG
PDWHULDOSURSHUWLHV:KHQWKH&38SURJUDPLQVWUXFWV
WKH *38 WR XVHDGLIIHUHQWPDWHULDOPRGHOLWVKRXOG
FRPSXWHWKHVHSDUDPHWHUVDQGGRZQORDGWKHPWRWKH
*38DVXQLIRUPYDULDEOHV
$FFRUGLQJ WR RXU WHVWV WKH SURSRVHG VLPSOLILFDWLRQV
GR QRW UHGXFH LPDJH TXDOLW\ EXW UHGXFH UHQGHULQJ
WLPHV WR WKHLU KDOI RU WKLUG 7KH IROORZLQJ WDEOH
VXPPDUL]HVWKHUHODWLYHFRPSXWDWLRQWLPHV
)UHVQHOIRUPXOD
6FKOLFN¶VIRUPXOD
5HVFDOHG6FKOLFN¶VIRUPXOD
(UURUFRPSHQVDWLRQ
&21&/86,216
7KLV SDSHU SURSRVHG WZR QHZ DSSUR[LPDWLRQV RIWKH
)UHVQHOIXQFWLRQ8QOLNHSUHYLRXVDSSURDFKHVZHGLG
QRW DVVXPH WKDW WKH LPDJLQDU\ SDUW RI WKH UHIUDFWLRQ
LQGH[LVQHJOLJLEOHWKXVRXUPRGHOFDQEHDSSOLHGIRU
D ZLGHU UDQJH RI PDWHULDOV HJ PHWDOV 2XU WZR
DSSUR[LPDWLRQV GLIIHU LQ DFFXUDF\ DQG FRVW RI
HYDOXDWLRQ7KHPRUHDFFXUDWHDSSUR[LPDWLRQFDOOHG
³HUURUFRPSHQVDWLRQ´LVZRUWKDSSO\LQJLIWKHUHLVD
VLJQLILFDQW EDFN OLJKWLQJ LQ WKH VFHQH ,Q RWKHU FDVHV
WKHUHVFDOHGPRGHOSURYLGHVVDWLVIDFWRU\UHVXOWV
5()(5(1&(6
>$VKLN@ $VKLNKPLQ 0 DQG 3UHPR]H 6 DQG
6KLUOH\ 3 $ 0LFURIDFHWEDVHG %5') *HQHUDWRU
6,**5$3+
>&RRN@ &RRN 5 DQG 7RUUDQFH . $ 5HIOHFWDQFH
0RGHO IRU &RPSXWHU *UDSKLFV &RPSXWHU *UDSKLFV
9RO1XP
>*ODVV@ $6*ODVVQHU 3ULQFLSOHV RI 'LJLWDO ,PDJH
6\QWKHVLV9RO0RUJDQ.DXIPDQQ3XEOLVKHUV,QF
6DQ)UDQFLVFR,6%1
>+H@ +H ; DQG 7RUUDQFH . DQG 6LOOLRQ ) DQG
*UHHQEHUJ'$&RPSUHKHQVLYH3K\VLFDO0RGHOIRU
/LJKW5HIOHFWLRQ&RPSXWHU*UDSKLFV9RO1XP
>.HOH@ &V .HOHPHQ DQG / 6]LUPD\.DORV $
0LFURIDFHW %DVHG &RXSOHG 6SHFXODU0DWWH %5')
0RGHO ZLWK ,PSRUWDQFH 6DPSOLQJ 6KRUW
3UHVHQWDWLRQV(852*5$3+,&6
>19@ )UHVQHO 5HIOHFWLRQ 19LGLD 7HFKQLFDO
5HSRUW
-XO\
KWWSGHYHORSHUQYLGLDFRPDWWDFK
>6FKO@ &K 6FKOLFN $Q LQH[SHQVLYH %5') PRGHO
IRU SK\VLFDOO\EDVHG UHQGHULQJ 3URFHHGLQJ RI WKH
,QWHUQDWLRQDO&RQIHUHQFH(XURJUDSKLFV
6FKOLFN¶VPRGHO 5HVFDOHGPRGHO
&RPSHQVDWHGPRGHO
([DFW)UHVQHOWHUP
)LJXUH&RSSHUVLOYHUDQGDOXPLQXPULQJVUHQGHUHGZLWKGLIIHUHQW)UHVQHODSSUR[LPDWLRQV