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TRNG I HC KINH TTHNH PHHCH MINHKHOA TI CHNH

BMN QUN TRRI RO

Mt nh gi ton din vcc phng phpValue at risk (VaR)

A comprehensive review of Value at Riskmethodologies

Pilar Abad, Sonia Benito, Carmen Lpez

GVHD: PGS.TS. Nguyn ThNgc TrangNhm thc hin: Nhm 6C

Lp TCK1 - Kha 37

Nguyn ThKim Chi TC02

Nguyn ThThu Tho TC02

Thn ThThm TC02

L ThThanh Hng TC03

L ThThanh Thi TC03

Thnh phHCh Minh thng 9 nm 2014

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Nhm 6 .TCKI.K37

MC LC

1. Gii thiu ............................................................................................................................... 5

1.1. Sra i ca VaR ........................................................................................................ 51.2. C|c phng ph|p u tin tnh VaR ................................................................... 5

2. M hnh VaR ......................................................................................................................... 7

2.1. Nhc li kin thc thng k .................................................................................... 7

2.1.1. Hm phn phi xc sut ........................................................................................ 7

2.1.2. Hm mt xc sut ............................................................................................... 7

2.1.3. Phn v............................................................................................................................ 8

2.1.4. Hm phn phi xc sut chun ha. ................................................................ 8

2.2. Tip cn VaR ................................................................................................................. 9

2.3. M hnh VaR ................................................................................................................ 10

2.4. Cc m hnh VaR trong thc hnh ..................................................................... 11

2.5. M hnh VaR cho TSSL ............................................................................................ 12

3. C|c Phng ph|p tnh VaR:......................................................................................... 14

3.1. Phng ph|p phi tham s ..................................................................................... 14

3.1.1. Phng php lch s.............................................................................................. 14

3.1.2. Phng php mt phi tham s. .................................................................. 15

3.2. Phng ph|p tham s ............................................................................................. 19

3.2.1. M hnh bin ng (Volatility model): ................................................... 203.2.2. Hm smt .......................................................................................................... 27

3.2.3. Nhng moment bc cao c iu kin thay i theo thi gian: .......... 30

3.3. Phng ph|p b|n tham s .................................................................................... 31

3.3.1. Phng php lch sc trng sbin ng (....................................... 313.3.2. Phng php m phng lch slc (FSH) ................................................... 33

3.3.3. M hnh CAViaR ( Conditional autoregression Value at risk) ............ 35

3.3.4. L thuyt gi trcc tr(Extreme value theory EVT) ......................... 40

3.3.5. Monte Carlo ............................................................................................................... 51

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Nhm 6 .TCKI.K37

4. Kim tra li phng ph|p lun VaR (Back-testing) .......................................... 55

4.1. C sca cc kim nh tnh chnh xc. .......................................................... 55

4.1.1. Unconditional coverage test. ............................................................................. 55

4.1.2. Conditional coverage test. ................................................................................... 59

4.1.3. Kim nh phn vng(DQ). ............................................................................ 62

4.2. Hm tn tht. .............................................................................................................. 62

5. So s|nh c|c phng ph|p VaR .................................................................................... 63

6. Mt schquan trng ca phng ph|p VaR.............................................. 65

7. Kt lun................................................................................................................................. 68

8. TI LIU THAM KHO ................................................................................................... 70

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Tng quan nhng phng phpVaR PGS.TS. Nguyn ThNgc Trang

Nhm 6 .TCKI.K37

LI M U

B{i nghin cu n{y trnh b{y |nh gi| l thuyt ca nhng t{i liu hin nayv VaR v{ tp trung c th v{o s ph|t trin ca c|c phng ph|p mi

c lng n. T|c gi thc hin mt ph}n tch tin tin, ci tin c|c

phng ph|p chun o lng VaR tt hn, ng thi l{m ni bt im

mnh v{ im yu ca tng phng ph|p. T|c gi cng s xem xt c|c th

tc kim tra li c s dng |nh gi| hiu qu ca c|c phng ph|p

VaR. T gc thc t, t{i liu thc nghim cho thy L thuyt gi| tr cci v{ Phng ph|p lch s ~ c lc l{ nhng phng ph|p tt nht

d b|o VaR. Phng ph|p tham s vi skewed and fat-taildistribution

cung cp kt qu y ha hn, c bit khi b qua gi nh rng t sut sinh

li(TTSL) chun ha c lp v{ ph}n phi ng dng v{ khi s thay i

thi gian c coi l{ Momen bc cao c iu kin. Cui cng mt s phn

m rng khng i xng ca phng ph|p Caviar cung cp kt qu cng y ha hn. Nh vy, mc tiu ca nghin cu l{ cung cp cho c|c

nh{ nghin cu ri ro t{i chnh vi tt c c|c m hnh v{ c|c ph|t trin

c xut c tnh VaR,a h n tm cao ca kin thc trong lnh

vc ny.

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1.Gii thiu

1.1.Sra i ca VaR

Trong hot ng ca Ng}n h{ng ngo{i c|c hot ng cn ti s lu ng ca

dng tin th Ng}n h{ng cng s phic mt lng d tr vn nht nh v

nhiu l do, do ph|p lut quy nh hoc vi c|c mc ch kh|c. Trong c|c mc

ch vic d tr mt lng vn khi c nhng bin c bt thng xy ra

chng hn nh vic kinh doanh gp mt khon l ln khi Ng}n h{ng phi

s dng s tin d tr gii quyt hu qu do bin c n{y g}y ra. Thc t,

trc nm 1988 ~ c nhiu ng}n h{ng sp do khng c lng vn d

tr cn thit chi tr cho kh|ch h{ng trong trng hp h phi chu nhng

khon l khng l do bin ng bt thng ca th trng.

Nm 1988, Basel I cn c gi l{ Basel Accord l{ mt tha thun t bi y

Ban Basel ca Ng}n h{ng gi|m s|t (BSBC) ~ khc phc tnh trng n{y. Basel I

cung cp c|c qui nh lin quan n tn dng ng}n h{ng, ri ro th trng v{

ri ro hot ng. Mc ch ca n l{ m bo rng c|c t chc t{i chnh duy

tr vn trn t{i khon |p ng c|c ngha v v{ i ph vi c|c khon l

bt ng.

Vy nh th n{o l{ ?

C}u hi n{y ch c th tr li khi ta |nh gi| c khon l ti a c th xy ra

khi gi| ca danh mc t{i sn gim trong mt thi k nht nh. Vy thc o

n{o cho khon l n{y ? chnh l{ VaR( Value at risk).

Nh vy, VaR i din cho khon l ti a nh{ u t c th mt i trong mt

thi k nht nh vi mt x|c sut nht nh.

1.2.Cc phng php u tin tnh VaR

Phng ph|p phng sai - hip phng sai, ( phng ph|p tham s)

Phng ph|p lch s( phng ph|p phi tham s)

Phng ph|p Monte Carlo ( phng ph|p b|n tham s)

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Tt c c|c phng ph|p n{y thng c gi l{ m hnh chun, c rt nhiu

thiu st, ~ dn n ph|t trin ca c|c phng ph|p mi.

Trong c|c phng ph|p tham s, m hnh u tin c lng VaR l{

Riskmetrics, ca Morgan(1996).

Trong khun kh phng ph|pphi tham s

Mt s phng ph|p c lng mt phi tham s ~ c thc hin,chng

~ ci thin c kt qu thu c t phng ph|p lch s

Trong khun kh ca phng ph|p b|n tham s, nhiu phng ph|p mi ~

c xut

Phng ph|p lch s ~ c lc, xut bi Barone-Adesi v{ cng s (1999)

Phng ph|p Caviar, xut bi Engle v{ Manganelli (2004)

C|c phng ph|p c iu kin v{ v iu kin da trn L thuyt gi| tr cc

tr.

Khi nim VaR

Gi| tr c ri ro VaR i in cho s tin ti thiu m{ nh{ u t c th

mt i trong mt khong thi gian nht nh vi mt x|c sut nht nh.

VD: VaR =5 triu vi x|c sut 5% c ngha l{ cng ty d kin l t nht 5

triu trong mt ng{y vi x|c sut 5%. Hay ta c th ph|t biu mt c|ch kh|c

l c kh nng x|c sut 95% khon l ca cng ty khng vt qu| 5 triu.

Vi c|ch hiu th 2 n{y VaR tr th{nh s tin ti a m{ nh{ u t c

th mt i trong mt khong thi gian nht nh vi mt x|c sut nht nh.

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2. M hnh VaR

2.1.Nhc li kin thc thng k

2.1.1.Hm phn phi xc sut

Nu X l{ bin ngu nhin lin tc th h{m ph}n phi x|c sut ca bin ngu

nhin X (k hiu l{ F(x)) c x|c nh bi cng thc sau:

F(x)= P(X

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F(-2)= P(X

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ChsZ cho ta bit c quan s|t m{ chng ta ang xt xt lch so vi

trung bnh ca n bao nhiu lch chun.

Gisti im X= tng ng vi Z=2 cho ta thy, ti }y binngu nhin X lch so vi trung bnh ca n

Vic chuyn X vchsZ nhm mc ch n gin ha tnh ton v so

snh cc dliu khng cng n vv Z khng c n v.

Mc ch n gin tnh ton l by githay v tnh tch phn tm ra xc sut th ta chcn tra trong bng Z: P(Z

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Hnh 1.1: Biu din thay i gi trti sn sau khong thi gian .l mt bin ngu nhin khi cng l{ mt bin ngu

nhin. Fk(x) l hm phn phi xc sut ca bin ngu nhin )(kV . Nu ta xem

xt P( )(kV x) = , vi 0 < < 1, th gi| trxgi l{ Phn vmc ca hm

phn bFk.

2.3.M hnh VaR

Hnh 1.2: thmt xc sut biu din mc phn v.

N

ti ngng gi tr}m n{y chnh l{ VaR. Nh vy VaR ca mt danhmc vi chu kk v{ tin cy (1- )100% l{ mc phn v ca hm phn b

Fk(x). Khi i lng n{y c k hiu l{ VaR(k, ) v{ mang gi| trm.

P( )(kV VaR(k, )) = .

P(X

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iu ny dn n hai nh ngha ca VaR trn.

nh ngha 1: VaR =2 vi xc sut 5%

S tin ti thiu m{ nh{ ut c th mt i l{ 2 triu trong mt khong thigian nht nh vi x|c sut 5%

nh ngha 2: VaR =2 vi xc sut 95%

S tin ti am{ nh{ ut c th mt i l{ 2 triu trong mt khong thi

gian nht nh vi x|c sut 95%.

2.4.Cc m hnh VaR trong thc hnh

Li sut danh mc trong chu kk c nh ngha l{: iu nysuy ra . Do tV l{ x|c nh trc nn tm VaR ca danh mcta chcn tnh VaR ca li sut tr .

Nh vy by githay v tm VaR ca bin ngu nhin ta i tmVaR ca bin ngu nhin r (TSSL ) sau nh}n ngc trli vi

ta sthu

c VaR ca

nh ngha 1 nh ngha 2

5%95%

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2.5.M hnh VaR cho TSSL

t ..l{ c|c bin ngu nhin i in cho TSSL. S dng F(r) biu th h{m ph}n phi tch ly c iu kin , F(r)= Pr |. Tc l{x|c sut bin ngu nhin nh hn gi| tr r vi iu kin mi thng tin vbin ngu nhin

~ c sn cho n thi im t-1. Bi v

tu}n theo mt

qu| trnh ngu nhin nn ta c: Cng thc n{y c suy ra tcng thc chun ha X = .By giv z v

thay i nn ta thm ui t.

l{ h{m ph}n phi chun ha (~ c gii thch trn)t+ + zt c h{m ph}n phi c iu kin G(z), G(z)=Pr |.

Nh ~ ni trn VaR ca TSSL chnh l{ ph}n v th ca h{m ph}n phi

x|c sut F(r). Ph}n v c tnh nh sau:

VaR()= = () (*)

r

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Din gii (*)

H{m nghch o (*) c hiu nh sau.

Ta c y=

=

Tng qut y= = c gi l yu tu v{o tnh y ( yu tu ra). Nh vy kh bityu tu ra y th yu tu vo s c bng c|ch invert ( dch l{ nghcho nhng n kh|c kh|i nim nghch o m{ chng ta hay gp)

* p dng v{o tnh VaR

Nh ta bit VaR() chnh l{ gi| tr r n{o m{ ti F( r) =P(

=

. Hay

= F(r) r = m r ny chnh bng VaR (

Tng t ta c= G(z) z = (*) cho ta thy tnh c VaR ta cn phi tm.

Hoc l

c lng nhng h{m n{y c|c phng ph|p sau sc sdng

(1) Phng ph|p phi tham s: Phng ph|p n{y tnh VaR bng cch tm

hm phn phi F( r ). N sdng phn phi thc nghim nh l{ mt hm xp

xca F(r)

(2) Phng ph|p b|n tham s:

(3) Phng ph|p tham s: Tnh ton VaR(bng cch sdng+ M hnh bin ng tnh + Hm mt tm G(z)

By gichng ta sln lt i tm hiu c|c phng ph|p n{y

Hm phn phi ca TSSL F(r)

Hm phn phi ca z chnh l G(z) v bin ng t

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3.Cc Phng php tnh VaR:

3.1.Phng php phi tham s

Gm 2 phng ph|p : Phng ph|p lch sv{ phng ph|p h{m mt phi

tham s

3.1.1.Phng php lch s

Cc bc tnh VaR ca phng php ny:

Bc 1. Tnh gi trhin ti ca danh mc u t

Bc 2. Tng hp tt ccc tsut sinh li qu khca danh mc u

t n{y theo tng hsri ro (gi trcphiu, tgi hi o|i, tlli sut...)Bc 3. Xp cc tsut sinh li theo thttthp nht n cao nht

Bc 4. Tnh VaR theo tin cy v sliu tsut sinh li qu kh.

Phng ph|p a ra gi thuyt rng s phn b t sut sinh li trong qu

kh c th ti din trong tng lainn n s dng d liu TSSL trong qu

khc tnh VaR v n ngh qu| khslp li.

u v nhc im ca phng php lch s

u im Nhc im

Dtnh ton

Khng phthuc vo ginh

phn phi ca TSSL

C thnm bt c phn phi cui rng v{ nh nhn

Phthuc hon ton vo bd

liu. (Nu bdliu ly trong

thi k bin ng mnh VaR s

c c lng qu| cao v{ ngcli)

Chtnh c nhng khon tin

cy ri rc

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3.1.2.Phng php mt phi tham s.

Phng ph|p n{y sdng hm mt phi tham skhc phc c mt

im yu ca phng ph|p lch s: l chtnh VaR ti nhng khong tin cy

ri rc.

Hm mt phi tham sc vra bng cch ni c|c im gia ti nh ca

cc ct ca histogram

Khi c c hm mt ta dd{ng tnh c VaR khi cho c tin cy. (

~ trnh b{y trn)

Mt hm mt phi tham sphbin l hm mt kernel (Kernel density

estimation)

kernel l mt phng ph|p c lng phi tham shm mt xc sut ca

mt bin ngu nhin tmu gi trca bin. Gischng ta c mt mu {X ,

,X 1 n } cc gi trca bin ngu nhin X , khi c lng thc nghim ca

hm mt xc sut c vit nh sau:

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Trong K l{ h{m kernel, h l{ chiu rng ca h{m kernel. Nh vy, im

quan trng ca phng ph|p n{y l{ vic chn hm kernel K v chiu rng h .

Mt shm kernel thng dng v brng c trnh by trong bng sau.

V dnh ta c 5 im dliu c vtrn histogram nh sau

Thay v dng histogram m ta d liu, ta l{m trn d liu bng cc s

dng phng ph|p kernel.

im d

liu

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Tc|c im dliu ngi ta sdng mt trong c|c h{m kernel ~ cho trn

vra mt phn phi lan ta ra tmi im dliu vi chiu rng h thch

hp.

Nu sdng h{m Gausian Kernel ta c c|c trng hp sau.

Hnh 1

Gaussine

Kernel

Chiu rng h

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Hnh 1 Sdng chiu rng h va phi nn dliu c l{m trn tng i

p v phn nh y phn phi ca dliu.Hnh 2 S dng h nh nn hm mt tr nn phc tp c gi l

undersmoothed tc l lm dliu cha c trn nhiu

Hnh 3 Sdng h qu ln nn hm mt qu| trn, khng phn |nh c

y phn phi dliu.

V vy vic chn chiu rng h rt quan trng v n phn |nh c mc lm

trn giliu. Nu h nh, th vic l{m trn cha hiu quv phn phi cn qurc ri , kh nm bt c. Nu h qu ln th d liu btr ha qu| nhiu,

khng phn |nh c bn cht phn phi ca c|c im dliu.

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3.2.Phng php tham s

Phng ph|p tham s o lng ri ro bng vic s dng ng cong x|c sut

cho b d liu v{ t suy ra VaR. Trong s c|c phng ph|p tham s , m

hnh u tin c tnh VaR l Riskmetrics ca Morgan (1996). M hnh ny

ginh rng cc TSSL ca danh mc u t tu}n theo ph}n phi chun. Theo

githuyt ny, VAR ca mt danh mc u t ti tin cy 1- % c tnhton bng:

VaR(

Trong l{ im phn vthca ph}n phi chun ha v{ l{ lch chun c iu kin ca TSSL danh mc u t.

c lng , Morgan s dng mt m hnh trung bnh di ng c trng sly tha ( EWMA). S trnh b{y ca m hnh n{y nh sau:

Nhng hn ch chnh ca Riskmetrics lin quan n c|c gi nh TSSL

tu}n theo ph}n phi chun. Bng chng thc nghim cho thy, TSSL khng

tu}n theo ph}n phi chun. C|c h s lch trong hu ht c|c trng hp

u }m v{ c ngha thng k, ng rng s ph}n b TSSL l{ lch sang bn

tr|i. Kt qu n{y khng l{ ph hp vi tnh cht ca mt ph}n phi chun, i

xng. Ngo{i ra, ph}n phi thc nghim v TSSL ~ c ghi nhn th hin

nhn qu| mc (ui v{ nh) (xem Bollerslev, 1987). Do , qui m ca

c|c khon l thc t l{ cao hn nhiu so vi d o|n ca mt ph}n phi

chun.

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Hn ch th hai ca Riskmetrics lin quan n m hnh c s dng

c tnh s bin ng c iu kin ca TSSL. M hnh EWMA nm bt mt s

c tnh phi tuyn ca s bin ng, nhng khng xem xt tnh bt i xng

v{ hiu ng n by (xem Black, 1976; Pagan v{ Schwert, 1990). Ngo{i ra, m

hnh ny c k thut km hn so vi c|c m hnh GARCH trong vic m hnh

ha s tn ti ca bin ng.

Hn ch th ba ca phng ph|p tham s truyn thng lin quan n gi

thit li nhun c lp v{ c ph}n phi ng dng(iid). C bng chng thc

nghim quan trng rng vic ph}n phi chun ca TSSL khng phi l{ c lp

v{ ng dng (xem Hansen, 1994; Harvey v Siddique, 1999; Jondeau v

Rockinger nm 2003; Bali v{Weinbaum, 2007; Brooks v{ cng s, 2005.).

Vi nhng hn ch ca phng ph|p nghin cu tham s ~ c thc hin

nhiu hng kh|c nhau. B{i nghin cu ~ a ra nhng hng i ng n

phn n{o khc phc nhng nhc im ca Riskmetrics.

u tin, tm kim mt m hnh bin ng phc tp hn nm bt c

c im quan s|t trong s bin ng ca TSSL . }y, ba h ca c|c m hnh

bin ng ~ c xem xt: (i) GARCH, (ii) bin ng ngu nhin v{ (iii) bin

ng thy r.

Th hai l{ iu tra h{m mt kh|c thy dc lch v{ nhn ca

TSSL.

Cui cng, hng th ba ca nghin cu cho rng c|c moment c iu

kin bc cao bin i theo thi gian.

3.2.1.M hnh bin ng (Volatility model): M hnh bin ng c a ra trong c|c t{i liu nhm nm bt nhng c

im ca TSSL c thc chia ra thnh 3 nhm: hGARCH, m hnh bin

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ng ngu nhin (stochastic volatility models) v m hnh bin ng nhn

r (realised volatility based models).

HGARCH

i vi hGARCH, Engle (1982) ~ a ra m hnh ARCH ( Autoregressive

Conditional Heteroskedasticity) c trng cho mt phng sai thay i

theo thi gian.

Bollerslev (1986) hn na ~ mrng m hnh bng vic thm vo m hnhARCH tng qut (GARCH). M hnh ny chr v{ c lng 2 phng trnh:

phng trnh u tin m t s pht trin ca tsut sinh li theo t sut

sinh li qu kh. Phng trnh hai m t s tin trin v bin ng ca t

sut sinh li (lch chun khng chphthuc vo nhiu trong qu khm

cn phthuc v{o lch chun trong qu kh). Cng thc tng qut ca m

hnh GARCH l{ m hnh GARCH (p,q) c i din bi biu thc sau:

Trong : : bnh phng nhiu : bnh phng lch chun trong qu kh

Hu ht cc nh nghin cu nghdng GARCH (1,1) c lng m hnh v

chng ph hp v tt nht i vi chui thi gian ti chnh. C dng nh sau:

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Mt sm hnh mrng ca hGARCH:

M hnh IGARCH ca Engle v{ Bollerslev (1986) thm iu kin =1trong phng trnh trn. Nhng c tnh phng sai c iu kin ca m

hnh IGARCH khng hp dn ng tquan im thc nghim do s loi b

rt chm nh hng ca c sc ln phng sai c iu kin .

M hnh FIGARCHa ra bi Baillie v cc cng s(1996): dng n gin

nht FIGARCH (1,d,0):

Nu cc tham s tu}n theo iu kin , phng sai ciu kin ca m hnh dng cho tt cc|c trng hp t. Vi m hnh ny, c

khnng l{ t|c ng ca ln sgy ra ssuy gim i vi tlnghyperbolic g khi k tng ln.

* C|c m hnh trc }y ~ c cp l khng hon ton phn nh bn

cht ca sbin ng chui thi gian t{i chnh. B chng khng ch n kt

qubt i xng ca li nhun trc v sau cc c shock tiu cc v tch cc

xy ra ( t|c ng n by). V c|c m hnh trc phthuc vo cc sai sbnh

phng ( )nn t|c ng gy ra bi nhng c shock tch cc ging vi tcng sinh ra bi nhng c shock tiu cc .Tuy nhin, thc tcho thy rng

trong chui thi gian ti chnh, c stn ti ca t|c ng n by, iu ny c

ngha l{ sbin ng tng cao bi nhng c shock tiu cc hn l{ c shock

tch cc. nm bt t|c ng n by, mt vi cng thc GARCH phi tuyn

c a ra. Trong bng 1, chng ti trnh by mt s cng thc ph bin

nht.

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M hnh EGARCH

( ) ||

:nhng c sc tiu cc trong qu khc t|c ng ln sbin ng c iukin ()mnh hn nhng c sc tch cc. Do , chng ti cho rng tham sm ( ).. : Sbin ng lin tc c

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Sbin ng tsut sinh li cng phthuc v{o quy m thng tin mi. Nudng, nhng thng tin mi tt hn trung bnh c t|c ng mnh hn tibin ng hin ti mnh hn nhng thng tin xu

M hnh n{y ~ xem xt t|c ng n by i vi sbin ng ca TSSL.

H{m Log m bo cho hsphng sai khng }m.

M hnh FIE-GARCH

Cui cng, nn c 1 m hnh nm bt c t|c ng n by v t|c ng tr

nh d{i., Bollerslev v{ Mikkelsen (1996) ~ thm v{o m hnh FIE -GARCH,nhm gii thch cho c t|c ng n by (EGARCH) v{ t|c ng tr nhdi

(FIGARCH). Phng trnh n gin nht ca h m hnh ny chnh l

FIEGARCH (1,d,0):

Mt s ng dng ca hcc m hnh GARCH trong ti liu VAR c thc

tm thy trong nhng bi nghin cu sau }y: Abad v{ Benito (2013), Sener

v cc cng s(2012), Chen v cc cng s(2009, 2011), Sajjad v cc cng

s(2008), Bali v Theodossiou (2007), Angelidis v cc cng s(2007), Haas

v cc cng s (2004), Li v Lin (2004), Cavalho v cc cng s (2006),

Gonzalez Rivera v cc cng s (2004) Giot v Lauren (2004), mittnik v

Paolella (2000...

Mc d khng c bng chng vmt m hnh tt nht nhng c|ckt qu

t c trong cc bi nghin cu n{y dng nh ch ra rng cc m hnh

GARCH bt i xng to ra nhiu kt qutt hn.

M hnh bin ng ngu nhin (SV)

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M hnh thay thcho c|c m hnh GARCH i din cho nhng thay i tm

thi i vi sbin ng l thng qua m hnh bin ng ngu nhin (SV) m

Taylor( 1982, 1986) a ra. }y, sbin ng trong t khng phthuc vo

nhng quan st trong qu khm phthuc vo mt bin skhng thquan

s|t c, thng l mt qu trnh thi quy ngu nhin. m bo phng

sai dng, phng trnh s bin ng c nh ngha theo logarit ca

phng sai.

M hnh m phng bin ng m{ Taylor (1982) a ra c th c vit nh

sau:

Trong i din cho trung bnh c iu kin ca tsut sinh li, idin cho phng sai c iu kin, v v l nhng qu trnh nhiu trng.

M hnh bin ng nhn r (RV)

Merton (1980) ~ tng cp ti khi nim ny, bng cch thm vo N li tc bnh

phng trong ni bhng ngy so vi mt khong thi gian t, do h{m rng

vic thm vo li tc bnh phng c th c dng c lng phng sai.

Taylor v Xu (1997) chra rng bin ng nhn r hng ngy c thc thc hin

bng cch thm li tc ni bhng ngy. Gisrng mt ng{y c chia ra thnh

N khong thi gian bng nhau v nu i din cho li tc ni bhng ngy cakhong thi gian i ca ngy t, bin ng hng ngy ca ngy t c thc biu dinnh sau:

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Andersen v cc cng s(2001a,b) ng rng phng ph|p o lng ny s

ci thin |ng k nhng d bo so vi nhng phng ph|p chun ch da

trn dliu hng ngy.

Cc kt quthc nghim ca m hnh bin ng trong VaR

Chen v cc cng s(2011)

Abad v benito (2013)

Niguez (2008)

Alonso v Arcos (2006)

Gonzalez-Rivera v cng s(2004)Huang v Lin (2004)

m hnh EWMA dbo VaR tnht

Fleming v Kirby (2003)) GARCH v{ SV u cho nhng kt qu

VaR ss c

Lehar v cng s(2002) Khng c skhc bit GARCH v SV

Chen v cng s(2011) SV v EWMA dbo tnht

Gonzalez-rivera v cng s(2004) SV dbo VaR tt nht

Ni chung, vi mt vi ngoi l, bng chng chra rng m hnh SV khng

ci thin kt qut c tm hnh hGARCH

Brownlees v Gallo (2011) m hnh RV tt hn m hnh

EWMA v GARCH

Giot v Laurent (2004) Phn phi chun: m hnh RV tt nht.

Phn phi t-student lch, m hnh

GARCH bt i xng v RV cung cp

kt quging nhau.

Mc d bng chng n{y hi m h, m hnh GARCH bt cn xng c v

nh cung cp c lng VaR tt hn m hnh GARCH c}n xng

Chen v cng s(2011). ginh phn phi chkhng phi

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m hnh bin ng mi l nhn tthc

quan trng trong vic c tnh VaR.

3.2.2.Hm smt

Nh ~ c cp t trc, phn phi thc nghim ca TSSL ~ c

chng minh l bt cn xng v th hin mt nhn qu mc (fat tail v

peakness). Do , gisrng mt phn phi chun vqun trri ro v{ c

trng cho vic c lng VaR ca mt danh mc khng to ra kt qutt v

thua lsnhiu hn.

V phn phi t-Student c phn ui rng hn ph}n phi chun. Bng chng

thc nghim ca kt quphn phi n{y trong c lng VaR rt m h.

Mt snghin cu chra rng phn phi t-Student thhin tt hn phn

phi chun (xem Abadv Benito, 2013; Polanski v Stoja, 2010; Alonso v

Arcos, 2006;So v Yu, 2006).

Phn phi t-Student nh gi qu cao tlnhng trng hp ngoi l.

(Angelidis v cng s. (2007), Guermat v Harris (2002), Billio v Pelizzon

(2000),v Angelidis v Benos (2004)).

Phn phi t-Student c thgii thch tt cho nhn qu mcc tm thy

phbin trong TSSL, nhng ph}n phi ny khng nm bt c s bt cn

xngca TSSL. Mt nh hng cho vic nghin cu trong qun trri ro linquan ti tm kim nhng hm phn phi khc m nm bt nhng c im

ny. Trong ni dung ca hphng ph|p VaR, mt shm mt c xem

xt. ( bng 2)

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Cc kt quthc nghim ca m hnh bin ng trong VaR

Cheng v Hung (2011) SS khnng dbo VaR ca phn

phi chun, t-Student, SSD, GED.=> phn phi SSD v GED cung cp

nhng kt qutt nht

Polanski v Stoja (2010) SS phn phi chun, t-Student, SGT v

EGB2

=> SGT, EGB2 c lng VaR chnh xc.

Bali v Theodossiou (2007) SS phn phi chun vi phn phi SGT.=> SGT cung cp c lng VaR chnh xc

hn.

c lng VaR t c di phn phi lch v phn phi fat-tail cung cp

mt VaR chnh xc hn nhng ci t c tphn phi chun v t-Student.

Hansen (1994)Zhangv Cheng (2005)

Haas (2009)

Ausn v Galeano (2007)

Xu vWirjanto (2010)

Kuester v cng s(2006)

Hn hp phn phi chun, t-Student hayGED cung cp c lng VaR tt hn ph}n

phi chun hoc t-Student.

c lng VaR t c vi mt hn hp cc phn phi chun (v phnphi t-student) nhn chung kh chnh xc.

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3.2.3.Nhng moment bc cao c iu kin thay i theo thi

gian:

Cch tip cn tham struyn thng cho VaR c iu kin ginh rng TSSL

c phn phi c chun ha bi trung bnh c iu kin v{ lch chun c

iu kin l iid. Tuy nhin , c bng chng thc nghim quan trng rng s

phn bTSSL c chun ha bi trung bnh c iu kin v{ lch chun

khng phi l iid.

V vy, mt snghin cu ~ ph|t trin mt phng ph|p mi tnh ton

Var c iu kin. Phng ph|p mi ny cho rng moment c iu kin bccao th thay i theo thi gian.

Bali v cng s(2008) M hnh SGT vi nhng tham sbin i theothi gian. Chng cho php nhng moment ciu kin bc cao ca hm mt SGT phthuc vo nhng bthng tin trong qu khvv vy ni lng cc ginh trong tnh ton Varc iu kin rng phn phi ca li nhun ctiu chun ha l(iid).

Hansen (1994) vJondeau v Rockinger(2003)

Lp m hnh nhng tham smoment bccao c iu kin ca SGT nh l{ mt qu trnhthi quy. c lng hp l cc i (MLE) chra nhng bin ng c iu kin theo bin itheo thi gian, hsbt i xng, bd{y ui,cc thng snhn ca ttrng SGT th c ngha thng k.

M hnh SGT-GARCH vi hsbt ixng v{ nhn thay i theo thi gian cungcp mt sph hp hn m hnh SGT-GARCHc hsbt i xng v{ nhn khng i.

Ergun v Jun (2010) Phn phi SSD c hslch thay i theothi gian. Nhng m hnh da trn GARCH xemxt hsbt i xng v{ nhn c iu kincung cp mt c tnh VaR chnh xc.

Polanski v Stoja (2010) GCE ginh phn phi chun ha i vi 4moment u tin thay i theo thi gian.

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Phng ph|p n{y cung cp mt cng clinhhot i vi vic lp m hnh phn phi thcnghim ca dliu ti chnh, bn cnh sbinng n cn biu din hsbt i xng thay

i theo thi gian, nhn vt chun(t riro). Phng ph|p n{y cung cp mt c tnhvng v chnh xc ca VaR.

Tt ccc nghin cu c cp trc }y, ~ so s|nh c tnh VaR c

ginh l phn phi blch v{ c ui ln vi cc thng sc nhn v{

lch l{ khng i. Hpht hin rng chnh xc ca c tnh VaR c cithin khi nhng thng sc nhn v bt i xng thay i theo thi gian

c xem xt. Nhng nghin cu cho rng trong khun khca phng ph|p

tham s, nhng k thut m lp m hnh hiu qu bin ng ca nhng

moment bc cao c iu kin (bt i xng v{ nhn) cung cp kt qutt

hn so vi nhng moment bc cao khng i.

3.3.Phng php bn tham s

Phng ph|p b|n tham s kt hp gia phng ph|p tham s v{ phng

php phi tham s. Phng ph|p b|n tham squan trng nht l m phng

lch sc trng sbin i, v m phng lch sc lc (FSH), phng ph|p

CaViaR v{ phng ph|p da trn l thuyt gi trcc tr.

3.3.1.Phng php lch sc trng sbin ng (L do chn phng phpPhng ph|p m phng lch struyn thng khng xem xt nhng bin ng

gn }y khi tnh to|n. V vy, Hull v{ White (1998) ~ xut mt phng

php mi bao gm nhng u im ca phng ph|p m phng lch s c

trng si vi m hnh bin ng. tng c bn ca phng ph|p n{y l{

cp nht nhng thng tin tsut sinh li xem xt nhng thay i gn }y

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v tnh bin ng bng c|ch iu chnh d liu lch si vi mi bin th

trng phn nh skhc bit gia cc bin ng lch sso vi bin ng

hin ti ca cc bin thtrng, vic sdng dliu h{ng ng{y trong 9 nm

12 tgi hi v 5 chschng khon vi phng ph|p lch scho thy c s

ci tin |ng k.

Ni dung

Chng ti xem xt mt danh mc u t phthuc vo mt sbin thtrng

v cho rng phng sai ca mi bin th trng trong giai on bao gm

trong d liu lch s c theo di bng cch s dng hoc l m hnhGARCH hoc EWMA. Chng ti quan t}m n c tnh VaR cho danh mc u

t v{o cui ngy N-1 (tc l, cho ngy N).

t rt,il tsut sinh li qu kh ca ti sn i vo ngy tht trong mu qu

khca chng ta (hay phn trm thay i lch strong bin i vo ngy t ca

thi kbao gm trong mu lch s(t

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Cch tip cn n{y (c gi tt l HW) l mt phn mrng dhiu ca m

phng lch struyn thng (c gi tt l HS). Thay v sdng phn trm

thay i lch sthc ttrong cc bin thtrng cho mc ch tnh to|n VaR,

chng ti sdng nhng thay i lch s~ c iu chnh phn nh t

lbin ng hng ngy ti thi im quan st. Gis20 ng{y trc sthay

i t lquan st trong mt bin th trng l 1,6% v s bin ng hng

ng{y c c tnh l 1%. Nu sbin ng hng ngy by gic c tnh

l 1,5%, phn trm thay i mu tnh tquan s|t 20 ng{y trc l 2,4%.

Kt qu

Phng ph|p n{y xem xt mt cch trc tip sthay i bin ng, trong khi

phng php m phng lch sbqua chng. Hn na, phng ph|p n{y to

ra mt c tnh ri ro ci m nhy cm mt cch thch hp vi nhng c

tnh sbin ng hin ti. Nhng bng chng thc nghim c to bi Hull

v{ White (1998) ~ chra rng phng ph|p n{y to ra mt c tnh VaR tt

hn phng ph|p m phng lch s.

3.3.2.Phng php m phng lch slc (FSH)

L do la chn

Phng ph|p m phng lch slc (FSH) c xut bi Barone Adesi v

cng s(1999) bng vic sdng m hnh GARCH m hnh ha phn phi

tng lai ca gi tr ti sn v gi tr ho|n i. Phng ph|p n{y kt hpnhng u im ca phng ph|p m phng lch svi mnh v tnh linh

hot ca m hnh bin ng c iu kin. Sthay i gi ca cc quyn chn

c tnh bng c|ch |nh gi li y vmc thay i ca ti sn c bn.

Phng ph|p n{y ngm xem xt mi tng quan ca cc ti sn m khng

hn ch gi tr ca chng theo thi gian hoc tnh ton chng mt cch r

rng. Gi tr VaR cho danh mc u t chng khon phi sinh c c m

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khng cn stng ln tuyn tnh ca chng. Phng ph|p lch sgn xc sut

bng nhau cho cc tsut sinh li trong qu kh, bqua c|c iu kin ca th

trng hin ti. Phng ph|p FHS l{ mt phng ph|p s{ng lc li phng

php lch s.

Ni dung

Gischng ta sdng m phng lch slc c tnh VaR ca danh mc

ti sn gin n vi n vthi gian l 1 ngy. Vmt thc hin phng ph|p

n{y, u tin l lm cho m hnh bin ng c iu kin ph hp vi dliu

tsut sinh li m ta c. Barone-Adesi v cng s(1999) ~ xut m hnhGARCH bt i xng. Tsut sinh li c cng bsau c tiu chun

ha bng cch chia mi t sut sinh li ng vi mi bin ng tng ng

zt=t/t. Nhng tsut sinh li c chun ha ny cn phi c lp v{ c

phn phi mt c|ch ng nht v{ do ph hp vi phng ph|p lch sm

phng. Bc th3, bao gm vic khi ng mt lng ln hnh mu tbd

liu mu ca tsut sinh li ~ c chun ha.

Gismt thi gian nm giVaR l 1 ng{y, giai on th3 bao gm vic rt

ra c chn lc bdliu ca cc tsut sinh li ~ c chun ha: chng ta

ly mt lng ln s liu t b d liu, m{ chng ta xem nh l{ mt mu,

thay thmi c|i sau khi n c rt ra v nhn vi mi ln rt mt cch ngu

nhin bng sdbo tnh bin ng ca n 1 ngy tip theo:

Vi z* l tsut sinh li chun ha c m phng. Nu chng ta ly M mu

ra, chng ta c c 1 mu ca M t sut sinh li c m phng. Vi

phng ph|p n{y, VaR() l phn v % ca mu t sut sinh li c m

phng.

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Nhng bng chng thc nghim gn }y chra rng phng ph|p n{y hot

ng tng i tt trong vic c lng VaR

Kt lun

Phng ph|p lch slc dn n mt |nh gi| nhanh chng ca VaR. l{ c

thbi v n i hi mt m phng lch sn gin c kch hot mi

ngy thng qua mt b lc chui thi gian nh sn. S lng cc tnh ton

tng tuyn tnh vi s lng ti sn. tin cy ca |nh gi| ph thuc vo

cht lng ca cc blc c sdng trong phn tch chui thi gian. Mt

blc tt hn l{ theo nh ngha dn n mt |nh gi| tt hn vri ro.

3.3.3.M hnh CAViaR ( Conditional autoregression Value at

risk)

L do sdng:

Stht thc nghim cho thy rng sbin ng ca nhm tsut sinh li th

trng chng khon qua thi gian c thgii thch bng nh lng (phng

sai hay lch chun) m phn phi ca chng bttng quan. Kt qul ,

VaR do lin kt cht chvi phn phi ca s bin ng ny phi th hin

h{nh vi tng t, c ngha l{ b t tng quan. V vy, Engle v Manganelli

(2004) ~ xut mt k thut nhm chnh thc ha c trng t tng

quan ny trong vic tnh VaR gi l CAViaR - m hnh VaR thi quy c iukin (Conditional Autogression Value at Risk). Phng ph|p n{y da trn

c lng phn v, thay v lp m hnh cho ton bphn phi hxut lp

m hnh trc tip cc phn v.

Ni dung:

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t l vecto chtsut sinh li t{i chnh c quan st ti thi im t v l mt vecto p ca nhng tham scha bit. t ( ) lphn v

ca phn phi ca t sut sinh li danh mc c hnh thnh ti

thi im t-1, m ti t|c gixa chsdi ca thun tin vmtk hiu.M hnh CAViaR tng qu|t nh sau:

Trong :

l{ kch thc ca (s lng tham s trong m hnh); lmt hm ca 1 s hu hn cc gi tr quan s|t c tr. Mc t hi

quy, vi = 1q m bo rng cc phn vthay i trn trutheo thi gian. Vai tr ca

(

) l{ lin kt

) vi cc bin quan st

nm trong bthng tin. Mt sla chn tnhin cho l tsut sinh lic tr. Mt thun li ca phng ph|p n{y l{ n khng c gi nh phnphi cthi vi tsut sinh li ca ti sn. Hcho rng trnh tu tin l

cho sdng trong thc tin:

Trong khun khm hnh CAViaR, 3 m hnh thi quy sau c thc xemxt thay th:

- Gi trtuyt i i xng - SAV ( symetric absolute value):

- GARCH(1,1) gin tip (Indirect GARCH(1,1)):

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Trong hai m hnh trn, t|c ng ca tsut sinh li v{ phng sai ln thc

o VaR c m hnh ha mt c|ch i xng. dhnh dung, ta quan s|t

thsau: (vi trc honh l tsut sinh li , trc tung l )

a) SAV b)INDIRECT GARCH(1,1)

gii thch cho s bt i xng trn th trng ti chnh, thng qua hiu

ng n by (Black, 1976), m hnh SAV ~ c Engle v Manganelli (2004)

mrng th{nh m hnh dc bt i xng AS (Asymetric slope):

Trong ,

v

c sdng nh nhng

hm s.

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c) AS

Nhng tham strong m hnh sc c lng bng phng ph|p hiquy phn vnh c gii thiu trong Koenker v Basset (1978). Hcho thy

lm thn{o mrng khi nim mt mu phn vthnh mt m hnh hi

quy tuyn tnh.

L do tc gisdng Phng php hi quy phn vthay v OLS c

lng cc tham s?

Hi quy phn vc thgii quyt cc vn vn l{ nhc im khi p dng

OLS trn thc t:

(i) Thng thnh phn sai skhng phi l{ khng i trn ton bphn bvth~ vi phm tin vtnh thun nht ca OLS (tin nh sau: phng

sai ca thnh phn sai sl cnh)

(ii) OLS thng qua vic coi gi tr trung bnh l{ o vv tr, thng tin v

ui ca phn bbmt i.

(iii) OLS rt nhy cm vi cc gi trngoi lai c thlm sai lch kt qu|ngk.

(iv) Trong m hnh CAViaR c tn ti t tng quan gia cc bin, nn vi

phm githit ca OLS l khng c sttng quan gia cc bin.

Thun li:

-

Khng to ra nhng ginh phn phi cthtrn TSSL ca ti sn.

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- Nm bt c nhng c trng phi tuyn ca TSSL ti chnh

Bt li:

-

Kh thc hin

Mt snghin cu mrng ca m hnh CAViaR:

nm bt c tc dng n by v{ c|c c tnh phi tuyn khc ca tsut

sinh li ti chnh, mt smrng ca m hnh CAViaR ~ c xut:

Tc gi Ni dung nghin cu

Yu v cng s(2010) M rng m hnh CAViaR tnh n c m hnhThreshold GARCH (TGARCH) (mt m rng ca

m hnh ngng kp ARCH (double threshold

ARCH) (vit tt l DTARCH ca Li vLi (1996)) v

mt hn hp (mt mrng ca hn hp ARCH ca

Wong v Li (2001)).

Chen v cc cng s(2011)

xut mt hphn vphi tuyn nh mt phn mrng tnhin ca m hnh AS.

Bao v cng s(2006)

Polanski v Stoja

(2009)

Nhn nh m hnh CAViaR c xut bi Engle

v Manganelli (2004) tht bi trong vic cho ra

mt c tnh VaR chnh xc mc d n c thcho ra

1 c tnh VaR chnh xc trn 1 thi k n nh

Gerlach v cng s(2011)

Yu v cng s(2010)

xut m rng CAViaR ~ hot ng tt hntrong vic c tnh VaR. Nh trong trng hp i

vi phng ph|p tham s, khi dng 1 phin bn

bt i xng ca m hnh CAViaR, c tnh VaR c

bit c ci thin.

Sener v cng s

(2012)

Trong mt vi s so snh vi mt s m hnh

CAViaR (i xng v bt i xng), h pht hin

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3.3.4.L thuyt gi trcc tr(Extreme value theory EVT)

L do sdng:

L thuyt gi tr cc tr (EVT) hay cn gi l l thuyt cc bin c him, l

nhng bin ct xy ra nhng khi xy ra th gy thit hi rt ln. Nhng bin

cn{y thng tp trung phn ui ca phn phi v{ khng c thhin

r r{ng trn th.

C|c phng ph|p tham s v phi tham s truyn thng hot ng rt tt

trong nhng khu vc phn phi thc nghim m ti c rt nhiu quan st

dthy, nhng chng li hot ng rt km ti khu vc phn phi phn ui

cc tr. }y r r{ng l{ mt bt li bi v vic qun trnhng ri ro cc tri

hi phi c lng cc phn vv xc sut ui m{ thng khng thquan

st trc tip td liu. gii quyt vn n{y, EVT ra i tp trung vo

vic m hnh ha phn ui ca phn phi thua l bng vic ch s dng

nhng gi trcc trthay v sdng ton b tp d liu. Ngoi ra, EVT cn

cung cp mt c lng tham sca phn phi ui, iu n{y cho php a

ra mt vi suy lun ngoi tp dliu.

Ni dung:

rng m hnh bt i xng tt hn so vi kt qut

m hnh CAViaR chun.

Gerlach v cng s

(2011)

So snh 3 m hnh CAViaR (SAV, AS v Threshold

CAViaR) vi pp tham s m s dng m hnh h

GARCH bin ng khc nhau (GARCH-Normal,

GARCH-Studentt,GJR-GARCH, IGARCH, Riskmetric).

tin cy 1%, m hnh Threshold CAViaR th

hin tt hn bt cm hnh no khc.

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EVT tp trung vo phn phi gii hn tsut sinh li cc trc quan st

trong mt thi k di, m chyu phthuc vo sphn bca chnh tsut

sinh li . Hai m hnh chnh ca EVT l:

(1)M hnh cc i khi Block maxima model (BMM) c pht trin bi

MC Neil, 1998

(2)nh vt ngng Peak over threshold (POT)

M hnh th 2 c cho l hu ch nht trong ng dng thc tin v n s

dng d liu ti cc gi trcc trhiu quhn. Trong m hnh POT, c hai

loi phn tch:

M hnh bn tham sc xy dng xung quanh c lng Hill (Beirlant v

cng s 1996; Danielsson v cng s 1998)(Semi-parametric models built

around the Hillestimator)

M hnh tham shon ton da trn phn phi Pareto tng qut (Embrechts

v cng s 1999). (the fully Parametric models based on theGeneralisedPareto distribution )

Trong phn tip theo, tng m hnh sc m t.

3.3.4.1.M hnh cc i khi BMM

1

3

2

4

2X

5X

7X

11X

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Phng ph|p n{y bao gm vic tch cc phm vi vthi gian thnh cc khi

hay cc phn bng nhau, c tnh n gi trti a trong tng thi k. Nhng

quan st c gi tr ti a c chn n{y hnh th{nh nn trng hp cc tr,

cn c gi l 1 cc i khi. Khi nim c bn ca BMM cho thy lm th

n{o la chn chnh x|c di ca thi k, n, v cc khi dliu trong thi

k . i vi cc gi tr n ln, BMM cung cp mt chui cc cc i khi m c thc iu chnh bng phn phi tng qut ca gi trcc tr(GEV). Khon thua lcc i trong mt nhm gm n dliu c nh

ngha l{

= max (

,

).

i vi mt nhm quan st c phn phi ng nht, hm phn phi cac trnh b{y nh sau:

Trong thc t, do khng c mt m tchnh xc hon ton phn phi ca

nn cc tc gi ~ s dng nh l Fisher v{ Tippet m t gn ng cho

phn phi n{y. Phng ph|p tim cn i vi da trn gi trcc ichun ha c dng nh sau:

Trong v ln lt l tham svtr (v dnh median, mean, mode)v tham squy m (variance). nh l Fisher v{ Tippet x|c nh rng nu hi t ti mt phn phi khng b suy bin khi n tin ti v cng (c tv

mu khng ng thi bng 0) th phn phi ny l phn phi GEV.

Biu thc i scho phn phi GEV nh sau:

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Trong : > 0, - <

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Trong hu ht c|c trng hp, cc khi c la chn theo cch m chiu

di ca chng ph hp vi mt khong thi gian trong nm v{ n l{ squan

st trong khong thi gian . Phng ph|p n{y c s dng ph bin

trong cc ng dng vthy vn v{ kthut nhng khng thch hp lm cho

chui thi gian ti chnh do bi hin tng gp nhm xut hin rt nhiu

trong tsut sinh li ti chnh.

3.3.4.2.M hnh nh vt ngng (Peaks over threshold

model) (POT)Mt phng ph|p kh|c l{ m hnh POT, m hnh n{y ph}n tch c|c gi| tr

vt mt ngng cao cho sn. M hnh POT thng c xem l hu ch nht

trong ng dng thc tin v n sdng dliu ti cc gi trcc trhiu qu

hn. Trong m hnh n{y bao gm 2 loi phn tch:

M hnh tham shon ton da trn phn phi Pareto tng qut (GPD)

M hnh bn tham sc xy dng xung quanh c lng Hill.

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a.Phng php phn phi Pareto tng qut (GPD)

Trong scc bin ngu nhin i din cho TSSL ti chnh (r1, r2, r3, , rn), tc

gichn mt ngng u thp v kim tra tt cgi tr(y) vt qu u: (y1, y2,

y3,, yNu), trong yi=ri -u v l sdliu mu ln hn u. Sphn bcaphn thua ld ra vt ngng u(chnh l phn bca y) c nh ngha

l:

Trong : l phn b ca phn thua l d ra vt ngng u v

Gi s, cho mt gi tr c nh, phn b ca phn thua l d ra vtngng l mt phn phi Pareto tng qut: [ ]

Thai hm trn, ta c hm phn phi ca tsut sinh li nh sau:

4

5

u

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Nhn vo m hnh (22), ta thy xy dng mt c lng phn ui ca

biu thc ny, yu tbsung duy nht m chng ta cn l{ c lng l{m c iu , t|c gily mt cng thc thc nghim hin nhin sau:

(n-Nu)/n, sau hsdng phng ph|p m phng lch s. Sau khi c c

lng bng phng ph|p m phng lch sv{ t , ta c clng ui nh sau:

[ ]

Vi mt xc sut cho trc , c lng VaR c tnh ton bngcch nghch o c lng hm phn phi ui nh sau: [ ]

C|c phng ph|p c xy dng da trn l thuyt gi trcc trc lng

im phn vVaR cp trn }y c gi l phng php l thuyt gi

tr cc tr v iu kin bi v chng khng phn |nh c bi cnh bin

ng hin ti.

Vi c im phng sai sai sthay i c iu kin ~ nu ca hu ht cc

dliu t{i chnh, McNeil and Frey (2000) xut mt phng ph|p lun mi

c lng VaR m kt hp gia l thuyt gi trcc tr(EVT) vi m hnh

bin ng v{ c gi l phng php l thuyt gi tr cc tr c iukin(c iu kin }y l{ c xt n sbin ng). Cc tc gixut m

hnh GARCH c lng sbin ng hin ti v l thuyt gi trcc tr

c lng sphn bui ca cc c sc trong m hnh GARCH.

Nu tsut sinh li ti chnh l mt chui thi gian cnh cht chv tun

theo phn phi Pareto tng qut, k hiu l Gk,(), ph}n v c iu kin ca

tsut sinh li c thc c tnh nh sau:

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Trong i din cho phng sai c iu kin ca tsut sinh li ti chnh(c tnh bng m hnh GARCH) v l phn vth ca GPD c thc tnh nh sau:

[ ]

b.c lng Hill

Tham stp trung c|c tnh nng ca phn phi ui l{ chsui, =-1

. Hill~ xut nh ngha ca chsui nh sau:

Trong i din cho tsut sinh li ngng v u l squan st bng hocnhhn tsut sinh li ngng . c lng Hill l trung bnh ca u gi tr

quan st cc tr nht tr i n+1 quan s|t . c lng phn v c linquan l (xem Danielsson and de Vries, 2000):

Cc vn c t ra bi c lng ny l s thiu ht c|c phng tin

ph}n tch chn ra gi trngng u theo cch tt nht. V vy, nh mt sthay th, ngi ta s dng th Hill. Cc gi tr khc nhau ca ch s Hill

c tnh ton cho cc gi tru khc nhau; cc gi trc lng Hill trthnh

i din trong mt biu hoc thda trn u, v gi tru c la chn

tvng ni m{ c|c c lng Hill l{ tng i n nh (nghing thHill

gn nh theo chiu ngang). tng trc quan c bn c t ra trong

thHill l{ khi u tng ln, phng sai c lng gim, do , sai lch tng ln.

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Do , khnng dbo mt scn bng gia hai xu hng l c thxy ra.

Khi mc n{y c t n, sc lng khng i.

Xem xt mt sbi nghin cu lin quan:

Ti liu hin c vm hnh EVT tnh ton VaR rt nhiu.

i vi BMM:

Tc gi Mc tiu nghin

cu

Kt qu

Silva v Melo

(2003)

Xem xt v c|c

rng khc nhau ca

cc i khi

Phng ph|p gi| tr cc tr ca

c lng VaR l mt cch tip

cn thn trng hn trong vic xc

nh cc yu cu vvn so vi cc

phng ph|p truyn thng.

Bystrm

(2004)

p dng c hai m

hnh EVT v iu

kin v{ c iu

kin qun tr

nhng ri ro th

trng cc tr

trong th trng

chng khon v

Pht hin ra rng m hnh EVT c

iu kin cung cp c|c o lng

VaR c bit chnh xc

Bekiros and

Georgoutsos

(2005)

Tin hnh mt

|nh gi| so s|nh v

hiu qu d bo

ca cc m hnh

VaR khc nhau, vi

s nhn mnh c

bit vo hai

Cc kt qu ca h cng c cc

kt qu trc v chng minh

rng mt s phng ph|p

"truyn thng" c th mang li

kt qu tng t tin cy

thng nhng c|c phng ph|p

lun EVT to ra cc dbo chnh

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phng ph|p lun

lin quan n EVT,

POT v BM

xc nht v thit hi qu mc

tin cy rt cao.

Tolikas v cng

s(2007)

So snh EVT vi

c|c phng ph|p

truyn thng

(phng ph|p

tham s, HS v

Monte Carlo)

ng vi Bekiros and

Georgoutsos (2005) da trn

hiu qutt hnca c|c phng

php EVT so vi phn cn li, c

bit l tin cy rt cao.

Danielsson v

de Vries, 2000

EVT v iu kin th hot ng

tt hn c|c phng ph|p HS

truyn thng hay phng ph|p

tham s khi mt phn phi bnh

thng i vi TSSL c gi

nh v m hnh EWMA c s

dng c lng sbin ng

c iu kin ca TSSL

Nozari v cng

s(2010)

Zikovic v Aktan

(2009)

Gencay v

Selcuk (2004)

Nhng phng ph|p tip cn

EVT c iu kin thhin tt nht

i vi dbo VaR.

Trong cc m hnh POT, mt mi trng xut hin m trong cc bi nghin

cu xut mt sci tin trn cc kha cnh nht nh:

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Tc gi Ni dung ci tin

Brooks v cng s

(2005)

Tnh ton Var bng phng ph|p b|n phi

tham s s dng mt phi iu kin, m

hnh GARCH (1,1) v{ EVT, xut phng

php tip cn bn phi tham sbng cch s

dng GPD, v{ phng ph|p n{y c ch ra

to ra mt VaR chnh x|c hn so vi

phng ph|p kh|c.

Marimoutou v cng

s(2009)

S dng nhng m hnh khc nhau v xc

nhn rng qu trnh lc l quan trng c

c nhng kt qutt hn.

Ren v Giles (2007) Gii thiu khi nim chc nng truyn thng

qu mc nh mt cch mi la chn

ngng.

Ze-To (2008) Pht trin mt m hnh c da trn EVT c

iu kin kt hp vi m hnh GARCH-jump

d bo nhng ri ro ln. M hnh ny

c so snh vi EVT v iu kin v nhng

m hnh EVT-GARCH c iu kin di

nhng phn phi kh|c nhau nh ph}n phi

chun v phn phi t-student. ng y ch ra

rng m hnh EVT-GARCH-jump c iu kin

hiu qu hn nhng m hnh GARCH v

GARCH-t.

Chan v Gray (2006) xut mt m hnh c th cha s t hi

quy v mang tnh chu k hng tun cgi tr

trung bnh c iu kin v s bin ng c

iu kin ca TSSL cng nh hiu ng n

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by thng qua mt thng s k thut

EGARCH. Ngo{i ra, EVT c thng qua

to ra mt cch r rng nhng phn ui ca

phn phi TSSL.

Cui cng, lin quan n chsHill:

Mt stc gi~ sdng c lng ~ cp, nh Bao v{ c|c cng s(2006),

trong khi nhng ngi kh|c nh Bhattacharyya v{ Ritolia (2008) ~ sdng

mt c lng Hill ~ c sa i.

Thun li ca EVT:

Nm bt c cutoris v sthay i tnh bin ng(ETV c iu kin)

Bt li ca EVT:

- Phthuc vo nhng ginh phn phi ca TSSL cc tr

-

Kt quca n phthuc vo bdliu cc tr

3.3.5.Monte Carlo

L do sdng:

M phng cho php ngi lp m hnh tngtc vi cc tnh hung c thxy

ra khc nhau. Kh nng ca cc m hnh m phng trong gii quyt cc bi

ton phc tp l cho php thu c cc ktqukhc nhau ng vicc tnh

hungkhc nhau, phn tch nhnghnh vi binng trong ngnhn.Do m phng tr thnh cng c hu ch vi cc nh qun tr. M phngMonte

Carlo ara nhngt,ginhvphn phichuncatsutsinh likhng

cn ngna.cbitktqungunhin nhvo nhngphn phixc sut

c gi nh v mtlot nhng bin s u vo. Theo , ta s phn tch

nhngktqutm ra riro lin quan vinhngskin.Khi |nhgi VaR,

ta dng m phngMonte Carlo ara nhngtsutsinh lidanh mcmt

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cch ngunhin. M phngny ta c th gi nhbtkphn phi xc sut

no m ta cho l thch hp. Trong nhiu ng dng thc i vi nhng sn

phm phi sinh, vn qun tr riro ca nhng cng c ny c bao

gmbinhiuyutvinhngtham sngunhin c thnhhngnv

th tng hp trong khi nhng tham s ny thng khng phi phn phi

chunv hnnachngthngtc ngqua livinhau mtcch phctp.

Ni dung m phng Monte Carlo:

Th tc Monte Carlo n gin nht c lng VaR vo ngy th t trong

mt ngy ti mc ngha 99% bao gm vic m phng N quan st rt ra tphn phi ca TSSL vo ngy th t+1. VaR mc ngha 99% c c

lng bng cch c nhn t ti v tr N/100 (1%xN) sau khi sp xp li N

quan st rt ra khc nhau tTSSL trong 1 ngy, tc l{ c lng VaR c

c lng mt cch thc nghim nh ph}n vVaR ca phn phi m phng v

TSSL.

Vn t ra }y l{ l{m thn{o m phng tsut sinh li trong tng

lai. l{m c iu ny chng ta c thsdng phn mm excel to ra

cc m phng mt cch tng bng cch sdng cc lnh vng lp v hm

chc nng. Sau }y l{ mt c|ch m phng TSSL, c|c bc thc hin nh

sau:

-

Td liu v t sut sinh li hng ngy trong qu kh, ta tnh cc thng ssau: tsut sinh li trung bnh (u), phng sai (v{ lch chun (

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- p dng cng thc sau tnh gi trcphiu tng lai:

TP = S . Trong : TP: Gi cphiu ngy t+1

S: Gi cphiu ngy t

r = 2 + . NORMSINV(RAND())u: TSSL trung bnh:phng sai

Cm NORMSINV(RAND()) c sdng to ra cc gi trngu nhin

Nh vy, ta sm phng c mt tp dliu cphiu trong tng lai. Tdliu gi cphiu va to, tnh TSSL. Vi mc ngha , VaR c c tnh lquan st ti v tr N. ca tp d liu gm N TSSL tng lai c sp xptheo mc tthp ti cao.

Thunlicaphngphp mphngMonte Carlo:

}yl phngphp linh hotnhtbiv:

-

Cho php ngisdngginhmcphn phixc sutbtk

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- C thnmgicc danh mctngiphctp.

- Slng ln kch bn c to ra cung cp mt bin php ton din v{ |ng

tin cy hn vri ro hn l{phng ph|p ph}n tch

-

Nm bt c li ca cc cng cphi tuyn v sthay i trong bin.

Btlicaphngphp m phngMonte Carlo:

- ihitnh ton bngmy tnh nhiunhtvitnh chnh xc cng cao khi s

lngm phngcng ln.Mcd vy,phnlnspht trintrong lnhvc

cng nghthng tin ~lm cho phngphp Monter Carlo trthnh kthut

quntrriro hng u.

-

Phthuc vo qu trnh ngu nhin c chi tit ha v dliu lch sc

la chn to ra nhng gi trc tnh cui cng ca danh mc v cui cng

l VaR.

Nhn nh ca cc tc gikhc vMonte Carlo:

Tc gi Nhn nh

Estrella v cng s

(1994)

Monte Carlo l mt k thut th v, c s

dng c tnh VaR cho cc danh mc u t

phi tuyn bi v n khng i hi ginh vs

phn phi chung ca dliu. Tuy nhin, chi ph

tnh ton qu ln l mt ro cn hn ch ng

dng ca n vo nhng vn ngn chn ri ro

thgii thc.

Srinivasan v Shah

(2001)

xut cc thut ton thay thi hi phi c

chi ph tnh ton va phi

Antonelli v Iovino

(2002)

xut mt phng ph|p lun ci thin hiu

qu tnh ton ca m phng Monte Carlo

c tnh VaR.

Abad v Benito (2013) C|c c tnh VaR t c bng c|c phng

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Huang (2009)

Tolikas v cng s(200

Bao v cng s (2006)

ph|p kh|c c chnh xc ln hn so vi

Monte Carlo

4.Kim tra li phng php lun VaR (Back-testing)

Value-at-Risk ~ trthnh mt trong nhng cng co lng ri ro phbin

nht trong lnh vc ti chnh. Tuy nhin, cc m hnh VaR hu ch chkhi nu

h{ng ng{y l{ 99%, chng ta mong i mt ngoi l xy ra trong mi trung

bnh 100 ngy giao dch.

Nhiu tc giquan tm vtnh chng do|n chnh x|c nhng ri ro trong

tng lai. |nh gi| cht lng ca c|c c tnh VaR, cc m hnh nn lun

lun c kim tra li bng nhng phng ph|p thch hp.

Backtesting l mt thtc thng k nhm so snh li nhun v thua lthc tvi nhng c tnh VaR tng ng. Chng hn , nu tin cy c sdng

tnh ton VaR y ca c|c phng ph|p VaR, c bit l khi hso snh

mt v{i phng ph|p vi nhau. Cc bi nghin cu thng s dng hai

phng ph|p thay thso s|nh c|c phng ph|p lun VaR: c sca cc

kim nh tnh chnh xc v/hoc cc hm thua l(loss function).

4.1.C sca cc kim nh tnh chnh xc.

4.1.1.Unconditional coverage test.

i vi phng ph|p u tin, mt vi thtc da trn kim nh githuyt

thng k c xut trong cc ti liu v cc tc githng chn mt hoc

nhiu kim nh |nh gi| tnh chnh x|c ca cc m hnh VaR v so snh

chng. Nhng kim nh tiu chun vtnh chnh xc ca cc m hnh VaR l

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(i) unconditional and conditional coverage tests, (ii) chtiu back-testing

v (iii) kim nh phn vng. thc hin tt ccc kim nh ny, mt

chsngoi lphi c x|c inh v{ c tnh nh sau.

{

Kim nh POF ca Kupiec (1995).

Kupiec(1995) chra rng nu ginh xc sut ca mt ngoi ll{ khng i,th slng cc ngoi l tun theo phn phi nhthc B(N,) vi Nl squan st. Unconditional coverage test nhm m sngoi lca VaR, tc

l sngy (hoc thi k nm gi) c tn tht ca danh mc vt qu| c tnh

VaR. Nu sgi trngoi lb hn mc ngha c chn th ~ c tnh VaR

trc ~ c lng qu mc ri ro, v{ ngc li.

Githuyt:

H0 : p = =Mc ch l{ xem liu tltht bi theo quan st c khc bit |ng kso vitltht bi c xut bi mc tin cy (p) hay khng.

Thng k ca kim nh theo cng thc.

LRPOFtun theo quy lut phn phi (chi-bnh phng) vi mt bc tdo.

LRPOF > gi trtra bng ca phn phi th b|c bH0, m hnh c cho l

khng ng.

=

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LRPOF< gi trtra bng ca phn phi th chp nhn H0v{ m hnh c

cho l{ ng

Bng 1: Vng khng bc bcho kim nh POF di cc mc tin cy v kch

thc mu khc nhau (Kupiec,1995)

Vd, timc tin cy 95% vi 255 quan st, khong m hnh c chpnhn l [

655= 0.024; 55= 0.082]Vi 1000 quan st th khong

tng ng snhhn:[

7 = 0.037; 65= 0.065]T kt lun rng vi dliu ln hn sgip ddng loi bmt m hnhcha chnh x|c hn.

Kim nh ca Kupiec c u im l dthc hin v khng cn nhiu thng tin,

tuy nhin cng mc phi 2 nhc im chnh. Thnht, n yu vmt thng

k vi cmu phi ph hp vi khun khphp l hin h{nh (1 nm). V{ ch

xt n tn sut tn tht chkhng quan t}m n thi gian xy ra chng.Cc

khun khphp l:

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Theo quy nh ca y ban Basel, cc ngn hng vi hot ng giao dch |ng k

c yu cu thit lp mt khon dtrnht nh trong tng svn b p

cho nhng tn tht tim tng ca danh mc. Quy m ca ri ro thtrng vn

c x|c nh bng c|c c tnh VaR ca ngn hng.

Yu cu vc chbacktest nghim ngt ny sngn chn cc ngn hng bo

co sai vc|c c tnh ri ro ca h

Quy trnh Back-test c thc hin bng c|ch so s|nh c tnh VaR hng

ngy vi mc tin cy 99% trong 250 ngy gn nht vi kt qu giao dchhng ng{y tng ng. chnh xc ca m hnh c |nh gi| sau bng

c|ch m slng cc ngoi ltrong giai on ny (y ban Basel,1996).

Cng thc x|c nh yu cu vn i vi ri ro thtrng.

Phng ph|p Traffic Light

VaR c tnhhien ta i

VaR trung bnh cua nganhang trong 60 ngay giaodich gan ay

MCRt= max[VaR

t(0.01), S

t 6 VRt 59 +c

L ng von tangthem

St=

nu 4nu 9nu

Kha nang mo hnh ung la rat cao

Kha nang mo hnh kho ng u ng la khacao,nhng khong nhat thiet la mohnh sai trong vu ng nay.

Bac bo t o ng mo hnh VaR

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: l hstl(scaling factor) ca yu cu vn i vi ri ro thtrng, lsngoi ltrong 250 ngy giao dch.

4.1.2.Conditional coverage test.Mc ch:

Kim tra siu ha v sbin i theo thi gian ca dliu, ngha l{ xem

xt xem cc ngoi lc bng vi mong i hay khng v mc c lp ca

chng.

Mt c tnh VaR tt khng chcho thy cc ngoi lph hp m cc ngoi l

ny cn phi tri u theo thi gian. Nu cc ngoi ltthnh chm th cho

thy m hnh khng nm bt chnh xc sthay i trong nhng tng quan

v bin ng ca thtrng.

Kim nh ca Christoffersen

ng sdng khun khkim nh log-likelihood ging nh Kupiec nhng cmrng thm vo cc thng k tch bit i vi sc lp ca ngoi l

Kim tra xem liu xc sut ca 1 ngoi lvo bt cngy no c phthuc

vo kt quca ng{y trc hay khng? ng xut mt kim nh c lp,

vi mc ch loi bcc m hnh VaR c cc ngoi lhi tthnh chm.

Sau , x|c nh nij l sng{y m{ khi iu kin j xy ra gisrng iu kin i

~ xy ra v{o ng{y trc . Minh ha bng bng sau.

1 neu co ngoai le 0 neu khong co ngoai le It

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It-1= 0 It-1= 1

It= n00 n10 n00 + n10

It= n01 n11 n01 + n11

n00 + n01 n10 + n11 N

Cho ii din cho xc sut quan st thy mt ngoi lvi iu kin i xy ra

v{o ng{y trc

0=1=

v=

Githit

H0: 0 = 1 : M hnh ng l{ ngoi lhm nay khng phthuc vo liu c

hay khng mt ngoi l~ xy ra trc .

Cng thc thng k kim nh

Thng k kim nh chung

kim tra xem xt c 2 c tnh ca mt m hnh Var tt: t l tht bi

chnh xc v sc lp ca nhng ngoi l.

LRCC tun theo quy lut phn phi vi bc tdo l 2.

= -2 n00+n10n01+n110n000n011n101n11

LRCC

= LRPOF

+ LRind

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Nu LRCC > gi trtra bng , b|c bm hnh

Nu LRCC < gi trtra bng , chp nhn m hnh

u im:Cho php kim tra xem m hnh cha chnh x|c l{ do bao phcha chnh x|c hay do c|c ngoi lhi tthnh cm hoc do chai.

Hn ch:Kim nh chxem xt sphthuc ca nhng quan st gia 2 ngy

lin tip

Kim nh Kupiec hn hp gii quyt hn ch ca kim nh ca Christoffersen, Haas xut mt

kim nh Kupiec hn hp o lng thi gian gia cc ngoi l thay v ch

quan st liu ngoi lngy hm nay c phthuc v kt qung{y trc

hay khng.

Kim nh thng k cho mi ngoi l.

Trong vil thi gian gia hai ngoi li v i-1.

C c thng k LR cho mi ngoi l, mt kim nh thng k cho n ngoi l

vi gi thuyt Ho l cc ngoi lphi c lp vi nhau.

tun theo phn phi vi n bc tdo.Kim nh Kupiec hn hp:

= -2

1 1 11

= 11 1 1 11 1 1

LRmix

= LRPOF

+ LRind

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Thng k LRmixtun theo quy lut phn phi vi n+1 bc tdo

LRmix> gi trtra bng , b|c bm hnh.

LRmix< gi trtra bng , chp nhn m hnh.

4.1.3.Kim nh phn vng(DQ).

c xut bi Engle v Manganelli(2004), nhm kim tra xem liu cc

ngoi ll{ khng tng quan vi bt cbin no thuc bthng tin

c

sn khi VaR ~ c tnh ton.

Gi thuyt Ho l tt cdc trong m hnh hi quy u bng 0, vi Xj l

bin gii thch c trong

. VaR() thng l mt bin gii thch kim

nh xc sut ca mt ngoi lphthuc vo mc ca VaR.

4.2.Hm tn tht.

Thng tin trong cc khun khbacktesting c bn i khi bgii hn. Thay v

chquan s|t xem c|c c tnh VaR c vt qu hay khng, cn c mt mi

quan tm khc, chng hn nh ln ca cc ngoi l.

Lopez (1998, 1999) nghmt phng ph|p kim tra kha cnh n{y i

vi c|c c tnh VaR.Mu hnh chung ca hm tn tht l mt ngoi lc

cho im cao hn khng phi ngoi l.

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Trong l TSSL thc hin v l{ c tnh VaR tng ng. Ccim sca m hnh c tnh bng c|ch a dliu vo hm tn tht. im

stng ln cng vi mc tn tht. Mt backtest da trn phng php ny

sau sc tin hnh bng cch tnh ton trung bnh tn tht ca mu( T

quan st).

x|c nh liu tn tht trung bnh c qu ln so vi "nhng g n

cn c ", cn phi c mt sloi ca mt gi trchun. Trong thc t, iu

ny

c ngha l{ backtest thit lp mt ginh vhnh vi ngu nhin v phn phi

TSSL ca danh mc. Sau khi phn phi ~ c x|c nh, mt phn phi thc

nghim c th c to ra bng cch m phngTSSL ca danh mc. Gi trchun c ththu c tphn phi ny. Nu tn tht trung bnh ca mu ln

hn gi| trchun mc, m hnh nn bloi b..

5.So snh cc phng php VaR

Nghin cu thc nghim vphng ph|p VaR l{ kh| rng. Tuy nhin, khng

c nhiu bi nghin cu dnh ring cho vic so snh s hiu qu ca cc

phng ph|p VaR trn phm vi rng ln. Trong Bng 4, tc gi tip tc so

snh 24 bi nghin cu. Vc bn, phng php so snh trong cc bi nghin

cu l: HS (16 bi nghin cu), FHS (8 bi nghin cu), phng ph|p tham

s theo phn phi khc nhau (22 bi nghin cu theo chun, 13 bi nghin

cu theo phn phi t-student v ch5 bi nghin cu phn phi lch) v

phng ph|p tip cn da trn EVT (18 bi nghin cu). Chc mt vi trong

snhng nghin cu ny bao gm phng ph|p kh|c, chng hn nh Monte

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Carlo (5 bi nghin cu), CaViaR (5 bi nghin cu) v{ c|c phng ph|p c

lng mt phi tham sN-P (2 bi nghin cu) trong so snh ca h. Tc

gi|nh du nhng phng ph|p : mt du x v{ in m l nhng phng

php cho kt quc|c c tnh VaR tt nht.

Tbng 4, kt lun rng:

Cch tip cn da trn EVT l tt nht c lng VaR chim 83,3% cc

trng hp c so s|nh, sau l{ FHS, chim 62,5% c|c trng hp.

Phng ph|p CaViaR ng thba.

Cc kt qu ti nht thu c bng phng ph|p HS, Monte Carlo v{

Riskmetrics. Khng Phng ph|p n{o trong s nhng phng ph|p trn

c xp hng tt nht khi so s|nh. R r{ng l{ xut mi c tnh VaR

~ cc trso vi nhng phng ph|p truyn thng.

Tc gi nu bt nhng kt qu thu c bi Berkowitz v O'Brien (2002).

Trong bi nghin cu ny, cc tc gi so snh mt s m hnh VaR ni b

c cc ngn hng sdng vi mt m hnh tham sc tnh GARCH theo

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phn phi chun. Hnhn ra rng cc m hnh VaR sdng trong ngn hng

khng tt hn so vi mt m hnh tham sGARCH n gin. N cho thy rng

cc m hnh ni blm vic rt km trong vic c tnh VaR.

sbt i xng trong bin ng. Sener v cng s(2012) pht biu rng hiu

sut ca phng ph|p VaR khng phthuc hon ton vo vic n l tham s,

khng tham s, bn tham shoc loi no khc, m l vvic liu hc th

m hnh ha sbt i xng ca cc dliu c bn c hiu quhay khng.

Mc d khng c nhiu bi vit dnh ring cho cc so snh ca mt lot cc

phng ph|p VaR, nhng bi hin c cung cp kt qu kh thuyt phc.Nhng kt quny cho thy rng phng ph|p tip cn da trn EVT v FHS

l{ phng ph|p tt nht c tnh VaR. Tc gicng lu rng c tnh

VaR thu c tmt scc phn mrng khng i xng ca phng ph|p

CaViar v{ phng ph|p tham stheo phn phi skewed v fat tail cho kt

quy ha hn, c bit l khi ginh rng TSSL c chun ha l iid b

bqun v cc khonh khc iu kin bc cao (the conditional high-ordermoments) c xem xt ti l{ thay i theo thi gian.

6.Mt schquan trng ca phng php VaR

Nh ~ ni trongphn gii thiu, VaR n nay l{ phng ph|p h{ng u v

o lng ri ro danh mc u t c sdng ti c|c ng}n h{ng thng mi

ln v cc tchc t{i chnh. Tuy nhin, c|ch tnh n{y l{ khng tr|nh c s

ch trch. Mt s nh nghin cu ~ nhn xt rng VaR khng phi l mt

phng ph|p thtrng nht qun (xem Artzner v cng s1999.).

Nhng tc gin{y x|c nh mt tp hp cc tiu chun cn thit cho nhng g

h gi l{ o lng ri ro nht qu|n. C|c tiu ch n{y bao gm tnh thun

nht (danh mc c quy m cng ln th ri ro cng cao), n iu (danh mc

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c mc thua l tim n cao th ri ro cng cao), cng tnh di (ri ro ca

danh mc gm nhiu yu t ri ro }y l{ s nhhn hoc bngvi tng ri ro ca cc yu tri ro thnh phn) v{ iu kin phi ri ro (nh

tldanh mc u t u t v{o c|c t{i sn phi ri ro tng, ri ro danh mc

u t sgim). Hchra rng VaR khng phi l mt thc o ri ro nht

qun bi v n vi phm mt trong cc tin ca h. c bit VaR khng |p

ng c|c iu kin cng tnh di v n c thkhuyn khch a dng ha.

Vim ny, Artzner v cng s(1999) xut mt phng ph|p tnh ri ro

thay thlin quan n VaR c gi l{ Tail Conditional Expection, cn c

gi l gi trri ro c iu kin (CVaR). C|c CVaR o lng tn tht dkin

trong % trng hp xu nht v{ c cho bi Cng thc:

CVaR l mt thc o ri ro nht qun cho phn phi lin tc. Tuy nhin, nc thvi phm cng tnh di vi phn phi khng lin tc. Do , Acerbi v{

Tasche (2002) xut Thm ht k vng (ES) nh mt thc o ri ro nht

qu|n. ES c cho bi:

Trong Ch rng CVaR=ES khi phn phi

TSSL l lin tc. Tuy nhin, n vn nht qun nu phn phi TSSL l khng

lin tc. ES cng c mt su im khi so snh vi phng ph|p VaR ph

bin khc.

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Trc ht, ES th khng c ri ro ui v n c xt n thng tin vui ca

phn phi c bn. Vic s dng mt thc o ri ro khng c ri ro ui

trnh cc thua lcc trui. Do , ES l{ mt ng cvin tuyt vi thay

thVaR cho cc mc ch qun l ri ro ti chnh.

Mc d ES c nhng li th, nhng n vn cn t c sdng hn so vi

VaR. L do chnh cho bqua phng ph|p n{y l{ backtest ES th kh hn VaR.

Trong ngha , nhng nm qua mt sthtc backtesting ES ~ c pht

trin.

Bt klnh vc no m mt tchc ti chnh tham gia, tt ccc tchc nyc th gp ba loi ri ro: th trng, tn dng v hot ng. V vy, tnh

ton tng VaR ca mt danh mc u t l{ cn thit kt hp nhng ri ro

ny. C nhiu sgn ng kh|c nhau tin hnh vic n{y. u tin, mt gn

ng tng kt ba loi ri ro (VaR). V VaR khng phi l mt phng ph|p

cng tnh di, xp xn{y |nh gi| qu| cao tng sri ro hoc vn kinh t.

Thhai, giskt hp tnh tiu chun ca cc nhn tri ro, xp xny pt ui l{ mng hn so vi dbo thc nghim v{ |nh gi| thp |ng k

vn kinh tv cch tip cn thba |nh gi| tng hp ri ro c da trn

s dng copulas. c c tng VaR ca mt danh mc u t l{ cn

thit c c phn phi xc sut TSSL ng thi ca danh mc u t.

Copulas cho php chng ta gii quyt vn ny bng cch kt hp cc bn

phn phi bin c thvi mt hm ph thuc to ra phn phi xc sutng thi. tng c bn ca phng ph|p tip cn copula l mt phn phi

xc sut ng thi c thc tnh vo cc hm bin v hm phthuc, c

gi l{ copula. C|c iu kin copula da trn quan im ca s kt ni: cc

copula kt hp vi phn phi bin vi nhau to thnh mt phn phi xc

sut ng thi. Mi quan h ph thuc th ho{n to{n c x|c nh bi

copula, trong phng ph|p n{y, quy m v{ hnh dng ho{n to{n c xc

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nh bi bin. Sdng mt copula, ri ro bin m{ ban u c c tnh mt

cch ring bit sau c thc kt hp trong mt phn phi ri ro ng

thi m bo c tnh ban u ca bin. iu n{y i khi c gi l{ t c

mt mt ng thi vi bin x|c nh trc. Phn phi xc sut ng thi

c thc sdng sau tnh ton nhng phn v ca phn phi xc

sut TSSL ca danh mc, bi v TSSL danh mc l mt bnh qun c trng s

trn TSSL ring l. Embrechts v cng s(1999, 2002) l nhng ngi u

tin gii thiu phng ph|p n{y trong c|c t{i liu ti chnh. Mt sng dng

ca copulas tp trung vo skt hp gia cc ri ro cho cc tchc ti chnh

c thc tm thy trong Alexander v Pezier (2003), Ward v Lee (2002)

v Rosenberg v Schuermann (2006).

7.Kt lun

Trong bi vit ny tc gixem xt y spht trin c|c phng ph|p

c tnh VaR, tcc m hnh tiu chun n nhng xut gn }y v{ trnh

by nhng im mnh v{ im yu tng i ca chng tchai kha cnh lthuyt v thc tin.

Hiu quca phng ph|p tip cn tham s trong c tnh VaR ph thuc

vo phn phi xc sut c gi nh ca TSSL ti chnh v m hnh bin

ng sdng c tnh sbin ng c iu kin ca TSSL. i vi phn

phi TSSL, bng chng thc nghim cho thy khi phn phi bt i xng v

phn phi fat-tail c xem xt, c tnh VaR c ci thin |ng k.

Bt k sdng m hnh bin ng no, kt quthu c trong nghin cu

thc nghim cho thy nh sau:

- M hnh EWMA cung cp cc c tnh VaR khng chnh xc

-

Vic thc hin cc m hnh GARCH ph thuc mnh m vo gi nh phn

phi xc sut ca TSSL. Nhn chung, theo phn phi chun, c tnh VaR rt

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khng chnh x|c, nhng khi ph}n phi bt i xng v fat-tail c p dng,

kt quc ci thin |ng k.

- Bng chng cho thy vi mt sngoi lm m hnh SV khng ci thin kt

quthu c ttp hp cc m hnh GARCH.

- Cc m hnh da trn sbin ng th kh tt c tnh VaR, cc m hnh

GARCH c tnh rt tt da trn mt phn phi chun. Ngoi ra, Markov-

Switching GARCH tt hn so vi c|c m hnh GARCH c tnh trong trng thi

bnh thng. Trong trng hp ca cc m hnh bin ng, mt stc gicho

thy tnh u vit ca n so vi cc hGARCH l khng cao khi cc m hnh

GARCH c c tnh trn ginh phn phi TSSL bt i xng v fat-tail.

- Trong hGARCH, cc m hnh GARCH tch hp phn skhng tt hn so vi

cc m hnh GARCH.

- Mc d bng chng l{ kh| m h, cc m hnh bin ng bt i xng cung

cp mt c tnh VaR tt hn hn so vi m hnh i xng.

Tuy nhin, trong bi cnh ca cc m hnh bin ng c gii thiu, c bng

chng rng cc m hnh nm bt c bin ng l}u d{i hn scung cp cc

c tnh VaR chnh x|c hn. Nhng kt quny cho thy rng phng ph|p

tip cn da trn EVT v{ FHS l{ phng ph|p tt nht c tnh VaR. Tc

gicng lu rng c tnh VaR thu c tmt scc phn mrng khng

i xng ca phng ph|p CaViaR v{ phng ph|p tham stheo phn phi

the skewed v fat tail dn n kt quy ha hn, c bit l khi ginh

rng li nhun chun c idd b loi bv khonh khc iu kin bc cao

(the conditional high-order moments) c xem xt ti thi gian khc nhau.

R r{ng l{ xut mi c tnh VaR ~ cc trso vi nhng phng ph|p

truyn thng.

S rt th v khi tip tc nghin cu liu rng cho trong bi cnh ca mt

phng ph|p tip cn da trn EVT v FHS xem xt phn phi bt i xng

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v fat-tail m hnh sbin ng ca TSSL c thgip ci thin kt quthu

c bng c|c phng ph|p n{y hay khng. Theo hng ny, cc kt quc

thc ci thin hn na bng cch p dng m hnh bin ng c gii

thiu v m hnh Markov-switching.

8.TI LIU THAM KHO

Gio trnh Qun trri ro ti chnh Nguyn ThNgc Trang, trng i hc

Kinh tthnh phHCh Minh.

Gio trnh Kinh tlng, trng i hc Kinh tthnh phHCh Minh

Gio trnh Nguyn l thng k trng i hc Kinh tthnh phHCh Minh

Gio trnh Lp m hnh ti chnh, Trn Ngc Th V Vit Qung, trng i

hc Kinh tthnh phHCh Minh

Chan, K., Gray, P., 2006. Using extreme value theory to measure value-at-risk

fordaily electricity spot prices. International Journal of Forecasting, 283300.

Bali, T., Theodossiou, P., 2007. A conditional-SGT-VaR approach with

alternativeGARCH models. Annals of Operations Research 151, 241267.Bali,

T., Weinbaum, D., 2007. A conditional extreme value volatility estimatorbased

on high-frequency returns. Journal of Economic Dynamics & Control 31,361

397.

Barone-Adesi, G., Giannopoulos, K., 2001. Non-parametric VaR techniques.

Mythsand realities. Economic Notes by Banca Monte dei Paschi di Siena, SpA.

30,167181.

Bekiros, S., Georgoutsos, D., 2005. Estimation of value at risk by extreme

valueand conventional methods: a comparative evaluation of their predictive

per-formance. Journal of International Financial Markets, Institutions &

Money 15(3), 209228.

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Engle, R., Manganelli, S., 2004. CAViaR: conditional autoregressive value at

risk byregression quantiles. Journal of Business & Economic Statistics 22,

367381.

Escanciano, J.C., Olmo, J., 2010. Backtesting parametric value-at-risk with

estimationrisk. Journal of Business & Economic Statistics 28, 3651.

Kupiec, P., 1995. Techniques for verifying the accuracy of risk measurement

models.Journal of Derivatives 2, 7384.

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