statistiques pour la finance

7/25/2019 Statistiques pour la finance

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U]D]LU]LTRBUVARP ID CLHDHEB

O4 @CD ― O4 LHG

Dhtalhb ]dhguy



PDVVBI MB U]D]LU]LTRB



IBU OAOBH]U U]D]LU

Armrb mu oaobht Hao mu oaobht ]ypb m“lh

Oaobht m“armrb 4 Bspìrdheb (? oaybhhb) ]bhmdheb

Oaobht m“armrb 0 Sdrldheb (ìedrt-typb) Mlspb

Oaobht m“armrb 5 Unbwhbss Dsyo

Oaobht m“armrb = Nurtasls Dpidtlss

Pbodrqub ; bh ]EV, ah hb s“lhtìrbssbrd qu“dux oaobhts m“armrb 4 & 0 ; i“bspìrdhe



CAP

Vapuidtlah Bejdh

Bspìrdheb ι 4H

?

x x 4

H

Sdrldheb υ 4

H?

x ι s 4

H 4

Bedrt-typb υ s

Eavdrldheb υ 4H

?

x ι y ι s

4H 4

?



R]LILUD]LAH BH CLH

• Ah hb eahhdlt pds i“bspìrdheb bt i“ìedrt-typb m“uhb sìrlb mb rbh

• Ah malt bstlobr ebs pdrdoêtrbs, e“bst paurqual ah utlilsb ibs caroìejdhtliiahs.

Bspìrdheb Pbhtd l̀iltì oaybhhb bspìrìb

Bedrt typb rlsqub vaidtliltì



IB EABCCLELBH] MB SDP

• Eb eabcclelbht pbrobt mb eaopdrbr id mlspbrslah mb piuslburs sìrstdtlstlqubs dydht mbs oaybhhbs (bspìrdhebs) mlccìrbhtbs.

• Vius eb eabcclelbht bst ìibvì, pius ib rlsqub pdr rdppart æ id rbhtd`bspìrìb bst lopartdht.



BZBOVIB M“DVVILED]LAH

• Bxbopib ; eaopdrdlsah mb idvaidtliltì mb 0 detlahs

Detlah 4 Detlah 0

Bspìrdheb 4= 40

Bedrt-typb 2,4 =,:

Eabc. vdrldtlah 6,53 6,=6

@lbh qub i“ìedrt-typb mb

salt pius lopartdht qub e

i“detlah 0, ib eabcclelbht m

haus pbrobt mb valr, qub

vdrlb pius cartbobht qub

qudhm ah eaopdrb sd v

sah bspìrdheb mb rbhmb



MLUVB

Mlspbrslah d`saiub

• Sdrldheb / Bedrt-typb

• Mlspbrslah dutaur mb id oaybhhb

Vds mb eaopdrdlsah passl`ib bhtrbpiuslburs sìrlbs stdtlstlqubs

Mlspbrslah rbid

• Eabcclelbht mb vdrldtlah

• Hao`rb sdhs uhltì

Vbrobt id eaopdrdlsahpiuslburs sìrlbs stdtlstlqubs



VPAVPLÌ]ÌU U]D]LU]LTRÌIÌOBH]DLPBU



I“BUVÌ

B dZ dB Z

B Z ` B Z `

B dZ ` dB Z `B Z \ B Z B \

B Z \ B Z B(\)



ID SDP

S ` 6

S dZ dS Z

S dZ ` dS Z

S Z \ S Z S \ 0EAS(Z, \)

S Z \ S Z S \ 0EAS(Z, \)



ID SDP

S dZ ` dS Z υ+ d υ

• Ualbht h vdrld`ibs diìdtalrbs outubiibobht lhmìpbhmdhtbs bt mbvdrldheb υ

SDP ?

Z ?

SDP Z hυ

SDP Z υ

h



EASDP

EAS Z, \ EAS \, Z B Z\ B Z B \

EAS Z,Z S(Z)

EAS dZ `, e\ m de ∜ EAS(Z, \)EAS dZ `\, [ dEAS Z,[ `EAS \, [

SDP dZ `\ e dSDP Z `SDP \ 0d` ∜ EA



IB EABCCMB EAPPÌID]LAH IL

τ EAS(Z,\)υ ∜ υ

• 4 ≭ τ ≭ 4



EDU VDP]LE

• Z bt \ saht mbux vdrld`ibs lhmìpbhmdhtbs ;

B Z\ B Z B \

EAS Z, \ 6

τ 6SDP Z \ SDP Z \ SDP Z SDP \

• Ibs rìelpraqubs saht cdussbs !



ID IAL HAPODIB



VPÌUBH]

• Li s“dglt mb id ial id pius lopartdhtb paur mìerlrb uhb vdrld`ib diìdeahtlhub.

• E“bst id ial vbrs idqubiib tbhmbht ibs dutrbs ials mb pra`d`liltìs paeahmltlahs qub i“ah rbheahtrb crìquboobht mdhs id prdtlqub.

• Id saoob (au id oaybhhb) mb pius mb trbhtb vdrld`ibs diìdtalrbslhmìpbhmdhtbs qul sulvbht uhb oëob ial mb pra`d`liltì sultdppraxlodtlvbobht uhb ial harodib.



VPÌUBH]

• Li s“dglt m“uhb mbs ials mb pra`d`liltìs ibs pius dmdptìbs paur oampjìhaoêhbs hdturbis lssus mb piuslburs ìvìhbobhts diìdtalrbs(lhmìpbhmdhts)

• E“bst uhb ial mb pra`d`liltì d`saiuobht eahtlhub qul mìpbhm mb

pdrdoêtrbs ;

• I“bspìrdheb ; • I“ìedrt-typb ; • (Id vdrldheb ; )



DR]PBU EDPDE]ÌPLU

Lhmledtbur Sdibur

Bspìrdheb ιOamb ι

Oìmldhb ι

Sdrldheb υ

Bedrt-typb υUnbwhbss 6Nurtasls 5



MBHUL]Ì MB VPA@D@CAHE]LAH MB PÌVDP

p x 4υ 0φ b ∐ ∐



IAL HAPODIB EBH]PÌB-PB] EARP@B BH E

Id eaur`b mb id ial harodib bstdppbiìb Eaur`b mb Gduss.

Li s“dglt mb id rbprìsbhtdtlah id pius

eaoouhb, id oaybhhb bst ìgdib æ 6,i“ìedrt-typb bst ìgdi æ 4.

IAL HAPODIB EBH]PBB PBMRL]B



HA]D

• Ah suppasb uhb vdrld`ib diìdtalrb P qul sult uhb ial harodib.

• Utdtlstlqubobht, ebttb ial sb mìclhlt pdr sah bspìrdheb bt sd vdrld

P~H ι>υ

• Mdhs ib eaurs mb ]EV, ah vd utlilsbr i“bspìrdheb bt i“ìedrt-typb ;

~ >



HA]D

• Iarsqu“uhb vdrld`ib diìdtalrb sult uhb ial harodib (gdusslbhhb), agìhìrdibobht dvbe sd vdrldheb ;

~(,)• Iarsqu“uhb vdrld`ib d ìtì ebhtrìb puls rìmultb, ah id hatb gìhìrd

~(,)



EBH]PBP B] P

VARPTRALEBH]PBP B] PBMRLPB 1

• Ibs mahhìbs mbvlbhhbhtlhmìpbhmdhtbs mb i“uhltì au mbi“ìejbiib ejalslb

•

Ah a`tlbht mbs vdrld`ibs dydht uhboëob oaybhhb bt uhb oëobmlspbrslah

• Ah pbut dlhsl eaopdrbr piuscdelibobht mbs vdrldtlahs

EAOOBH]EBH]PBP B] PBMRLPB



ID IAL HAPODIB EBH]PÌB-P

• Mdhs ib eds aü Z sult uhb ial harodib, [ sult dussl uhb ial harodib.

• Ebel pbrobt mb rdobhbr taut edieui rbidtlc æ mbs vdiburs mb H(ι,υedieuis sur H(6,4) qub i“ah pbut trauvbr mdhs ibs td`ibs.



VPAVPLÌ]ÌU MB ID IAL HAPO

Ilhìdrltì mb ial harodib

• Ul Z~H(ι,υ) bt sl \ dZ `, diars \ sult ìgdibobht uhb ial harodib

~(> ) B Z ι B \ B dZ ` dB Z S Z υ S \ S dZ ` d°S(Z)

S Z υ S \ S dZ ` d υ



VPAVPLÌ]ÌU MB ID IAL HAPO

Dmmltlvltì mb id ial harodib

• Ul Z bt \ saht lhmìpbhmdhtbs bt sulvbht uhb ial harodib, diars id saoob

mlccìrbheb mbs mbux vdrld`ibs Z bt \ sulvbht ìgdibobht uhb ial harodib

• Ebttb praprlìtì m“dmmltlvltì sb gìhìrdilsb paur h vdrld`ibs diìdtalrbs lhmbt sulvdht tautbs mbs ials harodibs.

~(, ) ~(, ) B Z ι B \ ι ι ι ι ιM ι

S Z υ S \ υ υ υ υ υM



]JÌAPÊOB EBH]PDI-ILO

•

Ualt Z, Z, … , Z uhb sultb uhb h vdrldìbs diìdtalrbs lhmìpbhmdhtbial, m“bspìrdheb ι bt mb vdrldheb υ°, diars ;

U Z ι

υ h ~H(6,4)

•

Dvbe ; Z ?

Z

• Eb tjìarêob dcclrob qub tautb saoob mb vdrldìbs diìdtalrbs llm(lhmìpbhmdoobht bt lmbhtlqubobht mlstrlùìbs) tbhm vbrs uhb vdiìdtalrb gdusslbhhb.



]JÌAPÊOB EBH]PDI-ILO

• E“bst gràeb æ ebttb praprlìtì qub id ial harodib pbrobt m“dppraem“dutrbs ials bt mb oamìilsbr mbs obsurbs m“brrburs au mbs tbsts sti“dlmb mbs td`ibs mb id ial harodib.

• Bh tjìarlb id eahvbrgbheb d ilbu iarsqub tbhm vbrs i“lhclhl, ebpb

palht mb vub prdtlqub, ib ]EI bst dppilquì æ pdrtlr mb .

• Rh grdhm hao`rb mb pjìhaoêhbs hdturbis bst mu æ id supbrpasltm“ìvìhbobhts pius au oalhs lhmìpbhmdhts. Li bh rìsuitb qub id iaibs rbprìsbhtb mb odhlêrb rdlsahhd`ibobht bccledeb.



LH]BPSDIIBU PBODPTR



SDIBRPU PBODPTR

Sdibur erltlqub ?

hao`rb m“ìedrt-typbs

Ubuli m“brrbur ?

paurebhtdgb mb vdiburs jars mbi“ìedrt-typb

Bedrt-typb () % mb

4

0

5

Ubuli m“brrbur Sdib

4 %

2 %

46 %

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