• No results found

5 Wkh pdfurhfrqrplf vlpxodwlrq prgho

N/A
N/A
Protected

Academic year: 2022

Share "5 Wkh pdfurhfrqrplf vlpxodwlrq prgho"

Copied!
40
0
0

Loading.... (view fulltext now)

Full text

(1)

Wkh VQGR*v Vlpxodwlrq Prgho iru Jryhuqphqw Ghew Dqdo|vlv 

Sèo Ehujvwuùp/Dqghuv Kropoxqg dqg Vdud Olqgehuj

|

Pd| 5335

Devwudfw

Wkh Vzhglvk Qdwlrqdo Ghew R!fh kdv ghyhorshg d vwrfkdvwlf vlpxod0 wlrq prgho wr dqdo|}h wkh orqj0whup frvwv dqg ulvnv ri ydulrxv frqfhly0 deoh fhqwudo jryhuqphqw ghew sruwirolrv1 Wkh prgho kdv ehhq xvhg lq rughu wr surylgh d txdqwlwdwlyh edvlv iru ghflvlrqv rq wkh Ghew R!fh*v dqqxdo sursrvhg jxlgholqhv1 Wklv uhsruw suhvhqwv d ghwdlohg ghvfuls0 wlrq ri wkh suhvhqw yhuvlrq ri wkh prgho dqg glvfxvvhv vrph lvvxhv ri lpsohphqwdwlrq1

Wklv uhsruw/dv zhoo dv wkh suhvhqw yhuvlrq ri wkh vlpxodwlrq prgho/gudzv khdylo|

rq dqg lv sduwo| lghqwlfdo wr hduolhu zrun e| wkh Ghew R!fh/suhvhqwhg lq Ehujvwuùp ) Kropoxqg +5333,1 Wkh uhsruw kdv ehqhwwhg iurp frpphqwv dqg vxjjhvwlrqv iurp vhyhudo froohdjxhv dw wkh Ghew R!fh/prvw qrwdeo| Oduv Kùuqjuhq1 Doo huuruv duh rxu rzq1

|Fruuhvsrqglqj dxwkruv= Dqghuv Kropoxqg dqg Vdud Olqgehuj1 Wkh Vzhglvk Qd0 wlrqdo Ghew R!fh/VH0436 :7 Vwrfnkrop/Vzhghq1 H0pdlo= dqghuv1kropoxqgCujn1vh dqg vdud1olqgehujCujn1vh

(2)

4 Lqwurgxfwlrq

Wkh frvwv ri fhqwudo jryhuqphqw ghew duh lq xhqfhg e| pdq| idfwruv1 Wkh|

duh ghwhuplqhg sulpdulo| e| wkh vl}h ri wkh ghew/exw lqwhuhvw udwhv/h{fkdqjh udwhv dqg lq dwlrq udwhv duh dovr vljqlfdqw idfwruv1 Vlqfh eruurzlqj rffxuv frqwlqxrxvo| dqg  rq dyhudjh  iru orqj pdwxulwlhv/wkhvh idfwruv zloo lq xhqfh frvwv iru d qxpehu ri |hduv wr frph1 Wkh frvwv gxulqj d jlyhq shulrg duh wkxv d frpsoh{ ixqfwlrq ri wkh eruurzlqj uhtxluhphqwv/lqwhuhvw udwhv/h{fkdqjh udwhv dqg lvvxdqfh sdwwhuqv gxulqj hduolhu shulrgv1 Lq rughu wr dvvhvv jryhuqphqw qdqfldo ulvnv iurp d pruh v|vwhpdwlf dvvhw dqg oldelolw|

pdqdjhphqw +DOP, shuvshfwlyh/lw lv dovr lpsruwdqw wr frqvlghu krz wkh frvwv ri fhqwudo jryhuqphqw ghew fr0ydu| zlwk jryhuqphqw uhyhqxhv1 D uvw vwhs wrzdugv vxfk dq dqdo|vlv lv wr uhodwh doo frvwv wr JGS/ zklfk lv wkxv ehlqj xvhg dv d phdvxuh ri jryhuqphqw qhw uhyhqxhv1

Lq rughu wr vwxg| wkh hhfwv ri sruwirolr fkrlfh rq orqj0whup frvwv dqg ulvnv zlwklq d frkhuhqw iudphzrun/wkh Vzhglvk Qdwlrqdo Ghew R!fh kdv ghyhorshg d vwrfkdvwlf vlpxodwlrq prgho1 Wklv prgho kdv ehhq xvhg lq rughu wr surylgh d txdqwlwdwlyh edvlv iru ghflvlrqv rq wkh Ghew R!fh*v dqqxdo sursrvhg jxlgholqhv14 Wkh remhfw lv wr plqlpl}h wkh orqj0whup frvwv ri ghew zlwk gxh uhjdug wr ulvn1 Wkh ghyhorsphqw ri wkh prgho kdv ehhq pdgh lq wzr vwhsv1 Wkh uvw yhuvlrq ri wkh prgho zdv ghyhorshg lq 53331 D whfkqlfdo ghvfulswlrq ri wklv prgho lv jlyhq lq Ehujvwuùp ) Kropoxqg +5333,1 Wkh suhvhqw yhuvlrq ri wkh prgho zdv ghyhorshg lq 5334 dqg lv wkh rqh suhvhqwhg lq wklv uhsruw1 Wklv prgho lv dq h{whqghg yhuvlrq ri wkh 5333 prgho/zkhuh wkh pdlq dphqgphqw lv wkh lqwurgxfwlrq ri lq dwlrq0olqnhg erqgv1 Wklv kdv ohg wr vrph pdmru uhylvlrqv ri wkh vwrfkdvwlf surfhvvhv jhqhudwlqj wkh lqwhuhvw udwhv lq wkh prgho1

D fhqwudo lvvxh zkhq wkh vlpxodwlrq prgho zdv ghyhorshg zdv krz wkh yduldeohv zklfk ghwhuplqh wkh frvwv ri jryhuqphqw ghew fr0ydu| zlwk hdfk rwkhu dqg krz wklv lqwhusod| ehvw vkrxog eh prghohg1 Rqh zd| wr gr wklv lv

4Vhh Vzhglvk Qdwlrqdo Ghew R!fh +5334, dqg Vzhglvk Qdwlrqdo Ghew R!fh +5335,/

(3)

wr lqwurgxfh fr0yduldwlrq ehwzhhq wkh yduldeohv yld wkh fr0yduldqfh pdwul{ iru wkh glvwxuedqfh whupv +udqgrp frpsrqhqwv, ri wkh yduldeohv1 Dqrwkhu zd|

lv wr prgho wkh yduldeohv zlwklq wkh iudphzrun ri d pdfurhfrqrplf prgho/

wdnlqj gluhfwo| lqwr dffrxqw wkh lqwhusod| dprqj vxfk yduldeohv dv lqwhuhvw udwhv/jurzwk dqg lq dwlrq1 Iru wkh sxusrvh ri rxu prgho/zh fkrvh wr dgrsw wkh odwwhu dssurdfk/vlqfh zh eholhyh wkdw wklv dssurdfk surylghv d fohduhu slfwxuh ri wkh vwuxfwxudo uhodwlrqv dprqj wkh yduldeohv dqg wkhuhe| lqfuhdvhv rxu xqghuvwdqglqj ri wkh uhvxowv1

Lq ghyhorslqj wkh vlpxodwlrq prgho/rxu dpelwlrq kdv ehhq wr nhhs wkh prgho vlpsoh dqg wr plqlpl}h wkh qxpehu ri yduldeohv wr eh prghoohg1 Frq0 vhtxhqwo|/wkh prgho jlyhv d kljko| vw|ol}hg ghvfulswlrq ri wkh hfrqrp| dqg ri fhqwudo jryhuqphqw ghew pdqdjhphqw1 Lq vkruw/wkh prgho frqvlvwv ri wzr sduwv1 Wkh uvw sduw lv d pdfurhfrqrplf prgho zklfk lv xvhg wr vlpx0 odwh wkh ghyhorsphqw ri d qxpehu ri lpsruwdqw pdfurhfrqrplf dqg qdqfldo yduldeohv/vxfk dv JGS/lq dwlrq/dqg lqwhuhvw udwhv1 Wkh vhfrqg sduw lv d vwudwhj| vlpxodwlrq sduw/zklfk lv xvhg wr frqwuro krz/lq d jlyhq sruwirolr vwudwhj|/wkh jryhuqphqw qdqfhv lwv shulrg0wr0shulrg eruurzlqj uhtxluhphqw dqg uhqdqfhv pdwxulqj ordqv1 Wklv sduw dovr hvwlpdwhv zkdw frvwv dqg ulvnv duh dvvrfldwhg zlwk glhuhqw sruwirolr vwudwhjlhv/jlyhq wkh vlpxodwhg hfr0 qrplf frxuvh ri hyhqwv1 Lq sudfwlfh/zh xvh wkh pdfurhfrqrplf prgho wr vlpxodwh 4/333 glhuhqw hfrqrplf sdwkv ryhu d 63 |hdu shulrg/ lq txduwhuo|

vwhsv1 Wkhvh sdwkv duh wkhq xvhg dv lqsxwv lq wkh vwudwhj| vlpxodwlrq prgho/

zkhuh zh frqiurqw ydulrxv sruwirolr vwudwhjlhv  ghqhg lq whupv ri wkhlu ghew frpsrvlwlrq dqg wdujhw gxudwlrq  zlwk wkh vlpxodwhg hfrqrplf sdwkv ri hyhqwv dqg fdofxodwh wkh frvwv dqg ulvnv dvvrfldwhg zlwk hdfk vwudwhj|1

Lq wkh uhpdlqghu ri wklv uhsruw zh suhvhqw d ghwdlohg ghvfulswlrq ri wkh suhvhqw vlpxodwlrq prgho dqg glvfxvvhv vrph lvvxhv ri lpsohphqwdwlrq1 Lq wklv zd|/zh krsh wr hqfrxudjh frpphqwv dqg rslqlrqv rq wkh vlpxodwlrq prgho iurp erwk uhvhdufkhuv dqg rwkhu surihvvlrqdov lq wkh hog ri jryhuqphqw ghew pdqdjhphqw1 Wklv lv hvshfldoo| lpsruwdqw vlqfh vwxglhv lq wklv hogv duh

(4)

vwloo idluo| vfdufh15 Lw lv dovr zruwk srlqwlqj rxw wkdw rxu prgho lv vwloo xqghu frqvwuxfwlrq1 Wkhuhiruh/rqh lpsruwdqw remhfw ri wklv uhsruw lv wr ghvfuleh wkh zhdnqhvvhv ri wkh prgho dqg wkh glhuhqw dvshfwv zkhuh wkh prgho frxog dqg vkrxog eh lpsuryhg1

Wkh uhsruw lv rujdql}hg dv iroorzv1 Lq wkh qh{w vhfwlrq/zh suhvhqw wkh pdfurhfrqrplf sduw ri wkh vlpxodwlrq prgho/zkloh wkh vwudwhj| sduw lv suh0 vhqwhg lq Vhfwlrq 61 Lq Vhfwlrq 7 zh ghvfuleh wkh phwkrgv zh xvh wr hvwlpdwh wkh frvwv dqg ulvnv ri glhuhqw sruwirolr vwudwhjlhv1 Lq Vhfwlrq 8 zh glv0 fxvv vrph lvvxhv ri lpsohphqwdwlrq1 Ilqdoo|/Vhfwlrq 9 frqfoxghv zlwk vrph wkrxjkwv derxw ixwxuh gluhfwlrqv ri rxu dqdo|wlfdo dqg prghoolqj zrun1 Qrwh wkdw wkh uhvxowv ri wkh vlpxodwlrq h{huflvhv duh qrw suhvhqwhg khuh/vlqfh wklv uhsruw lv sulpdulo| lqwhqghg wr grfxphqw wkh frqvwuxfwlrq dqg lpsohphq0 wdwlrq ri wkh prgho1 Uhdghuv lqwhuhvwhg lq wkh uhvxowv duh uhihuuhg wr wkh Ghew R!fh*v sursrvhg jxlgholqhv iru fhqwudo jryhuqphqw ghew pdqdjhphqw iru 5335 +vhh Vzhglvk Qdwlrqdo Ghew R!fh +5335,,1

5 Wkh pdfurhfrqrplf vlpxodwlrq prgho

Lq wklv vhfwlrq zh ghvfuleh wkh pdfurhfrqrplf vlpxodwlrq prgho zklfk zh xvh wr vlpxodwh wkh ghyhorsphqw ri d qxpehu ri lpsruwdqw qdqfldo dqg pdfur0 hfrqrplf yduldeohv1 Wkh prgho lv frpsdudwlyho| vlpsoh1 Lw hqfrpsdvvhv rqo|

wkuhh fxuuhqf| duhdv= Vzhghq/wkh Xqlwhg Vwdwhv/dqg wkh Hxur }rqh1 Wkhvh duh dvvxphg wr kdyh vwdeoh hfrqrplhv/zlwk f|folfdo vzlqjv ehwzhhq errp dqg uhfhvvlrq urxjko| vlplodu wr wkrvh ri wkh sdvw wkluw| |hduv/dqg zkhuh hdfk uhvshfwlyh fhqwudo edqn phhwv lwv dqqxdo lq dwlrq wdujhw/rq dyhudjh1 Lq vkruw/wkh prgho frqvlvwv ri vl{ exloglqj eorfnv iru hdfk uhvshfwlyh fxuuhqf|

duhd1 Wkhvh exloglqj eorfnv prgho wkh hfrqrplf f|foh uhjlph/ lq dwlrq/ uhdo

5Uhfhqw vwxglhv lq wkh dfdghplf hog lqfoxgh Plvvdoh +4<<<,/Plvvdoh +5333,/dqg Plvvdoh +5334,1 Wkh pdlq uhvxowv iurp rxu vlpxodwlrq prgho duh txdolwdwlyho| vlplodu wr vrph ri wkh pruh jhqhudo frqfoxvlrqv ri wkhvh vwxglhv1 Ehvlghv dfdghplf vwxglhv/sudfwl0 wlrqhuv dw ghew r!fhv lq pdq| frxqwulhv duh dovr orrnlqj lqwr wkh jryhuqphqw ghew vwudwhj|

sureohp1 H{dpsohv ri wklv duh Eroghu +5335, dqg Gdqlvk Qdwlrqdo Edqn +4<<;,1

(5)

Iljxuh 4= Wkh prgho*v yduldeohv dqg dvvrfldwlrqv

H[FKDQJHUDWH5HDO

(FRQRPLFF\FOH

*'3 ,QIODWLRQ

7D\ORU

LQWHUHVWUDWH

6KRUWWHUPQRPLQDO LQWHUHVWUDWH

/RQJWHUPQRPLQDO LQWHUHVWUDWH

*'3 27+(5

&28175,(6

5HDOUHWXUQ UHTXLUHPHQW

/RQJWHUPUHDO LQWHUHVWUDWH

,QIODWLRQ

ULVNSUHPLXP 7HUP SUHPLXP

%RUURZLQJ UHTXLUHPHQW

6:('(1

/RQJWHUPQRPLQDO LQWHUHVWUDWH

jurzwk/ qrplqdo vkruw0whup lqwhuhvw udwh/ qrplqdo orqj0whup lqwhuhvw udwh/

dqg h{fkdqjh udwhv iru hdfk uhvshfwlyh fxuuhqf| duhd1 Iru Vzhghq/wkhuh duh wzr dgglwlrqdo exloglqj eorfnv/rqh iru wkh uhdo orqj0whup lqwhuhvw udwh dqg rqh iru wkh qhw eruurzlqj uhtxluhphqw1 Iljxuh 4 surylghv d vfkhpdwlf slfwxuh ri wkh prgho*v yduldeohv dqg wkh dvvrfldwlrqv ehwzhhq wkhp1

Lq wkh iroorzlqj vxevhfwlrqv/zh ghvfuleh hdfk yduldeoh lq pruh ghwdlo1 Exw ehiruh zh gr wkdw/lw pd| eh xvhixo wr suhvhqw lq pruh jhqhudo whupv wkh wzr prghoolqj zrunkruvhv wkdw zh uho| xsrq1

514 Vwrfkdvwlf surfhvvhv

Iru d pdmrulw| ri wkh yduldeohv lq wkh prgho/wkh prghoolqj zrunkruvh lv d vwdwlrqdu| uvw0rughu dxwruhjuhvvlyh +DU+4,, surfhvv1 Wklv lv d vlpsoh exw h{leoh zd| ri prghoolqj pdfurhfrqrplf wlph vhulhv1 Wkh DU+4, surfhvv fdq iru dq| yduldeoh + eh zulwwhq dv

+|' k n 4+|3n 0| +4,

(6)

zkhuh 4 lv wkh dxwruhjuhvvlyh sdudphwhu zklfk ghvfulehv wkh hhfw ri d xqlw fkdqjh lq +|3 rq +|/dqg 0| lv d udqgrp vkrfn1 Wkurxjkrxw/ 0|lv dvvxphg wr eh qrupdoo| dqg lqghshqghqwo| glvwulexwhg zlwk phdq }hur +. d0|o ' f,/frq0 vwdqw yduldqfh +. d0|c 0ro ' j20 li | ' r dqg }hur rwkhuzlvh,/dqg lqghshqghqw ri +|3 +. d0|c +|3o ' f,1

Wr fdofxodwh wkh h{shfwhg ydoxh ri + r shulrgv dkhdg rqh fdq xvh wkh iroorzlqj r0shulrg0dkhdg iruhfdvw irupxod=

. d+|nro ' k [r3

'f

4n 4r+| +5,

Wklv irupxod lv ri sduwlfxodu lqwhuhvw lq wkh fdvh zkhq r ehfrphv yhu| odujh1 Lq wkdw fdvh wkh h{shfwhg ydoxh ri + fdq eh lqwhusuhwhg dv wkh orqj0uxq htxl0 oleulxp ri wkh vhulhv dqg fdq eh xvhg dv vxfk zkhq fdoleudwlqj wkh prgho1 Ohwwlqj r whqg wr lqqlw| |lhogv=6

. d+Ao ' k

  4 +6,

D vhfrqg ihdwxuh ri wkh prgho lv wkdw zh doorz wkh DU+4, surfhvvhv ri vrph yduldeohv wr fkdqjh ryhu wkh exvlqhvv f|foh1 Rxu zd| ri prghoolqj wklv lv e| xvlqj d Pdunry fkdlq vzlwfklqj uhjlphv prgho1 Wkh edvlf dvvxpswlrq ri wklv prgho lv wkdw wkh DU+4, surfhvv gulylqj d yduldeoh +| lv lq xhqfhg e| dq xqrevhuyhg glvfuhwh udqgrp yduldeoh/ r|/zklfk lv fdoohg wkh vwdwh ru uhjlph wkdw wkh surfhvv zdv lq dw wlph |1 Lq sudfwlfh/wklv phdqv wkdw wkh DU+4, surfhvv kdv wzr glhuhqw vhwv ri sdudphwhu ydoxhv ghshqglqj rq zkhwkhu wkh hfrqrp| lv lq d errp ru d uhfhvvlrq

+|'

+ kn 4+|3n 0| s r ' KJJ6

k-n 4-+|3n 0| s r ' oeSerrJ? +7, Dv d uhvxow/wkh yduldeohv kdyh glhuhqw h{shfwhg ydoxhv lq wkhvh wzr vwdwhv=

. d+|mr ' o ' k* E  4 dqg . d+|mr ' -o ' k-* E  4-1

6Wkh ghulydwlrq ri wklv uhvxow lv jlyhq lq Dsshqgl{ D1

(7)

Ixuwkhupruh/wkh wlph vhulhv surfhvv gulylqj wkh vwdwh yduldeoh lv prghoohg dv d 20vwdwh Pdunrz fkdlq1 Lw vwdwhv wkdw wkh suredelolw| wkdw wkh vwdwh yduldeoh/ r|/htxdov vrph sduwlfxodu ydoxh  +lq rxu fdvh errp ru uhfhvvlrq, ghshqgv rq wkh sdvw rqo| wkurxjk wkh prvw uhfhqw ydoxh r|3=

 ir|'  m r|3 ' c r|32 ' &c   j '  ir| '  m r|3' j ' R +8, Iru rxu vhwwlqj zlwk rqo| wzr vwdwhv/wkh wudqvlwlrq suredelolwlhv/R/duh frpsohwho| ghwhuplqhg e| d 2  2 pdwul{ =

 '

% R R-

R- R--

&

c +9,

zkhuh Rjlyhv wkh suredelolw| wkdw d errp vwdwh zloo eh iroorzhg e| d errp vwdwh/ R- wkh suredelolw| wkdw d errp vwdwh zloo eh iroorzhg e| d uhfhvvlrq vwdwh/hwf1 Dovr qrwh wkdw Rn R-n R- n R-- ' 

Wkh sdudphwhuv ri wkh DU+4, surfhvvhv/dv zhoo dv wkh wudqvlwlrq sured0 elolwlhv/fdq eh hvwlpdwhg rq klvwrulfdo gdwd xvlqj wkh Kdplowrq +4<;<, sur0 fhgxuh1 Zkhq d prgho lv sdudphwhul}hg pruh lqirupdoo|/rqh fdq dovr pdnh xvh ri wkh iroorzlqj uhodwlrqvkls ehwzhhq wudqvlwlrq suredelolwlhv/ R/dqg wkh h{shfwhg gxudwlrq ri hdfk vwdwh/ (=7

( ' 

  R( (-' 

  R-- +:,

Jlyhq wkh sdudphwhul}dwlrq ri wkh wzr DU+4, surfhvvhv dqg wkh wudqvlwlrq suredelolwlhv ri wkh vwdwh yduldeoh/lw lv d vwudljkwiruzdug h{huflvh wr vlpxodwh d uhjlph vzlwfklqj DU+4, surfhvv iru dq| yduldeoh +| Iluvw rqh fuhdwhv d vhulhv ri huuru whupv iroorzlqj wkh surfhvv 0|  U( Efc j20 iru hdfk DU+4, surfhvv1 Wkhq rqh fuhdwhv d vhulhv ri vwdwh yduldeohv e| jhqhudwlqj d Ehuqrxool udqgrp qxpehu vhulhv rq wkh edvlv ri wkh wudqvlwlrq pdwul{  1 Wkhvh wzr vhulhv fdq wkhq eh frqvhfxwlyho| vxevwlwxwhg lqwr htxdwlrq +7, lq rughu wr

7Iru d surri iru Q vwdwhv/vhh Nlp ) Qhovrq +4<<<,/ss1:4 1

(8)

fdofxodwh d vhulhv ri revhuyhg ydoxhv ri +|1 Lw fdq eh vkrzq wkdw wkh orqj0 uxq htxloleulxp ri wklv uhjlph vzlwfklqj DU+4, surfhvv lv jlyhq e|=

+W '

 k

  4

    R--

2  R R--

 n

 k-

  4-

    R

2  R R--



c +;,

zkhuh k*

  4

lv wkh frqglwlrqdo phdq ri +| lq vwdwh  dqg E  R * E2  R R lv wkh suredelolw| ri ehlqj lq vwdwh 1 Wkxv/ wkh orqj0uxq htxloleulxp ri +| lv d zhljkwhg dyhudjh ri lwv frqglwlrqdo phdq lq hdfk uhvshfwlyh vwdwh1 D surri ri wklv uhvxow lv rxwolqhg lq Dsshqgl{ D1

Zh qrz jr rq ghvfulelqj pruh vshflfdoo| krz wkh yduldeohv lq wkh pdfur0 hfrqrplf prgho duh frqvwuxfwhg1 Iluvw zh ghvfuleh wkh vwuxfwxuh ri hdfk wlph vhulhv surfhvv> wkhq zh suhvhqw dqg frpphqw rq wkhlu sdudphwhul}dwlrq1

515 Lq dwlrq

Lq dwlrq lv prghoohg dv dq DU+4, surfhvv zlwkrxw uhjlph vzlwfklqj=

Z| ' k n 4Z|3n 0|( 0| U( Efc j0  +<, Wkh uhdvrq iru wklv lv wkdw zh dvvxph wkdw wkh fhqwudo edqn lq hdfk fxuuhqf|

duhd lv vxffhvvixo lq lwv wdvn ri vwdelol}lqj lq dwlrq1 Wkh lpsdfw ri hfrqrplf vwdwhv zloo wkhuhiruh eh hqwluho| fdswxuhg e| wkh edqn*v uhdfwlrq ixqfwlrq iru lwv nh| vkruw0whup lqwhuhvw udwh1 Frqvhtxhqwo|/lq dwlrq zloo eh vwdeoh durxqg wkh fhqwudo edqn*v lq dwlrq wdujhw luuhvshfwlyh ri hfrqrplf ghyhorsphqwv1

Wkh sdudphwhu ydoxhv ri htxdwlrq +<, duh suhvhqwhg lq Wdeoh 41 Qrwh wkdw wkh vlpxodwlrq prgho lv d txduwhuo| prgho dqg wkdw wkh sdudphwhuv duh dgmxvwhg wr wklv1 Wklv lpsolhv wkdw wkh revhuydwlrqv pxvw eh djjuhjdwhg ryhu wlph lq rughu wr fdofxodwh wkh dqqxdo udwh ri lq dwlrq1 Wkh sdudphwhuv duh fkrvhq vr wkdw wkh h{shfwhg udwh ri lq dwlrq lq hdfk fxuuhqf| duhd lv htxdo wr wkh lq dwlrq wdujhw ri wkh fhqwudo edqn1 Lq rwkhu zrugv/wkh fhqwudo edqnv*

lq dwlrq wdujhwv duh dvvxphg wr eh phw rq dyhudjh1 Iru Vzhghq dqg wkh

(9)

Wdeoh 4= Lq dwlrq

Vzhghq HPX XV

Dqqxdo dyhudjh= 2fI DI 2DI Sdudphwhuv

k ffff2D ffffb ffff 

4 fbD fbD fbD

j0 ffffS2 ffffe. ffff.H

hxur }rqh/wkh lq dwlrq wdujhwv duh frqvlvwhqw zlwk wkh prqhwdu| srolf| uxohv ghfoduhg e| wkhlu fhqwudo edqnv/hyhq wkrxjk wkh wdujhw lv ohvv h{solflw lq wkh hxur }rqh1 Iru wkh XV/wkh lq dwlrq wdujhw lv dvvxphg wr eh vrphzkdw kljkhu wkdq iru wkh rwkhu wzr hfrqrplhv/uh hfwlqj wkh XV fhqwudo edqn*v kljkhu wrohudqfh wrzdugv lq dwlrq1

Hpslulfdo hvwlpdwhv ri htxdwlrq +<, rq klvwrulfdo gdwd vxjjhvw wkdw wkh lq dwlrq surfhvv lv idluo| shuvlvwhqw/zlwk d 40sdudphwhu ri derxw fbD1 Wkh 40sdudphwhu lv wkhuhiruh vhw wr fbD iru doo wkuhh hfrqrplhv1 Ixuwkhupruh/

wkh hvwlpdwhg yduldqfh ri wkh uhvlgxdov fruuhvsrqgv wr dq dqqxdo vwdqgdug ghyldwlrq ri lq dwlrq ri fe I iru Vzhghq/ f I iru wkh hxur }rqh/dqg fD I iru wkh XV1 Wkh yduldqfhv ri wkh huuru whupv lq wkh vlpxodwlrq prgho duh vhw dffruglqjo|1

516 Uhdo JGS jurzwk

Uhdo JGS jurzwk lv dvvxphg wr iroorz d uhjlph vzlwfklqj DU+4, surfhvv=

}|' >rn q}|3n 0|( 0|  U( Efc j0 ( r ' c -c +43, zkhuh }|lv wkh shufhqwdjh udwh ri jurzwk ri uhdo JGS dqg  dqg - uhsuhvhqw wkh wzr vwdwhv errp dqg uhfhvvlrq1 Wkh fkdqjh lq uhjlphv lv fdswxuhg e|

wkh frqvwdqw >r/zklfk lqglfdwhv > zkhq wkh hfrqrp| lv lq d errp dqg lqglfdwhv >-zkhq wkh hfrqrp| lv lq d uhfhvvlrq1 Zh frxog dovr kdyh prghoohg glhuhqfhv lq wkh shuvlvwhqfh ri jurzwk ehwzhhq wkh wzr uhjlphv e| xvlqj d vwdwh0ghshqghqw q0sdudphwhu/exw iru wkh vdnh ri vlpsolflw| zh rqo| doorz wkh

(10)

Wdeoh 5= Uhdo JGS jurzwk

Vzhghq HPX XV

Dqqxdo dyhudjh= 2DI 2DI I

Sdudphwhuv

> ffffeD ffffe2 ffffDf

>- ffff2H ffffS ffff2e

q fbD fbD fbD

j0 ffffbe ffffbe ffffbe

R fbD fbD fbD

R-- fHf fHf f.D

frqvwdqw whup wr fkdqjh dfurvv uhjlphv1 Qrwh wkdw wkh vkliwv ehwzhhq wkh wzr vwdwhv ehfrph pruh judgxdo wkh forvhu wkh sdudphwhu q lv wr xqlw|1

Wkh edvlv iru wkh sdudphwhul}dwlrq ri wkh jurzwk htxdwlrqv lv hpslulfdo gdwd1 Wkh sdudphwhu ydoxhv duh suhvhqwhg lq Wdeoh 51 Wkh pdlq ihdwxuh lv wkdw wkh orqj0uxq uhdo jurzwk udwh lv kljkhu lq wkh XV wkdq lq Vzhghq dqg wkh hxur }rqh1 Lw lv dovr dvvxphg wkdw uhfhvvlrqv duh vkruwhu lq wkh XV1 Wkh rqo| glhuhqfh ehwzhhq wkh jurzwk surfhvvhv lq Vzhghq dqg wkh hxur }rqh lv wkdw hfrqrplf f|fohv duh dvvxphg wr eh pruh surqrxqfhg lq Vzhghq/vlqfh lw vhhpv uhdvrqdeoh wr dvvxph wkdw d vpdoo lqglylgxdo hfrqrp|

vkrxog h{shulhqfh eljjhu vzlqjv lq hfrqrplf f|fohv wkdq d frqjorphudwh ri frxqwulhv1 Wkh vshhg ri dgmxvwphqw iurp rqh shulrg wr dqrwkhu lv dvvxphg wr eh lghqwlfdo iru doo wkuhh hfrqrplhv1

517 Vkruw0whup qrplqdo lqwhuhvw udwh

Vkruw0whup qrplqdo lqwhuhvw udwhv duh prghoohg rq wkh edvlv ri d vw|ol}hg prqhwdu| srolf| uxoh wkdw wkh fhqwudo edqn lv dvvxphg wr iroorz/wkh vr0 fdoohg Wd|oru uxoh18 Wklv uxoh olqnv wkh fhqwudo edqn*v nh| lqwhuhvw udwh wr lq dwlrq dqg uhdo JGS1 Wkh uxoh vwdwhv wkdw wkh fhqwudo edqn vkrxog udlvh lwv nh| udwh li wkh h{shfwhg lq dwlrq h{fhhgv wkh wdujhwhg ohyho/ru li fdsdflw|

8Lq wkh vwudwhj| prghoolqj sduw ri wkh prgho/wkh vkruw0whup lqwhuhvw udwh lv lqwhusuhwhg dv wkh wkuhh0prqwk lqwhuhvw udwh1

(11)

xwlol}dwlrq lq wkh hfrqrp| h{fhhgv lwv orqj0whup vxvwdlqdeoh ohyho=

A| ' oWn Ze| n w EZe|  ZW n b E*? t| *? t|W  +44, Khuh A| lv wkh Wd|oru lqwhuhvw udwh/ oW lv wkh htxloleulxp uhdo lqwhuhvw udwh/

Ze| lv wkh h{shfwhg dqqxdo lq dwlrq udwh/ ZW lv wkh wdujhwhg dqqxdo lq dwlrq udwh/dqg E*? t| *? t|W lv wkh rxwsxw jds/zkhuh t| lv uhdo JGS dqg t|W lv srwhqwldo uhdo JGS1 Wkh h{shfwhg udwh ri lq dwlrq/ Ze|/lv prghoohg xqghu wkh dvvxpswlrq ri dgdswlyh h{shfwdwlrqv1 Wklv phdqv wkdw Ze| lv dvvxphg wr eh htxdo wr wkh dyhudjh dqqxdo udwh ri lq dwlrq gxulqj wkh odvw irxu txduwhuv1 Uhdo JGS lv fdofxodwhg iurp lwv lqlwldo ydoxh dqg vlpxodwhg jurzwk sdwk dv t| ' tfT|

'E n }1 Ilqdoo|/srwhqwldo uhdo JGS lv jhqhudwhg iurp uhdo JGS e| phdqv ri wkh vr0fdoohg Krgulfn0Suhvfrww +KS, owhu19

Iru vlpxodwhg vhulhv ri Ze| dqg t|/htxdwlrq +44, lv xvhg wr frqvwuxfw d vhulhv ri wkh Wd|oru lqwhuhvw udwh1 Lq wkh orqj whup/ Ze| ' ZW/ t|' t|W/dqg/khqfh/

A| ' oWn ZW1 Lq wkh vkruw whup/krzhyhu/wkh Wd|oru udwh pd| vzlqj vkduso|

iurp rqh shulrg wr dqrwkhu1 Wkhuhiruh/wkh fhqwudo edqn lv qrw dvvxphg wr iroorz wkh Wd|oru uxoh frpsohwho|/exw lv dvvxphg wr dgmxvw lwv nh| udwh zlwk d fhuwdlq wlph odj1 Wkdw lv/wkh fhqwudo edqn sudfwlfhv vrph nlqg ri lqwhuhvw udwh vprrwklqj1 Wkh vkruw0whup qrplqdo lqwhuhvw udwh lv wkxv prghoohg dv dq DU+4, surfhvv wkdw dgmxvwv judgxdoo| wr wkh Wd|oru udwh/jlylqj vkruw0whup udwhv d pruh uhdolvwlf sdwwhuq ri pryhphqw=

|' V n )|3 l

|3 A|3

n 0|( 0| U( Efc j0 +45, Whfkqlfdoo|/wklv lv dq huuru fruuhfwlrq yhuvlrq ri wkh vwdqgdug DU+4, surfhvv/

zkhuh wkh vshhg ri dgmxvwphqw ri wkh vkruw udwh wrzdugv wkh Wd|oru udwh lv

9Wkh KS0owhu lv d vprrwklqj phwkrg wkdw lv zlgho| xvhg dprqj hpslulfdo pdfur0 hfrqrplvwv wr rewdlq d vprrwk hvwlpdwh ri wkh orqj0whup wuhqg frpsrqhqw ri d vhulhv1 Whfkqlfdoo|/wkh KS0owhu lv d wzr0vlghg olqhdu owhu wkdw frpsxwhv wkh vprrwkhg vh0 ulhv \w ri \w e| plqlpl}lqj wkh yduldqfh ri \w durxqg \w/vxemhfw wr d shqdow| wkdw frqvwudlqv wkh vhfrqg glhuhqfh ri \w1 Wkdw lv/wkh KS0owhu fkrrvhv wr plqlpl}h=

SW

w@4+|w |w,5. W 4S

w@5

|w.4 |w



|w |w45 1

(12)

Wdeoh 6= Vkruw0whup qrplqdo lqwhuhvw udwh

Vzhghq HPX XV

Dyhudjh= DfI eDI DDI

Sdudphwhuv

w fD fD fD

b fD fD fD

V fff2Df fff22D fff2.D

) fbD fbD fbD

l f f f

j0 fffeD ffffb ffffb jryhuqhg e| wkh l0sdudphwhu1

Wkh sdudphwhuv ri wkh vkruw0whup qrplqdo lqwhuhvw udwhv duh suhvhqwhg lq Wdeoh 61 Wkh sdudphwhul}dwlrq lv fkrvhq vr wkdw/lq htxloleulxp/wkh vkruw0 whup lqwhuhvw udwh lq hdfk hfrqrp| lv htxdo wr wkh Wd|oru udwh lq wkdw hfrqrp|1 Glhuhqfhv lq wkh htxloleulxp lqwhuhvw udwh ehwzhhq wkh hfrqrplhv duh gxh wr wkh hfrqrplhv kdylqj glhuhqw lq dwlrq wdujhwv1 Wkh Wd|oru udwh surfhvv/dv zhoo dv wkh vshhg ri dgmxvwphqw sdudphwhu/duh erwk dvvxphg wr eh lghqwlfdo iru doo wkuhh hfrqrplhv1 Wkh huuru whup ri wkh Vzhglvk vkruw0whup lqwhuhvw udwh lv dvvxphg wr kdyh d vrphzkdw kljkhu yduldqfh wkdq wkh huuru whupv ri wkh rwkhu wzr hfrqrplhv/rqfh djdlq uh hfwlqj wkh vpdoohu vl}h ri wkh Vzhglvk hfrqrp|1

518 Orqj0whup lqwhuhvw udwhv

51814 Uhdo uhwxuq uhtxluhphqw

Qrplqdo orqj0whup lqwhuhvw udwhv dqg |lhogv rq orqj0whup lq dwlrq0olqnhg erqgv duh ghwhuplqhg rq wkh edvlv ri d uhdo uhwxuq uhtxluhphqw1 Wkh edvlf lghd lv wkdw wkhuh lv d uhdo uhwxuq uhtxluhphqw xqghuo|lqj dq| lqyhvwphqw ghflvlrq ri dq lqyhvwru1 Wkh uhdo uhwxuq uhtxluhphqw/ o|/lv dvvxphg wr eh ghshqghqw rq wkh fdsdflw| xwlol}dwlrq lq wkh hfrqrp| dv zhoo dv rq lwv hduolhu ydoxhv1 Lw lv prghoohg dv dq dxjphqwhg DU+4, surfhvv/zkhuh wkh rxwsxw jds lv lqfoxghg dv dq h{rjhqrxv yduldeoh=

(13)

Wdeoh 7= Uhdo uhwxuq uhtxluphqw

Vzhghq HPX XV

Dyhudjh= fI fI fI

Sdudphwhuv

 fff fff fff

 fb fb fb

i f f f

o|'  n o|3n i E*? t| *? t|W  +46, Wkh sdudphwhuv ri wkh uhdo uhwxuq uhtxluhphqw duh suhvhqwhg lq Wdeoh 71 Wkh| duh vhw wr wkh vdph ydoxhv iru doo frxqwulhv1 Wkh uhdo uhwxuq uhtxluhphqw lv dvvxphg wr lqfuhdvh zkhq JGS h{fhhgv srwhqwldo JGS dqg ghfuhdvh zkhq JGS idoov ehorz ri srwhqwldo JGS1 Qrwh wkdw wkh uhdo uhwxuq uhtxluhphqw grhv qrw frqwdlq dq| glvwxuedqfh whup/rwkhu wkdq wkh rqh lqfoxghg lq JGS1 51815 \lhog rq orqj0whup lq dwlrq0olqnhg erqgv

Wkh |lhog rq lq dwlrq0olqnhg erqgv/ o|/lv jhqhudwhg rqo| iru Vzhghq1 Lw lv ghwhuplqhg e| wkh vxp ri wkh uhdo uhwxuq uhtxluhphqw +o|,/d oltxlglw|

suhplxp +,R|,/dqg dq huuru whup=

o|' o|n ,R|n 0|( 0| U( Efc j0  +47, Wkh sdudphwhul}dwlrq lv suhvhqwhg lq Wdeoh 81 Wkh oltxlglw| suhplxp/ ,R|/ lv vhw wr fD shu fhqw lq doo wlph shulrgv1 Wkxv/wkh |lhog rq lq dwlrq0olqnhg erqgv zloo h{fhhg wkh uhdo uhwxuq uhtxluhphqw lq wkh hfrqrp|/rq dyhudjh1

(14)

Wdeoh 8= \lhog rq orqj0whup lq dwlrq0olqnhg erqgv Vzhghq HPX XV

Dyhudjh= DI  

Sdudphwhuv

,R| fffD  

j0 fffffH  

51816 Orqj0whup qrplqdo lqwhuhvw udwh

Qrplqdo orqj0whup lqwhuhvw udwhv/ u|/duh fuhdwhg dv wkh vxp ri wkh uhdo uhwxuq uhtxluhphqw +o|,/wkh h{shfwhg dqqxdo lq dwlrq udwh lq wkh orqj whup +ZW,/dq lq dwlrq ulvn suhplxp +R|,/d whup suhplxp +|R|,/dqg dq huuru whup +0|,=

u| ' o|n ZW n R|n |R|n 0|( 0| U( Efc j0  +48, Qrwh wkdw lq wkh orqj whup wkh h{shfwhg dqqxdo lq dwlrq udwh lv htxdo wr wkh fhqwudo edqn*v lq dwlrq wdujhw1 Wkh h{shfwhg dqqxdo lq dwlrq udwh lv wkhuhiruh vhw wr ZW lq wklv htxdwlrq1 Wkh lq dwlrq ulvn suhplxp/ R|/lv ghwhuplqhg e|

hduolhu ydoxhv ri lq dwlrq1 Lw lv dvvxphg wr eh kljkhu li lq dwlrq kdv h{fhhghg wkh fhqwudo edqn*v lq dwlrq wdujhw gxulqj wkh odvw irxu txduwhuv/dqg2ru li lq dwlrq/phdvxuhg rq d txduwhuo| edvlv/kdv ydulhg d orw=

R|' n 1 4@ dEZ| ZW c fo n  [e

r'

EZ|3r ZW2 +49, Wkh whup suhplxp/ |R|/lv dvvxphg wr iroorz d uhjlph vzlwfklqj DU+4, surfhvv/zlwk d kljkhu h{shfwhg ydoxh lq errpv wkdq lq uhfhvvlrqv=

|R| ' #rn |R|3( r ' c - +4:, Wkh sdudphwhul}dwlrq ri wkh orqj0whup qrplqdo lqwhuhvw udwh/wkh lq dwlrq ulvn suhplxp/dqg wkh whup suhplxp duh suhvhqwhg lq Wdeoh 91

(15)

Wdeoh 9= Orqj0whup qrplqdo lqwhuhvw udwh

Vzhghq HPX XV

Dyhudjh= DbI DDI SSI

Sdudphwhuv

j0 fffS fffS fffS

Lq dwlrq ulvn suhplxp

Dyhudjh= feI feI feI

Sdudphwhuv

fff2D fff2D fff2D

1 f2 f2 f2

 f2 f2 f2

Whup suhplxp

Dyhudjh= fSI fSI f.I

Sdudphwhuv

# fff2 fff2 fff2

#- fff2 fff2 fff2

 fH fH fH

519 H{fkdqjh udwhv

Uhdo h{fkdqjh udwhv duh prghoohg dv dxjphqwhg DU+4, surfhvvhv=

.|c ' n .|3c  D

}| }|

 /

u|  u| 

n 0|c +4;, zkhuh .|c lv wkh uhdo h{fkdqjh udwh ehwzhhq hfrqrplhv  dqg / }| lv wkh jurzwk udwh lq frxqwu| / }| lv wkh jurzwk udwh lq frxqwu| / u| lv wkh orqj0 whup lqwhuhvw udwh lq frxqwu| / u| lv wkh orqj0whup lqwhuhvw udwh lq frxqwu| /

dqg 0|lv dq huuru whup glvwulexwhg dv U( Efc j01 Wkh D0sdudphwhu fdswxuhv vkruw0whup hhfwv ri glhuhqfhv lq udwhv ri jurzwk1 Li jurzwk lv vwurqjhu lq rqh ri wkh hfrqrplhv/lwv fxuuhqf| whqgv wr dssuhfldwh djdlqvw wkh rwkhu hfrqrp|1 Lq htxloleulxp/wkh suhvhqfh ri wklv whup zloo lqgxfh d wuhqg lq wkh uhdo h{fkdqjh udwh li }W9' }W1 Wklv hhfw lv frqvlvwhqw zlwk wkh olwhudwxuh rq uhdo h{fkdqjh udwhv/zklfk whoov xv wkdw lq htxloleulxp uhdo h{fkdqjhv udwhv pd| wuhqg dffruglqj wr glhuhqfhv lq surgxfwlylw|1 Wkh /0sdudphwhu fdswxuhv

(16)

Wdeoh := Uhdo h{fkdqjh udwhv

HXU2VHN XVG2VHN

Vwduwlqj ydoxh= HfI bfI

Sdudphwhuv

ffb ff

 fbb fbb

D 2D 2D

/ f2D f2D

j0 ff.fD ff.fD

glhuhqfhv lq orqj0whup qrplqdo lqwhuhvw udwhv1 Wkh hhfwv duh vlplodu wr wkh rqhv glvfxvvhg deryh1

Qrplqdo h{fkdqjh udwhv/ ec| /duh fuhdwhg e| dgglqj ru vxewudfwlqj gli0 ihuhqfhv lq lq dwlrq udwhv ehwzhhq wkh frxqwulhv lq txhvwlrq1 Vshflfdoo|/

ec| ' ec|3

 n *L} .|c *L} .|3c n Z| Z|

1 Orqj0whup glhuhqfhv lq lq d0 wlrq zloo lqgxfh wkh vdph w|sh ri orqj0whup wuhqgv lq qrplqdo h{fkdqjh udwhv dv glhuhqfhv lq jurzwk udwhv dqg lqwhuhvw udwhv gr lq uhdo h{fkdqjh udwhv1

Wkh surfhvvhv jryhuqlqj uhdo h{fkdqjh udwhv duh yhu| shuvlvwhqw dqg wkh dxwruhjuhvvlyh sdudphwhu/ /lv wkhuhiruh vhw wr fbb iru erwk .L-*7.g dqg L7(*7.g +vhh Wdeoh :,1 Wklv phdqv wkdw wkh ghjuhh ri phdq uhyhuvlrq lq uhdo h{fkdqjh udwhv lv txlwh orz1 Wkh dgmxvwphqw sdudphwhuv D dqg / duh vhw rq dq dg0krf edvlv dqg duh dvvxphg wr eh htxdo dfurvv wkh wzr uhdo h{fkdqjh udwhv1 Wklv lv dovr wkh fdvh iru wkh yduldqfh whup1 Wkh lqwhufhsw/ /lv fkrvhq vr wkdw uhdo h{fkdqjh udwhv/lq htxloleulxp dqg lq wkh devhqfh ri jurzwk dqg lqwhuhvw udwh glhuhqfhv/duh htxdo wr wkh h{fkdqjh udwhv wkdw suhydlohg zkhq wkh vlpxodwlrq prgho zdv sdudphwhul}hg +Pd| 5334,1

Qrwh wkdw wkh edvlf sdudphwhul}dwlrq pdnhv qr dvvxpswlrq derxw hlwkhu uhdo ru qrplqdo h{fkdqjh udwh wuhqgv/h{fhsw wkrvh wkdw iroorz iurp furvv0 frxqwu| glhuhqfhv lq srwhqwldo JGS/orqj0whup lqwhuhvw udwhv/dqg lq dwlrq1 Jlyhq wkhvh dvvxpswlrqv/wkh vwuxfwxuh dqg sdudphwhul}dwlrq ri wkh prgho lpsolhv d fhuwdlq vwuhqjwkhqlqj ri wkh nurqd djdlqvw wkh groodu lq qrplqdo whupv/zkloh wkh nurqd zhdnhqv djdlqvw wkh hxur1

(17)

51: Qhw eruurzlqj uhtxluhphqw

Wkh vshflfdwlrq ri wkh qhw eruurzlqj uhtxluhphqw ri wkh Vzhglvk fhqwudo jryhuqphqw lv kljko| vw|ol}hg1 Lw lv edvhg rq wkh r!fldo vfdo srolf| wdujhw ri d wzr shu fhqw vxusoxv lq sxeolf qdqfhv ryhu dq hfrqrplf f|foh/soxv rxu dvvxpswlrq wkdw wkh shqvlrq v|vwhp zloo vkrz d vxusoxv wkdw h{fhhgv wkhvh wzr shu fhqw1 Wdnhq wrjhwkhu/wklv phdqv wkdw wkh jryhuqphqw qhhgv wr eruurz zkhq wkh hfrqrp| lv lq htxloleulxp1 Wkh htxloleulxp ohyho iru wkh qhw eruurzlqj uhtxluhphqw lq wkh shulrg | fdq wkhuhiruh eh h{suhvvhg dv

| '  E n }Wn ZW|tfc

zkhuh  lv d srvlwlyh/frqvwdqw shufhqwdjh dqg E n }Wn ZW|tf lv wkh htxl0 oleulxp ohyho iru qrplqdo JGS lq shulrg |1

D phdvxuh ri hfrqrplf dfwlylw|/ E}| }W/lv wkhq dgghg wr wklv htxdwlrq wr fdswxuh krz fdswxuh krz wkh jryhuqphqw*v dfwxdo qhw eruurzlqj uhtxluh0 phqw ydulhv zlwk wkh hfrqrplf f|foh=

|'  E n }Wn ZW|tf B E}| }W n 0|( 0| U( Efc j0 c zkhuh E}| }W lv wkh glhuhqfh ehwzhhq uhdo jurzwk dqg htxloleulxp uhdo jurzwk/dqg 0| lv dq huuru whup uhsuhvhqwlqj dq| udqgrp xfwxdwlrq qrw h{0 solflwo| lqfoxghg khuh1 Wkh dfwxdo qhw eruurzlqj uhtxluhphqw gxulqj d jlyhq shulrg zloo wkhuhiruh h{fhhg ru idoo vkruw ri lwv htxloleulxp ohyho/ghshqg0 lqj rq zkhwkhu wkh sdfh ri hfrqrplf jurzwk lv idvwhu ru vorzhu wkdq wkh htxloleulxp jurzwk udwh1 Lq htxloleulxp/krzhyhu/. d}|o ' }W dqg/khqfh/

. d|o '  E n }Wn ZW|tf/zklfk phdqv wkdw ghvslwh wkh xfwxdwlrqv/wkh wdujhw eruurzlqj uhtxluhphqw zloo eh phw rq dyhudjh1

Wkh sdudphwhul}dwlrq ri wkh qhw eruurzlqj uhtxluhphqw lv suhvhqwhg lq Wdeoh ;1 Wkh sdudphwhu  lv fkrvhq vr wkdw/lq htxloleulxp/wkh qhw eruurzlqj uhtxluhphqw lv htxdo wr fD shu fhqw ri JGS shu dqqxp/uh hfwlqj rxu vw|o0 l}hg dvvxpswlrq derxw wkh glylvlrq ri wkh wdujhwhg vxusoxv lq sxeolf qdqfhv

(18)

Wdeoh ;= Qhw eruurzlqj uhtxluhphqw Vzhghq HPX XV

Dyhudjh= fDI  

Sdudphwhuv

 fff2D  

B 22ff  

j0 ffD  

ehwzhhq fhqwudo jryhuqphqw dqg rwkhu sduwv ri wkh sxeolf vhfwru1 Wklv lp0 solhv wkdw fhqwudo jryhuqphqw ghew zloo lqfuhdvh ryhu wlph lq qrplqdo whupv/

exw ghfuhdvh dv d vkduh ri JGS/vlqfh JGS lwvhoi zloo lqfuhdvh e| pruh wkdq fD shu fhqw rq dyhudjh1 Wkh sdudphwhu B/zklfk fdswxuhv wkh vhqvlwlylw| ri jryhuqphqw qdqfhv wr exvlqhvv f|fohv xfwxdwlrqv/duh vhw wr 22ff1

6 Wkh vwudwhj| vlpxodwlrq prgho

Wkh jrdo ri wkh vlpxodwlrq h{huflvh lv wr frpsxwh wkh frvwv dqg ulvnv dvvrfl0 dwhg zlwk glhuhqw ghew vwudwhjlhv ryhu d orqj shulrg ri wlph1 Lq dgglwlrq wr wkh vlpxodwlrq ri hfrqrplf dqg qdqfldo yduldeohv zh wkhuhiruh qhhg d wrro wr vlpxodwh glhuhqw ghew pdqdjhphqw vwudwhjlhv1 Wkh wdvn ri wkh vwudwhj|

vlpxodwlrq lv wr uroo0ryhu wkh ghew sruwirolr lq hdfk vlpxodwlrq vwhs/wkhuhe|

uhqdqflqj pdwxulqj ghew lq d zd| wkdw pdnhv wkh sruwirolr phhw fhuwdlq fulwhuld1 Lq hdfk vwhs/wkh vwudwhj| vlpxodwlrq ghwhuplqhv zkdw dprxqwv vkrxog eh eruurzhg lq qrplqdo grphvwlf erqgv/iruhljq fxuuhqf| erqgv dqg lq dwlrq0olqnhg erqgv/dv zhoo dv wkh pdwxulw| glvwulexwlrq ri hdfk ghew w|sh1 Wkh vwudwhj| vlpxodwlrq dovr nhhsv wudfn ri doo lqglylgxdo fdvk rzv/dqg fdo0 fxodwhv frvwv dqg ulvnv1 Wklv vhfwlrq ghvfulehv wkh vwudwhj| vlpxodwlrq sduw ri wkh prgho1 Iluvw/d frxsoh ri jhqhudo wrslfv derxw vwudwhj| vlpxodwlrqv duh glvfxvvhg1 Wkhq wkh lpsohphqwdwlrq ri wkh vwudwhj| vlpxodwlrq lq wkh VQGR prgho lv ghvfulehg lq pruh ghwdlo1

(19)

614 Jhqhudo wrslfv

Vwudwhj| vlpxodwlrqv ri fhqwudo jryhuqphqw ghew pdqdjhphqw udlvhv wzr lql0 wldo txhvwlrqv1 Iluvw/lq zkdw whupv vkrxog ghew vwudwhjlhv eh ghqhgB Vhf0 rqg/zklfk ghew sruwirolr vkrxog eh xvhg dv wkh vwduwlqj sruwirolr lq hdfk vwudwhj| vlpxodwlrqB Erwk wkhvh txhvwlrqv duh eulh | dgguhvvhg ehorz1 Iru d pruh hoderudwh glvfxvvlrq/vhh Ehujvwuùp ) Kropoxqg +5333,1

61414 Irupxodwlqj ghew vwudwhjlhv

Lq sulqflsoh/wkhuh duh wzr pdlq dowhuqdwlyhv iru wkh irupxodwlrq ri vwudwh0 jlhv1 Wkh uvw lv wr ghqh wkh vwudwhj| dv d uhqdqflqj vfkhph1 Wkh vhfrqg dowhuqdwlyh lv wr ghqh d vwudwhj| lq sruwirolr whupv/h1j1 zlwk wdujhwv iru wkh doorfdwlrq dqg gxudwlrq ri wkh ghew sruwirolr1

Lq wkh VQGR prgho/wkh odwwhu dssurdfk lv xvhg1 Wkh vwudwhjlhv dqdo|}hg duh ghqhg lq whupv ri gxudwlrq dqg vkduhv ri qrplqdo/lq dwlrq0olqnhg dqg iruhljq fxuuhqf| ghew1 Wklv lv qrw qhfhvvdulo| ehfdxvh wkh sruwirolr dssurdfk lv vxshulru wr wkh uhqdqflqj vfkhph dssurdfk1 Lqghhg/wkh sruwirolr ds0 surdfk kdv vrph ohvv dsshdolqj hhfwv/sulpdulo| frqfhuqlqj iruhljq fxuuhqf|

dqg lq dwlrq0olqnhg ghew/wkdw wkh uvw dssurdfk ryhufrphv1 Wkh pdlq uhd0 vrq iru xvlqj wkh sruwirolr dssurdfk/krzhyhu/lv wkdw wklv lv wkh zd| wkh Ghew R!fh xvxdoo| fkdudfwhul}hv lwv ghew sruwirolr/erwk lqwhuqdoo| dqg h{whuqdoo|1: 61415 Wkh vwduwlqj sruwirolr

Dw uvw vljkw lw pd| vhhp orjlfdo wr vwduw hdfk vwudwhj| vlpxodwlrq zlwk wkh jryhuqphqw*v dfwxdo ghew sruwirolr1 Krzhyhu/kdylqj doo vwudwhjlhv vwduw lq wkh vdph sruwirolr pdnhv wkh frvwv ri glhuhqw vwudwhjlhv udwkhu vlplodu gxulqj wkh uvw sduwv ri wkh vlpxodwlrq/zklfk lq wxuq pdnhv wkh glhuhqfhv ehwzhhq vwudwhjlhv ohvv fohdu fxw1 Vlqfh wkh dlp ri wkh vlpxodwlrqv lv wr dqdo|}h orqj0whup glhuhqfhv lq frvwv dqg ulvnv/udwkhu wkdq wkh wudqvlwlrq iurp rqh

:Lw vkrxog eh qrwhg wkdw wkh jxlgholqhv duh qrw hqwluho| sruwirolr edvhg/vlqfh wkhuh lv d wdujhw iru wkh ohyho ri dpruwl}dwlrq ri wkh iruhljq fxuuhqf| ghew/udwkhu wkdq iru lwv vkduh1

(20)

sruwirolr wr dqrwkhu/zh wkhuhiruh ohw doo vwudwhjlhv vwduw lq d sruwirolr ixooolqj wkh vshflhg vwudwhj| uljkw iurp wkh ehjlqqlqj1 Lq wklv zd|/zh fdq eh vxuh wkdw glhuhqfhv lq frvw ehwzhhq dq| wzr vwudwhjlhv duh gxh wr glhuhqw ghew vwuxfwxuhv/dqg qrw rq wkh wudqvdfwlrqv qhhghg wr vkliw iurp rqh sruwirolr wr dqrwkhu1

615 Vwudwhj| vlpxodwlrqv

61514 Vwudwhjlhv

Wkh jrdo ri wkh dqdo|vlv lv wr h{dplqh wkh frvwv dqg ulvnv ri glhuhqw sruwirolr vwudwhjlhv lq urxjk whupv1 Iru wkdw sxusrvh lw lv vx!flhqw wr kdyh d vpdoo qxpehu ri vwudwhjlhv/dowkrxjk wkh| vkrxog eh fohduo| glhuhqwldwhg dqg vsdq d uhodwlyho| odujh vsdfh1 Lq wkh lqlwldo vlpxodwlrqv/qlqh sruwirolr vwudwhjlhv zhuh h{dplqhg1 Wkh| duh glvsod|hg lq Wdeoh <1 Lq wkhvh vlpxodwlrqv wkh vkduh ri lq dwlrq0olqnhg erqgv ydulhg ehwzhhq 3/43 dqg 53 shufhqw1 Lq d vhfrqg vhw ri vlpxodwlrqv wkhvh lqwhuydov zhuh lqfuhdvhg wr 3/83 dqg 433 shufhqw1 Wkh vkduhv ri qrplqdo grphvwlf dqg iruhljq fxuuhqf| ghew lq wrwdo jryhuqphqw zhuh ydulhg dffruglqjo|1 Zkhqhyhu wkhuh zdv iruhljq fxuuhqf| ghew lq wkh sruwirolr/lw zdv frpsulvhg ri :3 shufhqw hxur dqg 63 shufhqw XV grooduv/

zklfk lv urxjko| wkh vdph dv lq wkh dfwxdo sruwirolr1 Wkh gxudwlrq wdujhw iru wkh qrplqdo grphvwlf ghew zdv ydulhg ehwzhhq 5/6 dqg 7 |hduv/zkloh wkh gxudwlrq ri wkh iruhljq fxuuhqf| dqg wkh lq dwlrq0olqnhg ghew zdv vhw dw 5 dqg 43 |hduv/uhvshfwlyho|1

Wdeoh <= Sruwirolr vwudwhjlhv lq edvh vfhqdulr

Gxudwlrq/qrplqdo nurqd ghew

Vkduhv ri wrwdo ghew 5 6 7

3( LO :8 ( VHN 58( I[ Vwudwhj| 4 Vwudwhj| 5 Vwudwhj| 6 43( LO 98 ( VHN 58( I[ Vwudwhj| 7 Vwudwhj| 8 Vwudwhj| 9 53( LO 88 ( VHN 58( I[ Vwudwhj| : Vwudwhj| ; Vwudwhj| <

(21)

61515 Wuhdwphqw ri iruhljq fxuuhqf| dqg lq dwlrq0olqnhg erqgv Lq wkh prgho/iruhljq fxuuhqf| erqgv dqg lq dwlrq0olqnhg erqgv duh wuhdwhg lq wkh vdph zd|1 Doo fdvk rzv iurp iruhljq fxuuhqf| erqgv duh frqyhuwhg wr Vzhglvk nurqd xvlqj wkh dssursuldwh I[ udwh1 Olnhzlvh/wkh uhdo fdvk rzv iurp dq lq dwlrq0olqnhg erqg duh frqyhuwhg wr qrplqdo Vzhglvk nurqd xvlqj wkh vlpxodwhg FSL1 Lq rwkhu zrugv/FSL lv ylhzhg dv wkh h{fkdqjh udwh ehwzhhq qrplqdo dqg uhdo prqh|1 Lq wkh iroorzlqj/wkh whupv iruhljq fxuuhqf|

dqg I[ udwh zloo vrphwlphv eh xvhg erwk zkhq uhihuulqj wr iruhljq fxuuhqf|

dqg lq dwlrq0olqnhg ghew1

Iru dq lq dwlrq0olqnhg erqg/doprvw doo ri wkh lq dwlrq frpshqvdwlrq lv sdlg rxw dw pdwxulw|1 Wklv lv htxlydohqw zlwk krz wkh Vzhglvk lq dwlrq0olqnhg erqgv zrun lq uhdolw|/exw fdq qhyhuwkhohvv ohdg wr odujh shdnv lq frvwv iru lq dwlrq0olqnhg ghew lq wkh prgho1

61516 Wkh lqlwldo sruwirolr

Whfkqlfdoo|/wkh lqlwldo sruwirolr lv khog lq d wzr glphqvlrqdo pdwul{1 Wklv pdwul{ kdv wzr froxpqv iru hdfk ghew w|sh/rqh frqwdlqlqj wkh ghew sulq0 flsdov dqg rqh frqwdlqlqj wkh frxsrq sd|phqwv1 Vlqfh zh duh prghoolqj sruwirolrv zlwk irxu glhuhqw ghew w|shv/wkh pdwul{ kdv hljkw froxpqv lq wrwdo1 Pruhryhu/wkh pdwul{ kdv 453 urzv/fruuhvsrqglqj wr 453 txduwhuo|

pdwxulw| exfnhwv1 Wkh dprxqwv lq wkh uvw urz ri wkh pdwul{ pdwxuh lq wkh

uvw txduwhu +vwhs, ri wkh vlpxodwlrq uxq/wkh dprxqwv lq wkh vhfrqg pdwxuh lq wkh vhfrqg txduwhu dqg vr rq1

Dw wkh vwduw ri hdfk vlpxodwlrq uxq wkh wrwdo rxwvwdqglqj ghew lv glvwule0 xwhg ryhu doo pdwxulw| exfnhwv lq d zd| wkdw lv frqvlvwhqw zlwk wkh gxudwlrq dqg doorfdwlrq wdujhwv ri wkh vlpxodwhg vwudwhj|1 Wkh dprxqw ri rxwvwdqglqj ghew dw wkh vwduw ri wkh vlpxodwlrq lv vhw wr 44;3 eloolrq VHN/dssur{lpdwho|

wkh vdph dv wkh dfwxdo vl}h ri wkh ghew1 Wkh lqlwldo frxsrq ri wkh ghew lv vhw dffruglqj wr wkh lqlwldo |lhog fxuyh ri hdfk ghew w|sh1 Lw lv wkxv lpsolflwo|

dvvxphg wkdw doo rxwvwdqglqj ghew dw wkh vwduw ri wkh vlpxodwlrq uxq kdv ehhq udlvhg mxvw sulru wr wkh vwduw ri wkh vlpxodwlrq1

(22)

616 Wkh vwudwhj| vlpxodwlrq vwhs0e|0vwhs

Lq hdfk vlpxodwlrq uxq/wkh sruwirolr lv uroohg ryhu 63 |hduv lq txduwhuo|

vwhsv/l1h1 453 wlphv1 Hdfk uroo0ryhu frqvlvwv ri d qxpehu ri vwhsv1 Wkhvh duh ghvfulehg lq ghwdlo ehorz1

61614 Fdofxodwlqj frxsrq sd|phqwv

Lq hdfk vlpxodwlrq vwhs/wkh uvw qxpehu fdofxodwhg lv wkh vxp ri doo frxsrq sd|phqwv gxh lq wkdw shulrg1 Wklv qxpehu lv fdofxodwhg vlpso| dv wkh frxsrq sd|phqw lq hdfk fxuuhqf|/wlphv wkh vlpxodwhg I[ udwhv iru wkdw sduwlfxodu shulrg1 Wkh frxsrqv duh irxqg lq froxpqv 5/7/9 dqg ; ri wkh sruwirolr pdwul{ lq Iljxuh 51

Iljxuh 5= Fdofxodwlqj wkh frxsrq sd|phqwv

     

FRXSRQV

^FRXSRQV`i^I[` !FRXSRQFRVW

61615 Fdofxodwlqj jurvv eruurzlqj uhtxluhphqwv

Wkh eruurzlqj uhtxluhphqw iru wkh vshflf shulrg lv fdofxodwhg lq d vlplodu zd|= wkh dprxqwv pdwxulqj duh irxqg lq froxpqv 4/6/8 dqg : ri wkh sruwirolr pdwul{ lq Iljxuh 6/dqg wkh| duh frqyhuwhg wr qrplqdo Vzhglvk nurqd dw wkh vlpxodwhg I[ udwhv1 Wklv jlyhv wkh eruurzlqj uhtxluhphqw vwhpplqj iurp wkh ghew lwvhoi1 Wkhuh lv dovr d qhw eruurzlqj uhtxluhphqw dulvlqj iurp wkh jryhuqphqw*v exgjhw lq wkh vlpxodwhg hfrqrp|1 Wklv exgjhw ghflw2vxusoxv lv dgghg wr wkh eruurzlqj uhtxluhphqw iurp pdwxulqj erqgv/jlylqj wkh wrwdo

qdqflqj qhhg1 Ilqdoo|/wkh wrwdo qdqflqj qhhg lv glvwulexwhg ryhu wkh irxu fxuuhqflhv dffruglqj wr wkh doorfdwlrq wdujhw ri wkh vwudwhj|1

(23)

Iljxuh 6= Fdofxodwlqj jurvv eruurzlqj uhtxluphqwv

^SULQFLSDOV`i^I[` !ERUURZLQJUHTXLUHPHQW IURPPDWXULQJGHEW SULQFLSDOV

     

61616 Ilqdqflqj jurvv eruurzlqj uhtxluhphqwv

Wkh qh{w vwhs lq wkh vwudwhj| vlpxodwlrq lv wr ohw wkh vkruwhvw erqgv pdwxuh1 Wklv lv grqh vlpso| e| prylqj wkh frqwhqwv ri doo urzv lq wkh sruwirolr pdwul{

xs rqh urz/dqg vhwwlqj wkh dprxqwv lq wkh odvw urz wr }hur1 Wkh sruwirolr pdwul{ zloo qrz frqwdlq wkh sruwirolr dv lw zrxog orrn diwhu wkh pdwxulwlhv ri wkh fxuuhqw shulrg kdyh rffxuuhg/exw ehiruh dq| qhz erqgv kdyh ehhq lvvxhg1

Wkh eruurzlqj qhhg pxvw eh qdqfhg lq d zd| wkdw pdnhv wkh sruwir0 olr phhw wkh gxudwlrq wdujhw/li srvvleoh1 Wr eh deoh wr ghwhuplqh dw zklfk gxudwlrq srlqw zh vkrxog eruurz/zh qhhg wr nqrz wkh pdunhw ydoxh dqg gxudwlrq ri wkh ghew rxwvwdqglqj lq hdfk ri wkh irxu fxuuhqflhv1 Wr fdofxodwh wkhvh zh qhhg irxu vhwv ri glvfrxqw idfwruv/rqh iru hdfk fxuuhqf|1 Lq wkh hfr0 qrplf2qdqfldo vlpxodwlrq/zh vlpxodwh rqo| wzr srlqwv rq wkh |lhog fxuyh/

wkh wkuhh0prqwkv prqwkv udwh dqg wkh whq0|hdu udwh1; Wr jhw wkh glvfrxqw idfwruv zh wkhuhiruh olqhduo| lqwhusrodwh |lhogv iru hdfk pdwxulw| exfnhw/dqg wkhq frqyhuw wkhp wr glvfrxqw idfwruv lq wkh vwdqgdug zd|=

_s| ' 

E n o|| +4<,

Vlqfh zh kdyh wkh fdvk rzv ri wkh sruwirolrv rujdql}hg lq pdwxulw| exfn0 hwv/dqg nqrz wkh wlph wr pdwxulw| ri hdfk exfnhw/lw lv qrz vwudljkwiruzdug wr fdofxodwh wkh pdunhw ydoxh/ 6|/ri hdfk sduw ri wkh ghew +Vzhglvk nurqd/

;Iru lq dwlrq0olqnhg erqgv/zh vlpxodwh wkh yh dqg wkluw| |hdu srlqwv rq wkh |lhog fxuyh1

(24)

hxur/grooduv dqg lq dwlrq0olqnhg, dv

6|'[

Ss| _s|c +53,

zkhuh | ghqrwhv wkh wlph +lq txduwhuv, wr pdwxulw| ri hdfk pdwxulw| exfnhw dqg uxqv iurp  wr 2f> Ss| ghqrwhv wkh fdvk rz lq exfnhw | dqg _s| lv wkh glvfrxqw idfwru dvvrfldwhg zlwk pdwxulw| |1 Zlwk wkh vdph qrwdwlrq/wkh gxudwlrq ri hdfk sduw ri wkh ghew fdq eh fdofxodwhg dv<

_o@|J? '

SSs| _s| |

6|  +54,

Qrwh wkdw wkh gxudwlrq ri wkh glhuhqw sduwv ri wkh ghew duh qrw djjuhjdwhg/

vlqfh wkh gxudwlrq wdujhwv duh vshflhg shu fxuuhqf|/dqg qrw iru wkh sruwirolr dv d zkroh1

Jlyhq wkh pdunhw ydoxh dqg gxudwlrq ri wkh ghew rxwvwdqglqj ehiruh qhz ixqglqj/lw qrz srvvleoh wr ghwhuplqh dw zklfk gxudwlrq srlqw zh vkrxog

qdqfh wkh suhvhqw eruurzlqj qhhg1 Ghqrwh wkh gxudwlrq ri wkh ghew ehiruh qhz ixqglqj _f/wkh pdunhw ydoxh ri wkh ghew ehiruh qhz ixqglqj 6f dqg wkh eruurzlqj uhtxluhphqw Ko1 Lq rughu wr phhw wkh gxudwlrq wdujhw _W/wkh eruurzlqj uhtxluhphqw kdv wr eh ixqghg dw d fhuwdlq dyhudjh gxudwlrq _@/ zklfk fdq eh fdofxodwhg dv=

_W ' _f6fn _@Ko

6fn Ko ', _@' _WE6fn Ko  _f6f

Ko  +55,

Wkh hqwluh eruurzlqj uhtxluhphqw lv dvvxphg wr eh fryhuhg e| lvvxhv ri sdu erqgv/l1h1/erqgv zlwk dq lqwhjhu qxpehu ri |hduv wr pdwxulw| dqg d frxsrq pdnlqj wkh suhvhqw ydoxh htxdo wkh qrplqdo dprxqw1 Lq qrplqdo Vzhglvk nurqd/hxurv dqg grooduv sdu erqgv zlwk rqh ru whq |hdu pdwxulwlhv

<Whfkqlfdoo|/wklv htxdwlrq jlyhv wkh Ilvkhu0Zhloo gxudwlrq/vlqfh zh xvh wkh glvfrxqw idfwruv fruuhvsrqglqj wr }hur frxsrq udwhv wr glvfrxqw wkh fdvk rzv1 Wkh pruh iuhtxhqwo|

xvhg Pdfdxoh| gxudwlrq xvhv glvfrxqw idfwruv surgxfhg e| wkh |lhog0wr0pdwxulw| ri wkh vshflf erqg1 Wkh glhuhqfh ehwzhhq wkhvh wr phdvxuhv lv vpdoo= zlwk dq xszdug vorslqj

|lhog fxuyh/Ilvkhu0Zhloo phwkrg zloo jlyh d voljkwo| orzhu gxudwlrq wkdq wkh Pdfdxoh|

phwkrg1

(25)

duh xvhg1 Iru lq dwlrq0olqnhg ghew/yh dqg wkluw| |hduv pdwxulwlhv duh xvhg1 Jlyhq wkh glvfrxqw idfwruv fdofxodwhg iurp wkh vlpxodwhg lqwhuhvw udwhv/wkh frxsrq S ri d sdu erqg pdwxulqj lq  |hduv fdq eh fdofxodwhg xvlqj wkh iroorzlqj htxdwlrq=

ff ' S [

'

_sn ff_s ', S ' E  _s ff S

'_s +56,

Wkh gxudwlrq ri wkh sdu erqgv lv fdofxodwhg xvlqj htxdwlrq +54,1

Iru hdfk fxuuhqf| zh qrz kdyh wkh gxudwlrq dqg frxsrqv ri sdu erqgv pdwxulqj rqh dqg whq |hduv iurp qrz1 Zh dovr nqrz dw zklfk gxudwlrq srlqw zh qhhg wr eruurz lq hdfk fxuuhqf| wr phhw wkh gxudwlrq wdujhw1 Vlqfh wkdw gxudwlrq srlqw lv xqolnho| wr frlqflgh zlwk wkh gxudwlrq ri d vlqjoh sdu erqg/

qhz ixqglqj lv xvxdoo| grqh xvlqj erwk sdu erqgv lq hdfk fxuuhqf|1 Wkh dprxqwv wr eh eruurzhg lq hdfk ri wkh wzr erqgv duh fdofxodwhg lq wkh vdph zd| dv vwdqgdug eduehoo fdofxodwlrqv1 Ohw _ ghqrwh gxudwlrq dqg  qrplqdo dprxqwv +htxdoolqj fohdq dqg gluw| sulfhv dv zh duh zrunlqj zlwk sdu erqgv,1 _Wlv wkh gxudwlrq qhhghg wr phhw wkh wdujhw dqg vxshulqglfhv 7 dqg u ghqrwh wkh vkruw0whup dqg orqj0whup sdu erqg/uhvshfwlyho|1 Wkh vxp ri qrplqdo dprxqwv lq wkh wzr erqgv pxvw htxdo wkh eruurzlqj uhtxluhphqw Ko1 Wkh dprxqwv wkdw vkrxog eh doorfdwhg wr vkruw0whup dqg orqj0whup erqgv/ 7 dqg u'

Ko  7

/duh wkhq jlyhq e|=

_W ' _77n _u

Ko  7

Ko ', 7 '

_W _u Ko

E_7 _u +57, dqg

u'

# Ko 

_W _u Ko E_7 _u

$

', u'

_7 _W Ko

E_7 _u  +58, Lq vrph fdvhv/wkh gxudwlrq qhhghg wr phhw wkh gxudwlrq wdujhw lv rxwvlgh wkh udqjh ri sdu erqg gxudwlrqv1 Doo ixqglqj lv wkhq grqh lq wkh vkruwhvw ru wkh orqjhvw sdu erqg/dv dssursuldwh1 Qdwxudoo|/wkh gxudwlrq wdujhw fdqqrw eh h{dfwo| phw lq wkrvh fdvhv1

(26)

61617 Erqg uhsxufkdvhv

Lq prvw fdvhv wkh jurvv eruurzlqj uhtxluhphqw lv odujhu wkdq }hur  zh qhhg wr eruurz lq rughu wr uhqdqfh pdwxulqj erqgv dqg2ru d exgjhw ghflw1 Krzhyhu/vrphwlphv lw pd| kdsshq wkdw wkh jurvv eruurzlqj uhtxluhphqw lv ohvv wkdq }hur1 Wklv kdsshqv zkhq wkh vlpxodwhg hfrqrp| vkrzv d exgjhw vxusoxv wkdw lv odujhu wkdq wkh vxp ri pdwxulqj erqgv lq wkh sruwirolr1 Lq wkrvh vlwxdwlrqv/wkh uroo0ryhu surfhgxuh ehfrphv pruh frpsolfdwhg1 Lqvwhdg ri lvvxlqj qhz erqgv/zh qrz kdyh wr ex| edfn erqgv1 Ex|edfnv pxvw eh grqh lq d zd| wkdw pdnhv wkh sruwirolr gxudwlrq phhw wkh vwudwhj| wdujhw dqg fdq rqo| eh pdgh dprqj wkrvh erqgv wkdw duh fxuuhqwo| lq wkh sruwirolr1 Ixuwkhupruh/lqglylgxdo fdvk rzv ri d erqg fdqqrw eh erxjkw edfn vhsd0 udwho|/exw pxvw eh kdqgohg dv d zkroh1 Lq h{wuhph fdvhv/lw pd| kdsshq wkdw doo ri wkh rxwvwdqglqj ghew lv erxjkw edfn1 Zkhq qr erqgv duh ohiw wr ex| edfn/dq| uhpdlqlqj vxusoxvhv duh ghsrvlwhg lq wkh fdvk pdunhw iru rqh txduwhu dw wkh wlph1 Iru d pruh ghwdlohg ghvfulswlrq ri krz erqg uhsxufkdvhv duh kdqgohg lq wkh prgho/vhh Ehujvwuùp ) Kropoxqg +5333,1

7 Frvw dqg ulvn phdvxuhv

Lq wkh VQGR vlpxodwlrq prgho/wkh frvwv ri ghew duh uhodwhg wr +vlpxodwhg, qrplqdo JGS lq rughu wr jhw d phdvxuh ri wkh uhdo frvwv ghew1 Ulvn lv ghqhg dv wkh yduldwlrq ri wkhvh frvwv dqg lv phdvxuhg lq wzr zd|v1 Wklv vhfwlrq jlyhv d ghwdlohg ghvfulswlrq ri krz frvwv duh fdofxodwhg lq wkh prgho/krz wkh| duh djjuhjdwhg ryhu wkh vlpxodwlrq krul}rq/dqg krz ulvnv duh ghqhg dqg fdofxodwhg1

714 Qrplqdo frvwv

Qrplqdo frvwv duh phdvxuhg rq d fdvk rz edvlv/phdqlqj wkdw frvwv rqo|

rffxu zkhq prqh| lv sdlg rxw1 Wkxv/xquhdol}hg pdun0wr0pdunhw hhfwv iurp ydu|lqj lqwhuhvw udwhv ru I[ udwhv duh qrw lqfoxghg1 Wkh uhdvrq iru

(27)

wklv lv wkdw zh duh rqo| frqfhuqhg derxw wkh frvwv wkdw dfwxdoo| dhfw wkh jryhuqphqw*v exgjhw1 Vlqfh wkh ghew lv orqj whup dqg erqgv duh qrupdoo|

ohiw rxwvwdqglqj xqwlo pdwxulw|/vzlqjv lq pdun0wr0pdunhw ydoxh duh lq prvw fdvhv qrw pdwhuldol}hg1 Wkhuhiruh/pdun0wr0pdunhw frvwv duh ylhzhg dv ohvv uhohydqw iru wkh ghflvlrq rq wkh orqj whup frpsrvlwlrq ri wkh ghew1

Lq wkh prgho/wkuhh hyhqwv dhfw wkh frvwv ri d vwudwhj|=

41 Frxsrq sd|phqwv1 Wkh frvw iru wkh vwudwhj| lqfuhdvhv zlwk wkh frxsrq sd|phqw lq orfdo fxuuhqf| wlphv wkh vlpxodwhg I[ udwh1

51 Uhghpswlrq ri iruhljq fxuuhqf| ordqv dqg lq dwlrq0olqnhg erqgv1 Dw pdwxulw| wkh glhuhqfh ehwzhhq wkh dprxqw uhfhlyhg lq edvh fxuuhqf|

dw wkh wlph wkh erqg zdv lvvxhg dqg wkh edvh fxuuhqf| dprxqw qhhghg wr uhghhp wkh erqg lv dgghg wr frvwv1 Iru iruhljq fxuuhqf| erqgv/wklv htxdov wkh glhuhqfh ehwzhhq wkh I[ udwhv dw wkh wzr srlqwv lq wlph/

wlphv wkh qrplqdo dprxqw1 Wklv hhfw fdq hlwkhu lqfuhdvh ru ghfuhdvh frvwv/ghshqglqj rq krz h{fkdqjh udwhv kdyh ghyhorshg1 Iru lq dwlrq0 olqnhg erqgv wkh lq dwlrq frpshqvdwlrq rq wkh qrplqdo dprxqw ri wkh erqg/l1h1 wkh dffxpxodwhg lq dwlrq ehwzhhq lvvxdqfh dqg pdwxulw|/

lv sdlg rxw dw pdwxulw|1 Wklv hhfw qrupdoo| lqfuhdvhv frvwv/vlqfh lq dwlrq lv sudfwlfdoo| dozd|v srvlwlyh1

61 Uhsxufkdvhv ri h{lvwlqj erqgv1 Zkhq frxsrq erqgv duh erxjkw edfn/

pdun0wr0pdunhw jdlqv ru orvvhv duh uhdol}hg1 Dowkrxjk wkh irfxv ri wkh VQGR vlpxodwlrq h{huflvh lv qrw rq pdun0wr0pdunhw frvwv/lw zrxog eh lqdssursuldwh qrw wr wdnh wkhvh uhdol}hg pdun0wr0pdunhw hhfwv lqwr dffrxqw1 Wkhuhiruh/zh dgg wkh glhuhqfh ehwzhhq wkh gluw| sulfh dw zklfk wkh erqg lv erxjkw edfn dqg lwv qrplqdo dprxqw wr wkh frxsrq frvw iru wkh shulrg1 Wkh pdun0wr0pdunhw frvw lv qrw shulrglvhg lq dq|

zd|/exw dhfwv wkh ghew frvwv e| wkh ixoo dprxqw lq wkh shulrg lq zklfk lw rffxuv1 Wkh hhfw rq frvwv fdq eh erwk srvlwlyh dqg qhjdwlyh/

ghshqglqj rq wkh uhodwlrq ehwzhhq wkh frxsrq ri wkh erqg erxjkw edfn dqg wkh suhvhqw ohyho ri lqwhuhvw udwhv1

(28)

715 Uhdo frvwv

Uhdo frvwv duh ghqhg dv wkh udwlr ri qrplqdo frvwv wr qrplqdo JGS1 Wr fdofxodwh wkh dqqxdo uhdo frvw ri ghew zh gr dv iroorzv1 Wkh qrplqdo frvw ri d fhuwdlq vwudwhj| lv fdofxodwhg lq hdfk vlpxodwlrq shulrg1 Dw wkh hqg ri hdfk vlpxodwlrq uxq/zh wkxv kdyh 453 txduwhuo| frvw jxuhv1 Wkhvh duh frqyhuwhg wr dqqxdo jxuhv dv wkh vxp ri irxu txduwhuo| frvwv/uhvxowlqj lq 63 dqqxdo frvw jxuhv1 Lq rughu wr rewdlq dqqxdo uhdo frvwv ri wklv vwudwhj|/wkhvh dqqxdo qrplqdo frvw jxuhv duh wkhq glylghg e| dqqxdo qrplqdo JGS1 Iru hdfk vwhs lq wkh vlpxodwlrq/JGS lv jhqhudwhg dw dq dqqxdo udwh1 Lq rughu wr jhw JGS iru d vshflf |hdu zh pxvw wkhuhiruh wdnh wkh dyhudjh ri irxu dqqxdo udwhv1 Wr eh h{dfw/dqqxdo uhdo frvwv/t/duh fdofxodwhg dv=

t ' Se

'c

e

Se

'tc(  ' c 2c    c fc +59, zkhuh c lv wkh frvw lq txduwhu  ri |hdu  dqg tc lv wkh dqqxdo udwh ri qrplqdo JGS lq wkh vdph txduwhu dqg |hdu1

Iru hdfk vlpxodwlrq uxq wkh dyhudjh dqqxdo uhdo frvw/ 7t/ri wkh vwudwhj|

lv dovr fdofxodwhg1 Dw wkh hqg ri rxu 4/333 vlpxodwlrq uxqv zh wkxv kdyh 4/333 hvwlpdwhv ri wkh dyhudjh dqqxdo uhdo frvw ri wkh vwudwhj|1 Wkh h{shfwhg frvw ri wkh vwudwhj| lv qdoo| ghqhg dv wkh phgldq +wkh 83wk shufhqwloh ydoxh, ri wkh vlpxodwhg glvwulexwlrq ri 7t=

. 7r|o@|e}+t 

' Df 7t

+5:, Wkh uhdvrq iru zk| zh xvh wkh 83wk shufhqwloh lqvwhdg ri wkh phdq lv wkdw wklv fruuhvsrqgv ehwwhu wr rxu ulvn phdvxuhv/zklfk lv ghvfulehg ehorz1

716 Ulvn phdvxuhv

Ulvn lv phdvxuhg lq wzr glphqvlrqv1 Lq wkh uvw glphqvlrq/ulvn lv phdvxuhg dv wkh yduldelolw| ri srvvleoh rxwfrphv ryhu d orqj shulrg ri wlph1 Zh uh0 ihu wr wklv ulvn glphqvlrq dv vfhqdulr ulvn1 Lq wkh rwkhu glphqvlrq/ulvn lv

(29)

phdvxuhg dv wkh yduldelolw| ri frvwv ehwzhhq glhuhqw |hduv iru d jlyhq hfr0 qrplf ghyhorsphqw1 Zh uhihu wr wklv dv wlph vhulhv ulvn1 Rqh pljkw vd| wkdw vfhqdulr ulvn h{suhvvhv krz edg wklqjv fdq jr jlyhq wkdw zh gr qrw nqrz zklfk rqh ri wkh 4/333 vlpxodwhg hfrqrplf sdwkv zloo eh uhdol}hg/ zkhuhdv wlph vhulhv ulvn h{suhvvhv krz pxfk dqqxdo frvwv fdq eh h{shfwhg wr ydu|

ryhu wlph iru dq duelwudu| hfrqrplf frxuvh ri hyhqwv1 Lw lv qrw hylghqw zklfk ri wkhvh ulvn phdvxuhv lv wkh pruh lqwhuhvwlqj rqh1 Lq wkh orqj whup/vfhqdulr ulvn lv suredeo| wkh ulvn wkdw wkh jryhuqphqw lv pruh hdjhu wr frqwuro1 Lq d vkruwhu shuvshfwlyh/krzhyhu/odujh vzlqjv lq ghew vhuylfh frvwv iurp rqh

|hdu wr dqrwkhu pd| eh mxvw dv xqghvludeoh1 71614 Vfhqdulr ulvn

Vfhqdulr ulvn lv fdofxodwhg dv iroorzv1 Lq hdfk vlpxodwlrq uxq wkh dyhudjh dqqxdo uhdo frvw ryhu 63 |hduv/ 7tc lv fdofxodwhg dv ghvfulehg deryh/jlylqj d glvwulexwlrq ri 4/333 rxwfrphv iru wkh dyhudjh frvw ri wkh vwudwhj|1 Wkh vfhqdulr ulvn wkhq phdvxuhv wkh zlgwk ri wklv vlpxodwhg glvwulexwlrq1 Vshfli0 lfdoo|/lw lv fdofxodwhg dv wkh uhodwlyh glvwdqfh ehwzhhq wkh <8wk dqg 83wk shufhqwlohv ri wkh vlpxodwhg glvwulexwlrq=

-7 ' bD 7t

Df 7t   +5;,

Wkh uhdvrq zh xvh wklv uhodwlyh shufhqwloh glvwdqfh lv wkdw wkh shufhqwloh glvwdqfh lq devroxwh whupv whqgv wr eh eljjhu/wkh kljkhu wkh h{shfwhg frvw lv1 Zlwk dq devroxwh phdvxuh/kljk frvw vwudwhjlhv wkhuhiruh dovr whqg wr orrn ulvnlhu/hyhq li wkh uhodwlyh yduldwlrq lq frvw pd| eh pxfk orzhu1

Iljxuh 7 vkrzv d judsklfdo looxvwudwlrq ri wkh vfhqdulr ulvn phdvxuh1 Wkh rvfloodwlqj olqhv uhsuhvhqw vlpxodwhg sdwkv iru wkh dqqxdo frvw wr JGS udwlr1 Wkh wkuhh grwwhg krul}rqwdo olqhv duh wkh fruuhvsrqglqj dyhudjhv ryhu 63

|hduv1 Lq wklv slfwxuh/wkh vfhqdulr ulvn zrxog eh jlyhq e| -7 ' 7* 72

1

(30)

Iljxuh 7= Vfhqdulr ulvn

7LPH

&RVW

_ C1

Distribution of averages = Scenario risk _

C2

_ C3

71615 Wlph vhulhv ulvn

Wlph vhulhv ulvn lv fdofxodwhg dv iroorzv1 Lq hdfk vlpxodwlrq uxq dqqxdo uhdo frvwv/ t/duh fdofxodwhg dv ghvfulehg deryh1 D vwudljkw olqh lv wwhg wr wklv vlpxodwhg frvw sdwk xvlqj ruglqdu| ohdvw vtxduhv +ROV,/jlylqj d yhfwru ri hvwlpdwhg frvwv dorqj d olqhdu wuhqg/ ut 1 Iru hdfk vlpxodwlrq uxq &/ d yhfwru ri devroxwh ghyldwlrqv ri frvwv iurp wkh olqhdu wuhqg lv wkhq fdofxodwhg dv

& 't  ut 

&

Wkh wlph vhulhv ulvn iru d vwudwhj| lv qdoo| ghqhg dv wkh dyhudjh uhodwlyh glvwdqfh ehwzhhq wkh <8wk dqg 83wk shufhqwlohv iru wkh devroxwh ghyldwlrq lq hdfk vlpxodwlrq uxq=

-A 7 ' 

fff [fff

&'

bDE&

DfE& 





Wkh uhdvrq zh phdvxuh wkh yduldelolw| ri frvwv dv ghyldwlrqv iurp d olqhdu wuhqg/dqg qrw lq dqqxdo uhdo frvwv gluhfwo|/lv wkdw wkh odwwhu zrxog pdnh vwudwhjlhv jhqhudwlqj d wuhqg lq frvwv orrn zruvh wkdq wkh| dfwxdoo| duh1 Iru lqvwdqfh/d vwudwhj| jhqhudwlqj d vwdeoh grzqzdug wuhqg lq frvwv zrxog kdyh d kljk uhodwlyh shufhqwloh glvwdqfh vlpso| ehfdxvh lw fryhuv d odujhu udqjh ri

(31)

dqqxdo frvwv/udwkhu wkdq ehfdxvh dqqxdo frvw xfwxdwhv d orw1 Judsklfdoo|/

wlph vhulhv ulvn fdq eh looxvwudwhg dv lq Iljxuh 81 Iljxuh 8= Wlph vhulhv ulvn

7LPH

&RVW

Variation around trend = Time Series risk

717 Vlpxodwhg frvw sdwkv

Wkh frvw sdwkv zklfk duh dfwxdoo| jhqhudwhg e| wkh prgho duh xqiruwxqdwho|

qrw dv w|slfdo dqg fohdu0fxw dv wkh rqhv lq wkh jxuhv deryh1 Lqvwhdg/wkh frvw sdwkv duh jhqhudoo| grzqzdug vorslqj +uh hfwlqj wkh idfw JGS jurzv dw d kljkhu sdfh wkdq jryhuqphqw ghew, dqg qrw yhu| yrodwloh1 Pruhryhu/wkh sdwkv iurp sruwirolrv zlwk glhuhqw vkduhv ri lq dwlrq0olqnhg ghew duh riwhq idluo| vlplodu1 Iljxuh 9 glvsod|v wkuhh vlpxodwhg frvw sdwkv ri sruwirolrv zlwk 3/83 dqg 433 shu fhqw lq dwlrq0olqnhg ghew/uhvshfwlyho| +wkh uhpdlqghu ri ghew ehlqj qrplqdo Vzhglvk nurqd ghew,1

(32)

Iljxuh 9= Frvw sdwkv iru sruwirolrv zlwk 3/83 dqg 433 shufhqw lq dwlrq0olqnhg ghew +uhsolfdwlrq qxpehu 754/edvh sdudphwulvdwlrq,

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

1 6 11 16 21 26

7LPH \HDUV

&RVW*'3

100% Nominal 100% Infl.linked 50/50

8 Lpsohphqwdwlrq dqg wlplqj lvvxhv

814 Lpsohphqwdwlrq

Wkh VQGR prgho lv lpsohphqwhg lq Plfurvriw H{fho dqg Ylvxdo Edvlf iru Dssolfdwlrqv +YED,1 Wklv surjudpplqj odqjxdjh rhuv d vlpsoh dqg h{leoh hqylurqphqw/dqg nqrzohgjh derxw lw lv zlghvsuhdg lq wkh qdqfldo frppx0 qlw|1 Wkh pdlq gudzedfn ri xvlqj lw lv wkdw lw lv vorzhu wkdq pdq| rwkhu surjudpplqj odqjxdjhv1 Krzhyhu/pxfk ri wkh vorzqhvv ri H{fho olhv lq wkh vsuhdgvkhhw sduw ri wkh dssolfdwlrq/zkhuhdv wkh YED odqjxdjh lv uhdvrqdeo|

idvw1 Vlqfh doo wkh fdofxodwlrqv lq wkh VQGR vlpxodwlrq prgho duh grqh lq YED/ wkh wlph qhhghg wr uxq wkh prgho fdq eh nhsw dw d pdqdjhdeoh ohyho1 Lw lv dovr yhu| hdv| wr pdnh xvh ri h{whuqdo frgh uhvrxufhv lq YED wkurxjk FRP whfkqrorj|/h1j1 iru lqwhqvlyh fdofxodwlrqv1 Lq wkh fxuuhqw lpsohphqwdwlrq zh kdyh xvhg Pdwode lq wklv zd| iru vrph vpdoohu sduwv ri wkh vlpxodwlrq1

Wkh vlpxodwlrq dojrulwkpv duh yhu| orrs lqwhqvlyh1 Iru lqvwdqfh/lq hyhu|

vwhs ri wkh vwudwhj| vlpxodwlrq wkhuh d vhyhudo orrsv wkurxjk d fdvk rz pdwul{1 Orrsv olnh wkhvh frxog eh kdqgohg lq d yhu| hohjdqw dqg h!flhqw zd|

zlwk d yhfwru edvhg odqjxdjh olnh Pdwode1 Pdwode dovr kdv d orw ri exlow0lq

(33)

ixqfwlrqv wkdw fdq eh xwlol}hg iru udqgrp qxpehu jhqhudwlrq/lqwhusrodwlrq/

fxuyh wwlqj hwf1

Iru ixwxuh ghyhorsphqw lw zrxog wkhuhiruh eh yhu| lqwhuhvwlqj wr uhzulwh vrph ri wkh prvw wlph0frqvxplqj sduwv ri wkh surjudp lq Pdwode dqg xvh lw wkurxjk wkh deryh phqwlrqhg lqwhuidfh wr H{fho1 Lq wklv zd|/zh frxog xvh wkh judsklfdo lqwhuidfh vwuhqjwkv ri H{fho/zkloh kdylqj Pdwode*v vwurqjhu fdofxodwlrq hqjlqh ehklqg1

815 Wlplqj

Wkh vlpxodwlrqv zhuh uxq rq SLLL :66 PK} 2 6;7 PE ghvnwrs frpsxwhuv1 D w|slfdo vlpxodwlrq zlwk d wkrxvdqg uxqv iru rqh vwudwhj| ryhu 63 |hduv zlwk txduwhuo| vwhsv wdnhv derxw 58 plqxwhv1 Wkh 45 vwudwhjlhv wkdw zhuh dqdo|}hg lq wklv |hduv zrun wkxv wrrn dssur{lpdwho| yh krxuv wr uxq1

Lw lv lqwhuhvwlqj wr dqdo|}h lq zklfk sduwv ri wkh frgh prvw wlph lv vshqw1 Shukdsv frqwudu| wr lqwxlwlrq/udqgrp qxpehu jhqhudwlrq dqg vlpxodwlrq ri hfrqrplf dqg qdqfldo yduldeohv grhv qrw wdnh xs d pdmru sduw ri wkh vlpx0 odwlrq wlph1 Lqvwhdg/pruh wkdq <3 shu fhqw ri wkh vlpxodwlrq wlph lv vshqw kdqgolqj wkh sruwirolr vwudwhj| dqg frpsxwlqj frvw dqg ulvnv1 Wklv uh hfwv wkh udwkhu ghwdlohg qdwxuh ri wkh vwudwhj| vlpxodwlrq1 Wdeoh 43 vxppdul}hv wkh dffxpxodwhg wlph vshqw lq glhuhqw sduwv ri wkh vlpxodwlrq1

Wkh pdlq uhdvrq wkdw vr pxfk ri wkh wlph lv vshqw lq wkh sruwirolr sduwv ri wkh vlpxodwlrq lv wkdw wkhvh urxwlqhv duh fdoohg pxfk pruh riwhq wkdq wkh urxwlqhv lq wkh hfrqrplf prghoolqj1 Iru h{dpsoh/gxudwlrq jxuhv dqg ghew frpsrvlwlrq iru wkh 630|hdu sruwirolr duh fdofxodwhg wzlfh lq hdfk ri wkh 453 txduwhuo| vwhsv lq hyhu| uhsolfdwlrq/zkhuhdv wkh hfrqrplf ghyhorsphqw lv rqo| vlpxodwhg rqfh iru wkdw vdph uhsolfdwlrq1

816 Udqgrp qxpehu jhqhudwlrq

Xqlirup udqgrp qxpehuv duh jhqhudwhg zlwk YED=v exlow0lq udqgrp qxpehu jhqhudwru1 Wkh xqlirup udqgrp qxpehuv +, duh wudqviruphg lqwr qrupdo

(34)

Wdeoh 43= Wlph vshqw lq glhuhqw sduwv ri wkh vlpxodwlrq

*HQHUDWHQRUPDOUDQGRPQXPEHUV 

*HQHUDWHHFRQRPLFUHJLPHV 

6LPXODWHHFRQRPLFGHYHORSPHQW 

+DQGOHSRUWIROLRDQGFDOFXODWHFRVWV ULVNV 

RIZKLFK &DOFXODWH\LHOGFXUYHV 

5ROOSRUWIROLR 

&RPSXWHSRUWIROLRGXUDWLRQDQGDOORFDWLRQ 

$OORFDWHERUURZLQJ 8SGDWHSRUWIROLR 

2WKHU 

2WKHU 

3DUWRIVLPXODWLRQ RIWLPH

ghyldwhv +5, xvlqj wkh vlpsoh vwdqgdug dojrulwkp=

5 '[2

'

 S +5<,

Lw vkrxog eh qrwhg wkdw wkh dojrulwkp xvhg lq wkh YED udqgrp qxp0 ehu jhqhudwru lv qrw wkh vdph dv wkh rqh xvhg lq H{fhov zrunvkhhw ixqfwlrq -(E1 Hyhq wkrxjk wkh YED jhqhudwru lv ehwwhu wkdq wkh fruuhvsrqglqj zrunvkhhw ixqfwlrq/zh duh dzduh wkdw wkh YED udqgrp qxpehu jhqhudwru pd| qrw eh vwdwh0ri0wkh0duw1 Lw lv d olqhdu frqjuxhqwldo jhqhudwru ri wkh irup43

n' E @ n S 4L_ 22ec +63, zkhuh @ ' ec fS.c eHD dqg S ' 2c H2fc S 1 Wkh pdlq gudzedfn ri wklv jhqhudwru iru rxu vlpxodwlrq h{huflvh lv wkdw wkh vhtxhqfh ri udqgrp qxpehuv lw surgxfhv lv wrr vkruw frpsduhg wr wkh qxpehu zh xvh1 Wkh shulrg ri wkh YED jhqhudwru lv Sc ...c 2S/ zklfk lv ri wkh vdph rughu dv wkh qxpehu ri xqlirup udqgrp qxpehuv zh qhhg iru d wkrxvdqg vlpxodwlrq uxqv1 Dffruglqj wr Suhvv/Whxnrovn|/Yhwwhuolqj ) Iodqqhu| +4<<5,/d uxoh ri wkxpe lv wkdw wkh

43Vhh Plfurvriw Nqrzohgjh Edvh duwlfoh T564;7:/dydlodeoh dw kwws=22vxssruw1plfurvriw1frp21

(35)

shulrg ohqjwk vkrxog eh dw ohdvw 2f wlphv wkh qxpehu ri udqgrp qxpehuv xvhg e| wkh dssolfdwlrq1 Dowkrxjk xqfohdu krz ru li wklv dhfwv rxu uhvxowv/dqrwkhu udqgrp qxpehu jhqhudwru vkrxog suredeo| eh xvhg iru ixwxuh vlpxodwlrqv1

9 Gluhfwlrqv iru ixwxuh zrun

Ryhu wkh odvw ihz |hduv/wkh Ghew R!fh kdv lq lwv dqqxdo sursrvdov iru jxlgh0 olqhv iru wkh pdqdjhphqw ri fhqwudo jryhuqphqw ghew fryhuhg wkh lpsruwdqw glphqvlrqv ri jryhuqphqw ghew fkdudfwhulvwlfv/l1h1 vwuxfwxuh dqg pdwxulw|1 Wklv grhv qrw phdq wkdw wkh Ghew R!fh*v dqdo|wlfdo dqg prghoolqj zrun kdv ehhq frpsohwhg1 Ixuwkhu vwhsv vkrxog eh wdnhq wrzdugv d pruh v|vwhpdwlf DOP dssurdfk wr jryhuqphqw ghew dqg lwv vwuxfwxuh1 Dprqj rwkhu wklqjv/

wklv vkrxog lqfoxgh lpsuryhg ghvfulswlrqv ri wkh vwuxfwxudo dqg f|folfdo idf0 wruv wkdw ghwhuplqh wkh eruurzlqj uhtxluhphqw  dqg wkxv jryhuqphqw ghew1 Rqh lpsruwdqw txhvwlrq lq wklv frqwh{w lv krz wkh sulpdu| eruurzlqj uhtxluh0 phqw lv dhfwhg e| ghyhorsphqwv lq wkh hfrqrp|/vlqfh wkh lqwhusod| ehwzhhq lqwhuhvw udwhv rq wkh jryhuqphqw ghew dqg wkh sulpdu| eruurzlqj uhtxluh0 phqw lv zkdw ghwhuplqhv wkh xfwxdwlrqv lq wkh wrwdo eruurzlqj uhtxluhphqw1 Wrgd|*v vlpxodwlrq prgho grhv qrw lqfoxgh vxfk ihhgedfn lq wkh qhw eruurz0 lqj uhtxluhphqw htxdwlrq1 Dv zh sodq rxu frqwlqxhg ghyhorsphqw zrun/zh zhofrph rslqlrqv dqg frpphqwv rq wkh prgho iurp erwk uhvhdufkhuv dqg sudfwlwlrqhuv lq wkh hog ri jryhuqphqw ghew pdqdjhphqw1

(36)

Uhihuhqfhv

Ehujvwuùp/S1 ) Kropoxqg/D1 +5333,1 D vlpxodwlrq prgho iudphzrun iru jryhuqphqw ghew dqdo|vlv1 Whfkqlfdo Uhsruw/Ulnvjçogvnrqwruhw +Vzhglvk Qdwlrqdo Ghew R!fh,1

Eroghu/G1 M1 +5335,1 Wrzdugv d pruh frpsohwh ghew vwudwhj| iudphzrun1 Edqn ri Fdqdgd Zrunlqj Sdshu/iruwkfrplqj1

Gdqlvk Qdwlrqdo Edqn +4<<;,1 Wkh lqwhuhvw dqg uhqdqflqj ulvn rq grphvwlf jryhuqphqw ghew 0 Frvw0dw0Ulvn1 Glvfxvvlrq Sdshu1

Kdplowrq/M1 +4<;<,1 D qhz dssurdfk wr wkh hfrqrplf dqdo|vlv ri qrqvwd0 wlrqdu| wlph vhulhv dqg wkh exvlqhvv f|foh/ Hfrqrphwulfd 1

Kdplowrq/M1 +4<<7,1 Wlph Vhulhv Dqdo|vlv/Sulqfwrq Xqlyhuvlw| Suhvv1/Qhz Mhuvh|1

Nlp/F10M1 ) Qhovrq/F1 +4<<<,1 Vwdwh Vsdfh Prghov zlwk Uhjlph Vzlwfklqj/

PLW Suhvv/Fdpeulgjh/Pdvvdfkxvhwv1

Plfurvriw +5334,1 LQIR= Krz ylvxdo edvlf jhqhudwhv svhxgr0udqgrp qxpehuv iru wkh UQG ixqfwlrq1 Plfurvriw Nqrzohgjh Edvh/duwlfoh T564;7:1 Dydlodeoh dw kwws=22vxssruw1plfurvriw1frp21

Plvvdoh/D1 +4<<<,1 Sxeolf Ghew Pdqdjhphqw/R{irug Xqlyhuvlw| Suhvv/R{0 irug1

Plvvdoh/D1 +5333,1 Krz vkrxog wkh ghew eh pdqdjhgB vxssruwlqj wkh vwd0 elolw| sdfw/ lq E1 P1 Euxqlod/D1 ) I1 Iudqfr +hgv,/Wkh Vwdelolw| dqg Jurzwk S dfw 0 Wkh Dufklwhfwxuh ri Ilvfdo S rolf| lq HPX1

Plvvdoh/D1 +5334,1 Rswlpdo ghew pdqdjhphqw zlwk d vwdelolw| dqg jurzwk sdfw/ Sxeolf Ilqdqfh dqg Pdqdjhphqw 41

Suhvv/Z1/Whxnrovn|/V1/Yhwwhuolqj/Z1 ) Iodqqhu|/E1 +4<<5,1 Qxphulfdo

(37)

Vzhglvk Qdwlrqdo Ghew R!fh +5334,1 Fhqwudo jryhuqphqw ghew pdqdjhphqw 0 sursrvhg jxlgholqhv1

Vzhglvk Qdwlrqdo Ghew R!fh +5335,1 Fhqwudo jryhuqphqw ghew pdqdjhphqw 0 sursrvhg jxlgholqhv1

References

Related documents

Dv fdq eh vhhq iurp Iljxuh  dqg Iljxuh 2 wkh htxdwlrq E  jlyhv d eldvhg uhvxow iru qlwh vdpsoh vl}hv1 Orrnlqj edfn dw wkh ghulydwlyhv ri htxdwlrq E  lw fdq eh vhhq wkdw

Iurp wkh vlpxodwlrqv zh frqfoxgh wkdw wklv prgho fdq eh xvhg wr txdolwdwlyho| ghvfuleh wkh hhfw ri vfdwwhu0 lqj ri xowudvrxqg iru wklv h{shulphqwdo vhwxs1 Lw lv fohdu wkdw wkh

 2SWLPLVDWLRQ RI WKH SURWHFWLRQ HTXLSPHQW GHSHQGLQJ RQ WKH YROWDJH VDJ  PDJQLWXGH DQG GXUDWLRQ  IRU D V\QFKURQRXV PDFKLQH WR NHHS V\QFKURQLVP. ZKHQ

'HDO RI WKH GD\ LV D QHZ EXVLQHVV PRGHO WKDW KDV EHHQ DGRSWHG

IURPWKH*UDPQHJDWLYHVFKHULFKLDFROLEDFWHULD DQG ZKHWKHU DQWLLQIODPPDWRU\ SKDUPDFRWKHUDSLHV FRXOG EH XVHG WR UHJXODWH WKH SURGXFWLRQ RI ,/ LQ WKHVH FHOOV :H DOVR H[DPLQHG ZKHWKHU

Lq wklv sdshu zh frqvlghu wkh sureohp ri krz wr prgho wkh hodvwlf surshuwlhv ri zryhq frpsrvlwhv1 Pruh vshflf/ zh zloo xvh pdwkhpdwlfdo krprjh0 ql}dwlrq wkhru| dv d uhihuhqfh

H[SRVXUH DERDUG +30&amp; DQG LQGLFDWHV WKH ULVN RI DGYHUVH KHDOWK DQG SHUIRUPDQFH HIIHFWV WR WKH. RFFXSDQWV DV D VLPSOH YLVLEOH DQG DXGLEOH DODUP 7KLV

VRIWZDUH DQG WHFKQLTXHV WKH LQIRUPDWLRQ VKRXOG EH SUHVHQWHG WR WKH SXEOLF LQ DQ HDV\WRXVH DQG HDV\WR XQGHUVWDQG ZD\ LQ RUGHU WR UHDFK WKH ODUJHVW SRVVLEOH SHUFHQWDJH RI WKH WDUJHW