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(16)

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(17)

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(20)

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(22)

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(23)

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(24)

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(25)

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(26)

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(27)

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(28)

0 0.005 0.01 0.015 0.02 0.025 0.03 0 1 2 3 4 5 6 7 Exponential Quantiles Ordered Data

QQ−Plot of magnitude of log(losses} for daily DEM/USD from 12/31/93 to 6/15/01

Concave departure

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(29)

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(31)

−0.030 −0.02 −0.01 0 0.01 0.02 0.03 0.005 0.01 0.015 0.02 0.025 0.03 Threshold Mean Excess

ME−Plot of magnitude of log(losses} for daily DEM/USD from 12/31/93 to 6/15/01

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(32)

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(33)

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(34)

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(35)

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(36)

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(37)

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(38)

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(39)

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(40)

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(41)

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(42)

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(43)

;d1 pVi]< YBIBjBk

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(44)

$R _0 ) (L 0 3 7)d 76 1 07L R 3 i)d#i_0i3

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(45)

BBjAB- b$t Ak %$t 7Y}}sIdx _{PB VqNV $R ZRI}

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(46)

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(47)

0 18.10.89 24.10.91 02.11.93 25.10.95 27.10.97 16.11.99 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2x 10 4

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(48)

18.10.89 24.10.91 02.11.93 25.10.95 27.10.97 16.11.99 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3

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(49)

;n 7kj$9I 3s{R

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(50)

0 50 100 150 200 250 300 350 −0.1 −0.05 0 0.05 0.1 0.15

Sample autocorrelation coefficients

0 50 100 150 200 250 300 350 −0.06 −0.04 −0.02 0 0.02 0.04 0.06 0.08 0.1 0.12

Sample partial autocorrelation coefficients

Lags

3$Z MU 7s8}j sZB{Bjs$Bt wB}D stI Rs8}j }s$sj sZB{Bjs$Bt wABB8D {BT ^{$tR PB ts$% jB ZtR Bt y7eTd(( $tI- qY IBI j$tR s x0 {BthIt{ $t%sjR B% bY${Y Y {B^{$tR s R$t$h{st b$Y x0 {BthIt{

(51)

0 50 100 150 200 250 300 350 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

Sample autocorrelation coefficients

0 50 100 150 200 250 300 350 −0.05 0 0.05 0.1 0.15 0.2 0.25 0.3

Sample partial autocorrelation coefficients

Lags

3$Z U 7s8}j sZB{Bjs$Bt wB}D stI Rs8}j }s$sj sZB{Bjs$Bt wABB8D {B^{$tR BP Y RJZsI ts$% jB ZtR bY${Y $R s }B-k PB %Bjs$j$k qY IBI j$tR s x0 {BthIt{ $t%sjR B% bY${Y Y {B^{$tR s R$t$h{st b$Y x0 {BthIt{ qY s %s$BZR R$t$h{st }s$sj sZB{Bjs$BtR bY${Y $tI${sR %Bjs$j$k {jZR$t $t y7eTd(( $tI- ]B8}s$t B 3$Z M Y sZB{Bjs$Bt BP %Bjs$j$k R8R B A 8Z{Y RBt Yst Y sZB{Bjs$Bt BP ZtR

(52)

qB I{$I sABZ Y PstRR BP s$jR tB8sj$k RR Ys s AsRI Bt Rs8}j R,btRR stI Rs8}j ,ZBR$R j$, Y FsJZT s tB8sj$k R s tB s}}BT }$s R$t{ `{$t tB8sj$k IZ B s R$t$h{st R,btRR B s R$t$h{st -{RR ,ZBR$R IBR tB t{RR$s PsTs$jtRR 3B $tRst{ s I$R$AZ$Bt 8sk A R,bI stI Y$t s$jI B Y 8}$${sj I$R$AZ$Bt 8sk Ys% -{RR ,ZBR$R B% tB8sj I$R$AZ$Bt AZ Y$t s$jI 3B -s8}j Zt$PB8 I$R$AZ$Bt YsR -{RR ,ZBR$R B% tB8sj I$R$AZ$Bt AZ $ $R Y$t s$jI R$IR RR ZR$tIss PB8 Y bYBj I$R$AZ$Bt s tB &{$% PB stsjkR$R PB{ZRI Bt s$jR R$t{ Yk s 8Z{Y 8B s&{I Ak BAR%s$BtR ts Y {t BP Y I$R$AZ$BtR qYPB YR tB8sj$k RR s $tBI stI $tRsI PB8jk $tBIZ{I s$j stsjkR$R R}{$h{ -}jBs$Bt BBjR s ZRI

3$Z d( }RtR s }s BP Y 8}$${sj I$R$AZ$Bt PZt{$Bt PB{ZRI Bt Y s$j y $%R st $Is BP Y I{sk s BP Y s$j qY 8st -{RR }jB wR 3$Z ddD $tI${sR s Ys%k jP s$j PB Y Zt I$R$AZ$Bt w$Y s$j BP jBRRR $R jP s$j BP ZtRD yt s8t b$Y Y 8st -{RR }jB Y ++T}jB $t 3$Z d1 sjRB I$R}jskR %$It{ PB s Ys%k s$jI I$R$AZ$Bt IZ B Y {Bt{s% I}sZ PB8 j$ts$k VjYBZY tB sR $tPB8s$% sR 8st -{RR B ++T_jBR PB s$j stsjkR$R Bt 8sk sjRB -s8$t Y Y$RBs8 BP Iss bY${Y $R }B%$II $t 3$Z dn 3B8 Y Y$RBs8 b$Y s RZ}$8}BRI AR tB8sj h $ {st A

(53)

{Bt{jZII Ys ABY Y R8sjj stI Y -8 sj$9s$BtR s 8B {B88Bt Yst RZRI Ak s tB8sj I$R$AZ$Bt bY$j Y PJZt{k BP 8I$Z8 R$9I sj$9s$BtR s jRR Yst $8}j$I Ak s tB8sj I$R$AZ$Bt

y {st A {Bt{jZII Ys Y Iss $R Ys%k s$jI VjRB s Y$jj}jB {st A }BIZ{I B Ys% st $Is sABZ Y s$j $tI- BP Y ZtIjk$tI$R$AZ$Bt bYt Y I$R$AZ$Bt $R Ys%k s$jI VR PB8jk I$R{ZRRI Y s$j $tI- Yj}R ZR Bt Isb$t{Bt{jZR$BtR Bt Y AYs%$B BP Y s$j BP s I$R$AZ$Bt 3B Bt BP Y Y }BRR$Aj PBjjBb$t{sRR $tPB8 ZR sABZ Y j$8$$tI$R$AZ$Bt BP 8s-$8sU ) ( k ( stI c ( qY hR {sR $R PB -}Btt$sj j$, s$j I$R$AZ$Bt $t Y j$8$ qY R{BtI {sR jsIR B s Ys%k 8}$${sj s$j AYs%$B sR Y Rs8}j R$9 s}}Bs{YR $tht$k bY$j Y jsR {sR $8}j$R s ht$ s$j $t Y j$8$ qY {$${sj }B$t $t <$jj R$8sR $R Y {YB${ BP Y tZ8A BP Z}} BI Rs$R${R B ZR $t Y R$8s$Bt <s%$ts <$jj}jB s YstI Y s$j $tI- {st A {YBRt PB8 s js$%jk RsAj $Bt BP Y Y$jj}jB qY Y$jj}jB BP y7eTd(( jB jBRRR $R I$R}jskI $t 3$Z d; qY js$%jk RsAj }B$Bt BP Y hZ $R Y Is, $Bt $t Y }jB 3B8 Y Y$jj}jB Bt {st {Bt{jZI Ys Y s$j $tI- R$8s $R $t Abt (1( stI (1x b$Y Y {BthIt{ AstIR $%t $t Y hZ qYPB Y Y$jj}jB B&R s }Bb I{sk$ts$j b$Y st -}Btt $t Abt ; stI x qY$R 8stR Ys $P Y }BAsA$j$k BP BAR%$ts Zt s Yst $R Yt Y }BAsA$j$k BP

(54)

BAR%$ts Zt s Yt > $R $t Abt >;_{stI >}x

(55)

0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0 0.02 0.04 0.06 0.08 0.1 x 1 − F(x)

3$Z d(U e8}$${sj s$j I$R$AZ$Bt !t Y %${sj s-$R ItBI s Y }BAsA$j$k BP %tR Zt{B%I Ak Y JZst$jR Bt Y YB$9Btsj s-$R

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0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 Threshold Mean Excess

3$Z ddU st -{RR }jB qY YB$9Btsj s-$R $R PB YRYBjIR B% bY${Y Y Rs8}j 8st BP Y -{RRR s {sj{ZjsI zsjZR Bt Y %${sj s-$R I$R}jskR Y {BR}BtI$t 8st -{RRR qY }BR$$% tI PB YRYBjIR sAB% s}}B-$8sjk ((M1 $tI${sR s Ys%k jP s$j R$t{ Y$R $R Y 8st -{RR }jB PB ts$% jBs$Y8${ ZtR bY${Y $R jBs$Y8${ jBRRR R$IR R$t{ st s}}B-$8sjk j$ts }BR$$% tI RZjR PB8 s _sB k} AYs%$B ws$j }BAsA$j$$R I{sk$t sR s }Bb PZt{$BtD $ {st A {Bt{jZII Ys -8 jBRRR Ys% s _sB k} AYs%$B

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−0.1 −0.05 0 0.05 0.1 0.15 0.2 0 1 2 3 4 5 6 7 8 9 Exponential Quantiles Ordered Data

QQ Plot with respect to exponential distribution

3$Z d1U ++T}jB w+Zst$jT+Zst$jD b$Y R}{ B -}Btt$sj I$R$AZ$Bt Vt s}}B-$8s j$ts$k $t Y s$j $Bt $tI${sR st -}Btt$sj s$j bY${Y $R $t Y {jsRR BP Y$t s$jR V {Bt%- I}sZ PB8 j$ts$k $tI${sR s j$Y s$j Yst -}Btt$sj bY${Y 8sk A sj$9s$BtR PB8 s ht$ s$jI I$R$AZ$Bt !t Y BY YstI s {Bt{s% I}sZ PB8 j$ts$k sBZtI Y$Y JZst$jR sR $ $R BAR%I $t Y$R }jB {st A s,t sR %$It{ BP s Ps s$j $t Y ZtIjk$t I$R$AZ$Bt

(58)

3$Z dnU qY Y$RBs8 BP ts$% jB ZtR stI Y AR hI tB8sj I$R$AZ$Bt ]w| , |D RZ}$8}BRI PB bY${Y | (3((1 stI | (3(n;M qY s$j $Bt $R 9BB8I $t Y Z}} jP }s BP Y hZ 3B8 Y 9BB8I s$j BP Y 8}$${sj I$R$AZ$Bt Y Ys%$ s$jR Yst tB8sj $R %$It

(59)

3$Z d;U zs$s$Bt BP Y <$jj R$8s BP Y s$j $tI- b$Y tZ8A BP Z}} BI Rs$R${R ZRI WB Ys Y <$jj R$8s $R %k RtR$$% B $t{sR$t B I{sR$t Y tZ8A BP Z}} BI Rs$R${R bYt s Pb tZ8A BP Z}} BI Rs$R${R ZRI PB R$8s$Bt VAB% s {s$t tZ8A BP BI Rs$R${R Y R$8s RsA$j$9R VP Ys $ A$tR B $t{sR 8BtBBt${sjjk bY${Y $R IZ B Y A$sR $t Y <$jj R$8sB qY s$j $tI- R$8s RYBZjI A {YBRt PB8 s $Bt bY Y R$8s $R js$%jk RsAj bY${Y $R BtI sk $t Y hZ qB Y $Y tI BP Y$R RsA$j$k $Bt Y {BthIt{ AstIR I{sRR R$t{ 8B Z}} BI Rs$R${R $R ZRI B }BIZ{ Y R$8s

(60)

;; YBIBjBk

yt Y$R }s Y 8YBIBjBk BP Y s}}j${s$Bt stI Y BAs$tI RZjR s I$R{ZRRI qY 8YBIBjBk $R BZ BP Rs8}j JZst$j R$8s$Bt b$Y Rj$I$t b$tIBb {Yt$JZ PB Y hR h% s}}Bs{YR AjBb

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qY 8B$%s$Bt AY$tI Y Rj$I$tb$tIBb {Yt$JZ $R Ys Y Iss }BAsAjk Ys% I$&t {Yss{$R${R $t I$&t }$BIR GY$j Y hR h% 8YBIR s sIs}$% $t Y RtR Ys s {s$t tZ8A BP Y 8BR {t BAR%s$BtR s ZRI B }PB8 Y t- Isk:R JZst$j PB{sRR Y jsR s}}Bs{Y $R tBtTsIs}$% R$t{ $ ZRR sjj Y s%s$jsAj Iss Z} B Y Isk Bt bY${Y PB{sRR s }PB8I qY I$&t b$tIBb R$9R s RI PBjjBb$t*st$jRRBt stI B$B8B w1(((D PB sjj Y 8BIjR ]BtR$I s b$tIBb R$9 d((( 3$R Y b$tIBb $R }js{I

(61)

Bt Y st Abt dR stI d(((Y BAR%s$BtR stI s JZst$j {BR}BtI$t B s {s$t }BAsA$j$k $R PB{sRI b$Y s{Y BP Y h% 8YBIR j$RI sAB% PB Y d((dY Isk qY b$tIBb $R Rj$II Bt R} PBbsI $t s{Y Zt B PB{sR JZst$jR PB d((1Y d((nY nnM1Y IskR

y $R }BRR$Aj Ys 8BIjR 8sk bB, A b$Y I$&t b$tIBb R$9R PB Y Rs8 JZst$j R$8s eR}{$sjjk p_* h$t8sk tI 8B Iss PB BZ BP Rs8}j PB{sR$tsR -8 %tR s s stI B R$8s Y }ss8R BP p_* {BthItjk s RZ^{$t tZ8A BP -8 %tR s tII

qY pVi]< 8BIjR s }ss8$9I sR Ys%$tBt sZBRR$% stI Bt 8B%$ts%s 8R R$t{ $ $R }s{${sjjk $8}BRR$Aj B htI Y AR }ss8T $9s$Bt PB s{Y BP Y 1nM1 BZ BP Rs8}j PB{sRR bY${Y $R sjRB s {BtRs$t PB Y p_* h$t $ Y I$^{Zjk $t {YBBR$t Y s}}B}$s YRYBjI %sjZ PB s{Y Zt BY Y sIs}$% p_* stI tBtTsIs}$% p_* JZst$j PB{sRR s }PB8I ZR$tY B} 1x0 BP Y Iss !t 8sk {YBBR I$&t }{tsR PB I$&t JZst$jR stI I$&t b$tIBb R$9R AZ Y$R 8sk $t{sR Y &{R BP Iss RtBB}$td

3B Y Y$RB${sj R$8Zjs$Bt }${b$R j$ts $t}Bjs$Bt $R {YBRt B 8s, Y 8}$${sj I$R$AZ$Bt PZt{$Bt Bt B Bt yt Ps{ tBtTj$ts $t}Bjs$Bt

d_{7 7Zjj$%st sj wdMD PB 8B $tPB8s$Bt Bt Iss RtBB}$t}

(62)

{Yt$JZR 8sk $% A RZjR IZ B Y Ps{ Ys Y -$RR s {Z%sZ $t Y 8}$${sj I$R$AZ$Bt PZt{$Bt stI s 8BIj s,$tY$R {Z%sZ $tB s{{BZt $%R A RZjR

qY RZjR $t 8R BP %$Bjs$BtdM _{sR BP Y R$8sI JZst$jR $t BZ BP}

Rs8}j PB{sRR s $%t $t qsAj d stI qsAj 1 z$Bjs$Bt sR s {sj{ZjsI Ak {BZt$tY Bsj tZ8A BP %$Bjs$BtR BP Y R$8sI JZst$jR stI I$%$I$t $ Ak Y Bsj tZ8A BP BZ BP Rs8}j PB{sRR qsAj d I$R}jskR Y RZjR PB (xY (xY (Y (xY stI (Y JZst$jR BP Y jP s$j bY$j qsAj 1 I$R}jskR Y RZjR PB Y $Y s$j qY h% JZst$jR s Ij$Asjk {YBRt sBZtI (Y JZst$j PB -s8$t$tY }PB8st{R BP Y h% 8YBIR Bt stI sBZtI Y$R JZst$j R$t{ $ $R $8}Bst PB {Bt8}Bsk $R, 8sts8t s}}j${s$BtR sR bjj sR ZjsBk {s}$sj JZ$8tR

qY RZjR $t qsAj d PB Y jBRRR BP y7eTd(( $tI- wjP s$j BP ZtRD RYBbR Ys zsT]B% 8YBI $R tB sIJZs R$t{ $ YsR Y bBR }PB8st{ s8Bt sjj -{} Y xY JZst$j bY $ $R Y AR }PB8$t8YBI BY b$Y pVi]<wddD Z R$t{ $t htst{$sj s}}j${s$BtR Y$Y JZst$jR Yst (xY $R BP {Bt{t zsT]B% 8YBI $R $tBI $t Y js I$R{ZRR$BtR pVi]<wddD sjT YBZY A Yst zsT]B% s}}Bs{Y IBR tB }PB8 bjj y {st A {Bt{jZII

dM_{V %$Bjs$Bt B{{ZR bYt s Zt s Yst Y R$8sI JZst$j $R sj$9I}

(63)

Ys bYt zsT]B% 8YBI $R -{jZII pVi]<wddD b$Y $R AR }PB8$t YB$9Bt $R bBR Yst Y BY 8BIjR: RZjR PB %t Y$ bBR }PB8$t YB$9BtR ]BtR$I$tY RZjR PB Y 8BIjR b$Y Y$ AR }PB8$tb$tT IBb R$9R R}ssjk PB I$&t JZst$jR pVi]<wddDT $%R Y AR RZjR PB JZst$jR Y$Y Yst (xY JZst$j -{} Y (Y JZst$j Y 8BR -8 Bt PB bY${Y tBtTsIs}$% p_* }PB8R AR VjYBZY sIs}$% p_* $R Y bBR PB (xY JZst$j $ $R Y R{BtI AR 8BIj PB (Y stI (xY JZst$jR

qsAj 1 I$R}jskR Y RZjR PB Y $Y s$j BP ZtR qY zsT]B% 8YBI $R ss$t Y bBR PB Y JZst$jR Y$Y Yst (xY JZst$j pVi]<wddD }PB8R R$t$h{stjk A PB Y$R s$j Yst PB Y jP s$j $t sjj Y JZst$jR Vs$t {BtR$I$tY RZjR PB Y 8BIjR b$Y Y$ AR }PB8$tb$tIBb R$9R R}ssjk PB I$&t JZst$jR Y RZjR s R$8$js -{} PB Y AT pVi]<wddD }PB8st{ VIs}$% p_* $R Y R{BtI AR PB (Y stI (xY JZst$jR bY$j pVi]<wddDT $%R Y AR RZjR PB JZst$jR Y$Y Yst (xY JZst$j -{} Y (Y JZst$j bY ss$t tBtTsIs}$% p_* }PB8R AR <$RB${sj R$8Zjs$Bt $R ss$t st s%s 8BIj

3B %$RZsj$9s$Bt BP Y }PB8st{ BP Y 8BIjR s R$8}j }PB8st{ $tI- { bY${Y }tsj$9R Y -{RR B RYBPsjj BP Y %$Bjs$BtR: s$B js$% B Y $Isj

(64)

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bY { $R Y }PB8st{ $tI- 8 $R Y s BP %$Bjs$Bt BP Y BZ BP Rs8}j JZst$j PB{sRR 8( $R Y $Isj %$Bjs$Bt s bY${Y $R 8( ) d bY } $R Y

}BAsA$j$k BP Y IR$I JZst$j qY 8s-$8Z8 %sjZ BP Y $tI- { $R d PB Y $Isj {sR

qbB R BP }PB8st{ $tI${R s {sj{ZjsI PB s{Y BP Y 8YBIR R}ssjk PB Y jP stI $Y s$jR yt Y {sj{Zjs$Bt BP }PB8st{ $tI${R PB stk Bt BP Y 8BIjR Y RZjR BAs$tI Ak ZR$tY b$tIBb R$9 PB bY${Y Y 8BIj $%R Y AR RZjR PB (Y JZst$j s ZRI qY }PB8st{ $tI${R PB Y jP s$j s I8BtRsI $t 3$Z dx bY$j Y $tI${R PB Y $Y s$j s I$R}jskI $t 3$Z dE qY zsT]B% $R -{jZII $t Y hZR R$t{ $ $%R -8jk ZtRs$RPs{Bk JZst$j R$8sR PB ABY s$jR

(65)

qsAj d zsi z$Bjs$Bt is$BR PB Y NP qs$j BP NB iZtR G$tIBb 7$9 x0 1x0 d0 (x0 (d0 pVi]<wddDT x(( ;;M0 1E(0 d;10 (0 (;0 d((( nM0 11n0 ddM0 (E0 (1d0 1((( nM0 11;0 (;0 (xd0 (110 pVi]<wddD x(( x1;0 nd0 dM0 d1x0 (EE0 d((( ;(0 1Mx0 dMx0 dn;0 (x0 1((( ;0 n;0 1d(0 dx10 (Ex0 zsT]B% x(( x1;0 nx;0 110 dM;0 (E0 d((( xn0 nnE0 1nd0 dE(0 (10 1((( x0 nE0 1n0 1d(0 d(0 <$RB${sj 7$8 x(( xn0 1d0 dEn0 d(M0 WV d((( x;E0 1n0 d110 (E0 (n;0 1((( xE;0 n(;0 dx0 (M0 (;n0 p_* h$t x(( dnn0 1M0 dnx0 (E10 (1M0 d((( E1d0 1n0 ddn0 (E0 (1x0 1((( xx(0 n(;0 dx10 (M(0 (10 WBtTsIs}$% p_* ;;d0 1E;0 dn0 (d0 (d0 3$$t xM

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qsAj 1 zsi z$Bjs$Bt is$BR PB Y i$Y qs$j BP NB iZtR G$tIBb 7$9 x0 1x0 d0 (x0 (d0 pVi]<wddDT x(( n10 dM;0 (;0 (nM0 (1d0 d((( n;0 dMd0 (MM0 (;10 (1d0 1((( nxx0 d;0 (10 (10 (0 pVi]<wddD x(( ;n0 1;0 dn0 (M(0 (1M0 d((( ;Mn0 1E0 d;0 (MM0 (;10 1((( ;0 ndM0 d;0 d(d0 (;n0 zsT]B% x(( ;ME0 n;(0 dM(0 d1x0 (;0 d((( ;(0 nd0 1(E0 d;n0 (x0 1((( x;n0 nE10 1xn0 dMM0 (;0 <$RB${sj 7$8 x(( x;x0 nd10 dxn0 (Mn0 WV d((( xn0 1Mx0 dn;0 (M;0 (n;0 1((( E(M0 10 d;0 dn0 (xM0 p_* h$t x(( d(1(0 n(0 d1M0 (xE0 (1M0 d((( E(0 1Md0 d110 (En0 (10 1((( xn0 10 d;0 d(d0 (10 WBtTsIs}$% p_* nM0 1x10 d;n0 (E0 (dn0 3$$t x

Extreme value theory and risk management in financial markets

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