Margrabe Formulas for a Simple Bivariate Exponential Variance-Gamma Price Process (I) Theory

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1 Irol Jourl of f Iovv hl srh IJI Volu I Issu I Augus- 3 PP -6 rourlsorg rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor Wrr Hürl Wolrs Klur Fl rvs flsrss 69 CH-88 Zürh rl rrhurl@olrsluro v: -6-3 vs: -7-3 Ap: Asr: For h purpos of sulous r oss vluo of sur lls /or ss prs fro fl rs lrv o h Bl-hols-Vs flor s rv I s s o spl ulvr pol vr-g pross sso o ulvr Lév pross hos opos r rf Bro oos hg oo p g suoror h logrh of h ulvr vr-g flor s lr h vr-g opos h prl of h s-pr flor pproh s osr rg h pr of h rgr hg opo h vr pol vr-g rl-orl or fl pr pross Applos o oh Isur F r o I spl vr pol vr-rlg ol h foruls splf o ll los-for prssos Kors: Bl-hols ol vr-g pross s-pr flor r pr of rs INOUCION I hs log osrv h sur ll fl rurs h o-ro sss uross hv ls hh o pur Guss pross A pl pl s h Bl-hols-ro logorl ol us opo prg or Aurl F s or or fousg o lrv sohs prosss h l h olg of o-guss hrrss Hovr h osruo of ulvr o- Guss prosss for h sulous olg of rl-orl sur lls /or ss prs fro fl rs s opl op hh slo ls o spl ll foruls orovr for r oss vluo o s o fl hs prosss h soll s pr flors or us quvl rgl sur for fl pr prosss s rgu h rs 4 hough grl frors for rvg s-pr flors s g [] [] hr r o pprs hh propos pl prssos for h hr orrspog sruo fuos h gol of our oruo s o-fol Frs propos lrv o h ulvr Bl-hols-Vs BV flor rou [3] s lso [4] For h rs rr rr h h rl [5] os so of h Bl-hols flor o or grl vrso h rs rs s ol sour of ross Fro hl vpo s url o vsg ohr grlos l h osro of lrv ss pr prosss for us opl fl rs I l us ssu h ss prs o rrg h hr ss uqu s-pr flor f ol f h r s opl Ohrs f h r s opl svrl s-pr flors s prg s o uqul f hrfor h su of s-pr flors s ov o of AC Pg

2 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor h prols of or F hh osss o urs h prg of rrr porfolos opl rs A vlul populr opor o h uquous ulvr pol Guss pross s h ulvr pol vr-g pross prs o I s o fro ulvr Lév pross hos opos r rf Bro oos hg oo p g suoror hs pross hs prvousl osr [6] [7] For r ursg of h s-pr flor pproh rll rfl o 3 h osruo of h BV flor Prog slrl h logrh of h ulvr vr-g flor s ssu o lr h vr-g opos s offs r pll r hor 4 As so gol h prl of h prs s-pr flor pproh s osr prg h rgr hg opo h vr pol vr-g rl-orl or fl pr pross hor 5 spls rgr foruls for h vr pol vr-g rl-orl pr pross All los-for prssos r o for h vr pol vr-rlg spl s Bs o h VG flor rv hor 6 rgr foruls for h orrspog fl pr prosss pl 6 llusrs oprg rgr opo prs h vr Bl-hols ol h vr vr-rlg ol o 7 s vo o furhr susso olusos g hls r prov App sl so of h ulvr vr-g ol pplo o so r s r prs [8] A IPL ULIVAIA VAIANC-GAA POC I s orgl rprso h uvr VG pross s f s rf Bro oo hg p g pross V fro h l s f hr G W G W s sr Wr pross h p suoror rsg posv Lév pross G ~ s g pross h u r vr r s Lév pross h s of h VG pross s r s sruo u I f h ro vrl : ~ VG follos hr prr sruo h uul grg fuo gf C u l [p u] l u u O os h h gf s ol f ovr h op rvl u 3 h forul s o fro h gf of h g ro vrl G : ~ / / oog usg h G ~ N G G s orll sru h sruo of VG s fl vsl h VG pross hs p sor rs hh lso follo VG sruo l G s s ~ VG / s 4 h sr s s us h orgl ol [9] [] h VG pross hs su pls g []-[4] I s spl s of h lrl g pross ohr pr sl prosss osr r pprs g [5]-[9] vrl ulvr vrsos of h VG pross hv osr so fr [9] frs rou ulvr sr VG pross suorg ulvr Bro oo hou rf oo g pross h sr vrso of hs Irol Jourl of f Iovv hl srh IJI Pg

3 Wrr Hürl ol hs vlop Co ov [6] Luo hous [7] Grlg hs uhors osr ulvr Lév prosss h VG opos of h p G G W 5 hr h W s r orrl sr Wr prosss suh h [ W W ] or opl ulvr VG ols hv lso osr g []-[4] sp ll s shorogs h us of h ol 5 s usf horll loog h vr of s VG rgs : ~ VG u l Vr [ ] 6 h vr oposs o osr opo h s ru o h Bro oo ogous opo h s u o h g sru hg of h Bro oo h prrs govr h posurs of h rgs o h glol r ur sur h oo prr lrl o os h h sss uross r lso ff h sgl rgl sgs h oo prr O h ohr h h ssl o ho vlop [8] s sussful pplo o rl-orl usfs s us prl or o f s for h s of spl h frs fous s hrfor o h ol 5 h o gf of hs ulvr pross prss los-for Proposo gf of h ulvr VG pross h o gf of h ulvr VG pross ~ VG / s h prrs r C Irol Jourl of f Iovv hl srh IJI Pg 3 u l{ u u u} u u u u 7 Proof h ool rgs r orll sru s G ~ N G G o os h rprso 7 fro h follog lulo u l [p u ] l [[p u G ]] l [p ug u ug ] C G G rs h ro vor u of h spl s hs so-ll ulvr sr Lpl sruo o ~ AL h hs svl su h oogrph [6] s lso [7] h prr so of h shf vrso ~ AL hs suss [8] [5] h ho s [8] o h ssl so of h shf vr-g ol VG 3 H BLACK-CHOL-VAICK FLAO ll h Bl-hols-Vs BV flor rou [3] Cosr ulpl rs oo h rs sss hos rl-orl prs follo logorl sruos Gv h urr prs of hs rs sss l ssu h h fuur prs r sr pol Bro oos of h p p v W 3 hr h W s r orrl sr Wr prosss suh h [ W W ] W ssu h h orrlo r s posv s-f h o-vshg r h qus v r rpr s sr vo pr

4 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor u of h -h ss logrh rur s os voll prr h rprso 3 lus o populr ss prg ols: Bl-hols ol: r h v W r ovr h rvl Vs Ors-Uhl ol: r r W h v h oo ol os lso rs-fr ss hh s ssu for spl o uul os r r pr u h BV flor of so hs h s for s h pr prosss 3 p W 3 for so p prr fuo vors o o 4 o uss h fg rloshp [ ] p h prsso 7 for h uvr gf h VG flor hs h s for s h pr pross 4 For so prrs o r o ss Irol Jourl of f Iovv hl srh IJI Pg 4 W W W W o f s-pr flor h sohs prosss 3 3 us ssf h rgl oos [ ] r [ ] hr [] os ool po h rsp o h foro l hor 3 BV flor of so Gv s fl r h rs-fr ss h os r of rur r rs sss h hv log-orl rl-orl prs 3 Assu o-sgulr posv s-f orrlo r h h BV flor 3 s r p W h 34 r C v W h qu r r [ v ] s ll r pr of h -h rs ss Proof h rgl oos 33 r quvl h h ss of lr quos r s [3] proof of Proposo 4 A A-PIC FLAO FO H ULIVAIA PONNIAL VG POC W g h h osruo of h uvr VG flor Cosr h follog ss prg ol Gv h urr pr of rs ss s fuur pr s sr pol VG pross p G W 4 G hr rprss h logrh r of rur of h rs ss pr u C l 4

5 Wrr Hürl p 43 No spl gf lulo shos h h s-pr flor rgl oos [ ] r [ ] 44 r quvl h h ss of o o-lr quos h hr uos : r l l 45 Isrg h frs quo o h so o ls h ssr rloshp r {l l } 46 As h ss 45 hs o gr of fro h uo hos rrrl s r 47 hh s rpr s h -p VG r pr of h rs ss Wh h rsro 4 o h VG prrs hs vlu s ls posv Isr o 46 usg 4 shos h h prr s r h o lr prssos p 48 I prulr oprg h frs hr r 48 shos h h prr s spl pol rsfor of h r pr hh s quvl o h logrh rloshp r l 49 Wh h ror srs for h logrh o ss h h VG r pr of rs s gv r 4 hr h ls qul h frs orr pproo follos fro 48 urg rrrgg h ov o os h follog VG flor rprso hor 4 uvr VG flor Gv s rs-fr ss h os rur r rs ss h rl-orl pr 4 h h VG flor 43 s r G p G W G ~ h 4 r C r l 4 N osr rs sss Gv h urr prs of hs rs sss l hr fuur prs r sr pol VG prosss of h p p 43 hr rprss h logrh r of rur of h -h rs ss pr u h ro vor pross follos spl ulvr VG pross h gf 7 slrl o 4 o hs l 44 h VG flor of so hs h s for s h pr prosss 43 For so prr vor oh o r o ss Irol Jourl of f Iovv hl srh IJI Pg 5

6 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor Irol Jourl of f Iovv hl srh IJI Pg 6 p 45 I hs suo h rgl oos hh f h s-pr flor r quvl h h o-lr ss of quos h uos us h pl for of h gf 7: } l{ } l{ r 46 h h vor oo As h ss 46 hs grs of fro h uos hos rrrl A ov ppropr ho hh ls o spl soluo of h ss 46 osss o s r 47 hh s rpr s h -p VG r pr of h -h rs ss No srg h frs quo of 46 o h so os g o ou 47 ls 48 A srghforr lulo shos h h opos of h prr vor r r h o lr prssos us 44 for h so o p 49 hh grl h rlo 48 I prulr oprg h frs hr r 49 shos h h prrs r spl pol rsfors of h r prs of rs hh r quvl o h logrh rloshps l 4 lrl o 4 o os h srs psos h frs orr pproos for h VG r prs of h rs sss ] [ ] [ 4 hr h ls qul follos fro 49 urg rrrgg h ov o os h follog ulvr VG flor rprso hor 4 VG flor of so Gv r rs sss h rl-orl prs 43 hr h ro vor pross follos ulvr VG pross h h VG flor 45 s r p h 4 C r 43 rs 4 I s sruv o o h 3 45 orrspo o sshr rsfor sur h hs log us opo prg g [9] orovr por oo h h sr o-rrg fror of hl F us o g [3] o 5 [3] Chp B h Ful hor of Ass Prg h ssupo of o-rrg for of h ff r hpohss s quvl h h s of

7 Wrr Hürl quvl rgl sur for fl pr prosss I opl rs h quvl rgl sur s uqu prf rplo of og ls hols srghforr prg ppls I opl rs oo ol s rqur o upo hh quvl rgl sur s ppropr No l P os h rl-orl sur * P quvl rgl sur h o hr or ur P hr h pr * prosss r fl h s-pr flor Alrvl o or ur P soug h pr prosss h h ou urr Worg h fl * srus ol o of ors ur P Bu f oll sur lls r osr o ors ur P s [3] r 3 A o-rvl pl s prg of h gur u flo h f GIB opo quo 54 [4] I h prs ppr osr h prl of h s-pr flor pproh for pol vr-g pr prosss of rgr p us sur fl rs I sur h rgr opo hs suss [3] [33] [34] os V4 o V6 [3] o 4 O h ohr h [8] offrs lrv pproh o lro s o ovl ulvr ssl o ho h uss ss s ovrs lso h osss ouross sors A rl-orl oprso of h pol vr-g ol h h uquous Bl-hols ol for prg h rgr opo s lso 5 AGAB FOULA FO H AL-WOL PIC POC Gv s h shf vrso of h Lév pross u h u shf ulvr VG ro vor ~ VG W ssu h fuur vlus of fl s r sr pol VG prosss of h for p 5 hs grl fror ls sulous ollg of rl-orl sur lls /or ss prs fro fl rs For r oss vluo o s o fl h h so-ll s pr flors s pl h rs 4 hh ll o h os I oh sgs rv grl los-for foruls for h osol rgr hg opo hr of h rl-orl p [ ] 5 hrfor h vr s 5 s of rs for hs s For spl hou loss of grl suffs o suss h u s B us of oo h s rov fro sohs pross h follog Coog o h oo g suoror o r [ [ ] G ] f f / 53 As usul os h sr orl sruo s h survvl fuo ' s h s h vr sr orl s s o ; p B fo 5 o os ; 54 Irol Jourl of f Iovv hl srh IJI Pg 7

8 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor Irol Jourl of f Iovv hl srh IJI Pg 8 h prsso h r of 54 s o-gv prov h No s possl o spr h oul grl s J us / / ; Wh hs h r grl rs / } { / J 55 A srghforr pplo of L A h App ls J g o ou h ov fo of h ulr fuo o rrs h rgus s h orl sruo fuos s h Furhror o os h No usg h L A of h App o os A lgr lulo s o h prssos for h offs ls furhr 56 W r r for h follog rsul hor 5 rgr forul for h rl-orl pol shf vr VG pross Gv s h vr pross u p h ~ VG Wh o hs / / ] [ 57 Proof I rs o sr 56 o 53 h hg of vrls r 5 O osrvs h h -fuo 57 s rl o h o s [6] p96 urop rs-url ll-opo pr for pol VG pr pross A prulr s for hh h forul 57 splfs osrl s h spl s h s hh s l o or ls I hs suo h -fuo

9 Wrr Hürl Irol Jourl of f Iovv hl srh IJI Pg 9 splfs o h lulo of h prsso h hg of vrls / ur h ssupo ] [ - L 58 h h grl fuo of orl p L 59 h ssupo 58 s h 57 ll f for prov oo hh s quvl h h s of h gf l G C of sr g ro vrl h shp prr sl prr I s h g sru suoror ~ G rus o rlg sru suoror ~ rlg G h gr prr h grl fuo 59 vlu org o h follog los-for forul proof App :!!!! L 5 6 AGAB FOULA FO H FLA PIC POC Cosr h rgr hg opo for h fl pr pross 5 suh h ] [ 6 h s-pr flor s of h for 4 h As o 5 s suss h u s Coog o h oo g suoror o rs / ] [ ] [ f G f 6 lrl o 55 s possl o spr h oul grl s J h h r grl / / J 63 A srghforr pplo of L A h App ls J g o ou h fo of h ulr fuo o rrs h rgus s h orl sruo fuos s

10 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor Irol Jourl of f Iovv hl srh IJI Pg h Furhror o os h No usg h L A of h App o os 64 p us of h follog rloshps for 33 s : 65 A lgr lulo s o h prssos for h offs ls 66 Furhror h offs of h url rs of 64 r rspvl qul o 67 W r r for h follog rsul hor 6 rgr forul for h fl pol shf vr VG pross Gv s h vr pross u p h ~ VG h vr flor p of hor 4 s h o hs / / ] [ 68 Proof I rs o sr 64 o 6 h ssr fos s o prfor h hg of vrls I h spl s h s f h prsso 68 vlu usg h forul 58 for h -fuo plg furhr o shf spl vr vr-rlg pr pross h gr prr o os v 5 los-for rgr foruls pl 6 Bvr Bl-hols vrsus vr vr-rlg ols

11 Wrr Hürl I s rsg o opr h lssl los-for forul rgr [35] h los-for vrs o fro 68 I h vr Bl-hols ol h fuur prs u r sr h quos 3 h s p Z 69 hr h Z s r orrl sr orl h orrlo off vr-ovr hrrss of 69 r gv B h s V B B [ Cov[ ] p ] B B {p B } 6 For llusro s Applg h Bl-hols flor fro hor 3 o os rgr s lssl hg opo pr l g [3] hor B ] [ 6 I h vr vr-rlg ol h los-for hg opo pr h fuur prs u r sr quos of h for 5 suh h p W W Z 6 h W ~ rlg h Z s r orrl sr orl h orrlo off V h orrspog s vr-ovr hrrss r B V V V [ Cov[ ] p{ l } ] p{ l V } B B 63 I s url o opr oh ols ur qul frs so orr os I s h quos of qul vr-ovr hh osss o qu 6 63 rsul o h follog prr osrs l l B Irol Jourl of f Iovv hl srh IJI Pg l V 64 Clulo of h fl hg opo pr 68 rqurs h prrs of h VG flor 43 hh r hrh r V r C 65 For h vr sr Lpl spl s h h spl prr ho V o os 66 l r 4 67 r C h rg prrs 68 h vlus 4 68 A srghforr lulo of 68 usg 58 5 for ls h sr Lpl rgr opo pr L r [ ] 69

12 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor B Nurll f r h % oprs h L 4975% h follo-up [8] provs so oprsos s o so r s 7 UL FUH ICUION AN CONCLUION Frs s usful o sur h hs oplsh h srg po s h sh o rh ulsol opo prg h so ulvr o-guss ols l o pur sss uross ohr sl fs fro osrv sur ll fl r I urs ou h o uh s o hs rsp spll h os o r oss vluo for us h Bsl III olv II pros o hv hs o hr or h quvl rgl sur for fl pr prosss or us spr flor o sou sur lls ss prs ur h rl-orl prol sur h so possl ph hs follo ulvr pol vrg pross s o of h populr lrv hos o h ulvr pol Guss pross h osruo of pl s-pr flor for s frs gol hh hs hv hor 4 A pplo o vr opo prg hs ur hor 6 hh spls rgr forul for h fl pol shf vr vr-g pross s oruo orovr ll los-for prssos for h vr pol vr-rlg spl s r lso o o s por o rr h our spl ol s s o or h u hs so srous rs For pl lr orrlo o f o h rgs r f orovr h ho of sgl prr uss gr fful h o lro o opo prs o h rgs s osrv [] o ovro hs ffuls hr r ls o possls sposl O hr ppl lrv so ho hh os o shr so of h ovs purpos of h follo-up [8] or osr or opl ulvr vr-g ols suls o h lr proposl ll prs lshr APPNI : Igrl s of orl p h rul s us h rvo of hor 5 r s prov sprl L A For rl urs / o hs h Irol Jourl of f Iovv hl srh IJI Pg A Proof Cosr frs h s Fro h rlo o gs Usg hs o os hg of vrls / / L A For rl urs o hs h / A Proof Cosr h fuos F G O os h F F' fro hh o gs F F F' O h ohr h o hs G F

13 Wrr Hürl ' G 3 / h G ' G G I follos h / G APPNI : Clos-for vluo of grl fuo of orl p I s s gr prr h vluo of h grl 59 s o hrough prl gro fg frs prv grl for Irol Jourl of f Iovv hl srh IJI Pg 3 of h for P A hr P s polol of gr h gr offs h follog rursv rloshp rs hs polol opll L A h polol P f A ssfs h follog rurso P P 3 P A Proof Frs of ll s ' s h s prv grl of h P For h rurso s sho uo For o pros s follos L H h prols Hr polol of orr hh ssfs h propr H I prulr o hs h 3 3 ' hs ls o h prv grl 3 3 '' 3 H P P h hh shos A for h uo sp fro o s sho prforg o sussv prl gros s follos: [ ] [ [ ] 3 hh shos h rurso for h l P P ] A sussv pplo of h rurso A ls h follog pl forul L A h polol P ssfs h pl rprso P! 3! A3 Proof Fro L A o os h P s polol v pors of s P Wh A o os h rursv rloshp 34

14 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor hh pls h! 3! No l us rv h forul 5 A prl gro of 59 usg A ls L P P Usg A3 follos h P P Irol Jourl of f Iovv hl srh IJI Pg 4 P P! L! / N o osrvs h h fuo s h prol s of h hlforl sruo h o grg fuo g [36] quo 9 p hrough uo o shos h rursv rlo 3 hh shos h h os of h hlf-orl sruo ssf h rurso 3 o ss h!! 3 h forul 5 s sho FNC [] lrss K Prsso A Prg r of rur gurs Hh-Jrro- oro fror Isur h oo [] Jl Yor Chs hl hos for Fl rs prgr F prgr-vrlg Loo L 9 [3] Hürl W A so of h Bl-hols rgr foruls o ulpl rs oo Appl h [4] Hürl W h lgr of opo prg: hor pplo I J of Algr ss [5] Hürl W Opo prg h ulvr Bl-hols r h Vs rs rs hl F Lrs -8 3 [6] Co ov P Fl ollg h Jup Prosss CC Fl hs rs Chp Hll 4 [7] Luo hous W A ulvr up-rv fl ss ol Quv F [8] Hürl W rgr foruls for spl vr pol vr-g pr pross II sl so pplo Apprs IJI 3 [9] h vr g ol for shr r rurs Jourl of Busss [] l F Opo prg h VG rgl opos hl F [] Crr P Chg h vr g pross opo prg urop F v

15 Wrr Hürl [] Purl souous ss prg prosss I: Jou Cv J usl s Opo Prg Irs s s g Crg Uvrs Prss Crg 5-53 [3] Crr P G H B Yor h f sruur of ss rurs: prl vsgo Jourl of Busss [4] G H Pur up Lév prosss for ss pr olg J of Bg F [5] Kühlr U pp Blrl g sruos prosss fl hs ohs Pross Appl [6] Kühlr U pp Opo prg lrl g so ols ss sos [7] Kühlr U pp pr sl sruos pplos o fl hs Prpr UL: hp://sohsu-hovr/fl/su/pf/_4pf [8] Kshv VK ohs pross us rhl B- spls: ollg ulvr ss pr s Aurl srh ppr o 95 Css Busss hool Loo [9] Bll F rur L Opo prg ool lrl g ol Prpr UL: hp://ssro/sr=46478 [] rro P A ulvr vr g ol for fl pplo I J of horl Appl F -8 8 [] Luo rro P g -hg Lév ss ols hrough ulvr suorors Collgo Crlo Alro Worg Ppr rs o 4 7 [] Luo rro P ulvr hgs for Lév ss ols: hrro lro J Copuol Appl h [3] Wg J h ulvr vr g pross s pplos ul-ss opo prg Ph hss Uvrs of rl Collg Pr 9 [4] H A rur L Porfolo lloo usg ulvr vr g Cpl rs: Ass Prg & Vluo Jourl 44 [5] Hürl W A o ho for h ulvr sr Lpl sruo ss & Prol Lrs [6] Ko Kouos J Pogors K h Lpl sruo grlos: rvs h pplos Brhäusr Boso [7] Ko Kouos J Pogors K A sr ulvr Lpl sruo 367 p Appl Pro Uv Clfor Brr 3 [8] Vs H O h prr so of h sr ulvr Lpl sruo Co s hor hos [9] Grr HU hu W Opo prg sshr rsfors h sussos rsos of h o of Aurs [3] Wührh V Bühl H Furrr H r-coss Aurl Vluo AA Lur Nos vol rvs lrg o prgr-vrlg [3] Wührh V r Fl olg Aurl Vluo olv Isur prgr F 3 [3] Bühl H Lf sur h sohs rs rs I: G Ov Fl s Isur prgr 995 [33] Hürl W A lr uf pproh o loss vr ous Bull of h ss Assoo of Aurs [34] Hürl W rl o hos ohs Orrs Applo Aurl srh oogrph 34p I: BAV - Bolí l Asoó á Vol Volu V u & u 8 [35] rgr W h vlu of opo o hg o ss for ohr Jourl of F [36] Pourh Cosruo of s-orl ro vrls: r h lr oos of orl hlf-orl? J s h A Appl Irol Jourl of f Iovv hl srh IJI Pg 5

rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor AUHO BIOGAPHY Wrr Hürl hs su hs phss HZ hr h o hs Ph 98 h hss hghr lgr Afr posoorl flloshps Yl Uvrs h Pl Isu Bo h 984 ur Wrhur Lf Psos sor ur Ao IG rl

16 rgr Foruls for pl Bvr pol Vr-G Pr Pross I hor AUHO BIOGAPHY Wrr Hürl hs su hs phss HZ hr h o hs Ph 98 h hss hghr lgr Afr posoorl flloshps Yl Uvrs h Pl Isu Bo h 984 ur Wrhur Lf Psos sor ur Ao IG rl 3-6 sor osul II Zürh 6-8 s urrl plo FGlol rl Wolrs Klur Cop H hs vsg sso profssor url s h Uvrs of oroo urg h r or foro s fou hs hopg hps://ssgooglo/s/hurl/ Irol Jourl of f Iovv hl srh IJI Pg 6

Factors Success op Ten Critical T the exactly what wonder may you referenced, being questions different the all With success critical ten top the of l

Factors Success op Ten Critical T the exactly what wonder may you referenced, being questions different the all With success critical ten top the of l Fr Su p T rl T xl r rr, bg r ll Wh u rl p l Fllg ll r lkg plr plr rl r kg: 1 k r r u v P 2 u l r P 3 ) r rl k 4 k rprl 5 6 k prbl lvg hkg rl 7 lxbl F 8 l S v 9 p rh L 0 1 k r T h r S pbl r u rl bv p p