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Mo
del
ing
Cli
ent
Rat
e an
d V
olu
mes
Mo
del
ing
Cli
ent
Rat
e an
d V
olu
mes
Mo
del
ing
Cli
ent
Rat
e an
d V
olu
mes
of
No
n-m
atu
rin
g A
cco
un
tso
f N
on
-mat
uri
ng
Acc
ou
nts
of
No
n-m
atu
rin
g A
cco
un
ts
Co
mp
uta
tio
nal
Man
agem
ent
Sci
ence
Co
nfe
ren
ce,
Co
mp
uta
tio
nal
Man
agem
ent
Sci
ence
Co
nfe
ren
ce,
Gen
eva,
May
200
9G
enev
a, M
ay 2
009
Gen
eva,
May
200
9
Cli
ent
Rat
e an
d V
olu
mes
Cli
ent
Rat
e an
d V
olu
mes
Cli
ent
Rat
e an
d V
olu
mes
mat
uri
ng
Acc
ou
nts
mat
uri
ng
Acc
ou
nts
mat
uri
ng
Acc
ou
nts
Co
mp
uta
tio
nal
Man
agem
ent
Sci
ence
Co
nfe
ren
ce,
Co
mp
uta
tio
nal
Man
agem
ent
Sci
ence
Co
nfe
ren
ce,
Gen
eva,
May
200
9G
enev
a, M
ay 2
009
Gen
eva,
May
200
9
Flo
ren
tin
a P
ara
sch
ivF
lore
nti
na
Pa
rasc
hiv
Mic
ha
el
Sch
ürl
eM
ich
ae
l S
chü
rle
Mo
del
ing
cli
ent
rate
Ag
end
aM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 2
Ag
end
aan
dv
olu
mes
of
NM
AP
age
2A
gen
da
•P
rob
lem
sta
tem
ent:
No
n-m
atu
rin
g A
cco
un
ts (
•P
rob
lem
sta
tem
ent:
No
n-m
atu
rin
g A
cco
un
ts (
•P
rob
lem
sta
tem
ent:
No
n-m
atu
rin
g A
cco
un
ts (
•M
oti
vat
ion
: M
ult
ista
ge
Sto
chas
tic
Pro
gra
mm
ing
•
Mo
tiv
atio
n:
Mu
ltis
tag
e S
toch
asti
c P
rog
ram
min
g
Mo
del
/Dy
nam
ic r
epli
cati
ng
po
rtfo
lio
ap
pro
ach
•M
oti
vat
ion
: M
ult
ista
ge
Sto
chas
tic
Pro
gra
mm
ing
M
od
el/D
yn
amic
rep
lica
tin
g p
ort
foli
o a
pp
roac
hM
od
el/D
yn
amic
rep
lica
tin
g p
ort
foli
o a
pp
roac
h
•C
lien
t ra
te m
od
el s
pec
ific
atio
n a
nd
res
ult
s•
Cli
ent
rate
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
•C
lien
t ra
te m
od
el s
pec
ific
atio
n a
nd
res
ult
s
•V
olu
mes
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
•V
olu
mes
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
•V
olu
mes
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
•C
ase
stu
dy
•C
ase
stu
dy
•C
ase
stu
dy
•C
on
clu
sio
n•
Co
ncl
usi
on
•C
on
clu
sio
n
mat
uri
ng
Acc
ou
nts
(N
MA
)m
atu
rin
g A
cco
un
ts (
NM
A)
mat
uri
ng
Acc
ou
nts
(N
MA
)
Mo
tiv
atio
n:
Mu
ltis
tag
e S
toch
asti
c P
rog
ram
min
g
Mo
tiv
atio
n:
Mu
ltis
tag
e S
toch
asti
c P
rog
ram
min
g
Mo
del
/Dy
nam
ic r
epli
cati
ng
po
rtfo
lio
ap
pro
ach
Mo
tiv
atio
n:
Mu
ltis
tag
e S
toch
asti
c P
rog
ram
min
g
Mo
del
/Dy
nam
ic r
epli
cati
ng
po
rtfo
lio
ap
pro
ach
Mo
del
/Dy
nam
ic r
epli
cati
ng
po
rtfo
lio
ap
pro
ach
Cli
ent
rate
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
Cli
ent
rate
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
Cli
ent
rate
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
Vo
lum
es m
od
el s
pec
ific
atio
n a
nd
res
ult
sV
olu
mes
mo
del
sp
ecif
icat
ion
an
d r
esu
lts
Vo
lum
es m
od
el s
pec
ific
atio
n a
nd
res
ult
s
Mo
del
ing
cli
ent
rate
Sim
pli
fied
ban
kb
alan
ceM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 3
Sim
pli
fied
ban
kb
alan
cean
dv
olu
mes
of
NM
AP
age
3S
imp
lifi
edb
ank
bal
ance
No
n-m
atu
rin
gac
cou
nts
:
•C
on
trac
tual
mat
uri
ty n
ot
spec
ifie
d
No
n-m
atu
rin
gac
cou
nts
:
•C
on
trac
tual
mat
uri
ty n
ot
spec
ifie
d
•C
on
trac
tual
mat
uri
ty n
ot
spec
ifie
d
•T
wo
op
tio
ns:
•T
wo
op
tio
ns:
•T
wo
op
tio
ns:
–C
lien
ts: o
pti
on
to
wit
hd
raw
liq
uid
ity
or
pre
pay
–
Cli
ents
: op
tio
n t
o w
ith
dra
w l
iqu
idit
y o
r p
rep
ay
cred
its/
mo
rtg
ages
cred
its/
mo
rtg
ages
–B
ank
: op
tio
n t
o a
dju
st c
lien
t ra
te
cred
its/
mo
rtg
ages
–B
ank
: op
tio
n t
o a
dju
st c
lien
t ra
te–
Ban
k: o
pti
on
to
ad
just
cli
ent
rate
•V
olu
me
may
flu
ctu
ate
sig
nif
ican
tly
, oft
en d
epen
din
g o
n t
he
lev
el o
f •
Vo
lum
e m
ay f
luct
uat
e si
gn
ific
antl
y, o
ften
dep
end
ing
on
th
e le
vel
of
ob
serv
ed i
nte
rest
rat
es•
Vo
lum
e m
ay f
luct
uat
e si
gn
ific
antl
y, o
ften
dep
end
ing
on
th
e le
vel
of
ob
serv
ed i
nte
rest
rat
eso
bse
rved
in
tere
st r
ates
•F
utu
re c
ash
flo
ws
are
un
cert
ain
•F
utu
re c
ash
flo
ws
are
un
cert
ain
•F
utu
re c
ash
flo
ws
are
un
cert
ain
bal
ance
.No
n-m
atu
rin
gac
cou
nts
bal
ance
.No
n-m
atu
rin
gac
cou
nts
bal
ance
.No
n-m
atu
rin
gac
cou
nts
AL
No
n-m
atu
rin
g a
cco
un
tsN
on
-mat
uri
ng
acc
ou
nts
AL
No
n-m
atu
rin
g a
cco
un
ts•
ov
erd
raft
fac
ilit
ies
No
n-m
atu
rin
g a
cco
un
ts•
sav
ing
s ac
cou
nts
•o
ver
dra
ft f
acil
itie
s•
no
n-f
ixed
mo
rtg
ages
•sa
vin
gs
acco
un
ts•
sig
ht
dep
osi
ts•
no
n-f
ixed
mo
rtg
ages
•o
ther
var
iab
le l
oan
s•
sig
ht
dep
osi
ts
Fix
ed-i
nco
me
po
siti
on
s:F
ixed
-in
com
e p
osi
tio
ns:
•sa
vin
gs
cert
ific
ates
Fix
ed-i
nco
me
po
siti
on
s:•
cred
its
•sa
vin
gs
cert
ific
ates
•is
sued
bo
nd
s•
cred
its
•fi
x-r
ate
mo
rtg
ages
•is
sued
bo
nd
s•
fix
-rat
e m
ort
gag
es•
bo
nd
sO
ther
lia
bil
itie
s•
bo
nd
s
Oth
er a
sset
s
Oth
er l
iab
ilit
ies
Equ
ity
capi
tal
Oth
er a
sset
sE
quit
y ca
pita
l
Co
ntr
actu
al m
atu
rity
no
t sp
ecif
ied
C
on
trac
tual
mat
uri
ty n
ot
spec
ifie
d
Co
ntr
actu
al m
atu
rity
no
t sp
ecif
ied
Cli
ents
: op
tio
n t
o w
ith
dra
w l
iqu
idit
y o
r p
rep
ay
Cli
ents
: op
tio
n t
o w
ith
dra
w l
iqu
idit
y o
r p
rep
ay
Ban
k: o
pti
on
to
ad
just
cli
ent
rate
Ban
k: o
pti
on
to
ad
just
cli
ent
rate
Ban
k: o
pti
on
to
ad
just
cli
ent
rate
Vo
lum
e m
ay f
luct
uat
e si
gn
ific
antl
y, o
ften
dep
end
ing
on
th
e le
vel
of
Vo
lum
e m
ay f
luct
uat
e si
gn
ific
antl
y, o
ften
dep
end
ing
on
th
e le
vel
of
Vo
lum
e m
ay f
luct
uat
e si
gn
ific
antl
y, o
ften
dep
end
ing
on
th
e le
vel
of
Fu
ture
cas
h f
low
s ar
e u
nce
rtai
nF
utu
re c
ash
flo
ws
are
un
cert
ain
Fu
ture
cas
h f
low
s ar
e u
nce
rtai
n
Mo
del
ing
cli
ent
rate
Mo
del
ing
NM
A: M
arg
in O
pti
miz
erM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 4
Mo
del
ing
NM
A: M
arg
in O
pti
miz
eran
dv
olu
mes
of
NM
AP
age
4M
od
elin
g N
MA
: Mar
gin
Op
tim
izer
•D
yn
amic
mo
del
ing
an
d o
pti
miz
atio
n o
f •
Dy
nam
ic m
od
elin
g a
nd
op
tim
izat
ion
of
•D
yn
amic
mo
del
ing
an
d o
pti
miz
atio
n o
f
•M
ult
ista
ge
sto
chas
tic
pro
gra
mm
ing
mo
del
th
at d
eter
min
es
•M
ult
ista
ge
sto
chas
tic
pro
gra
mm
ing
mo
del
th
at d
eter
min
es
an o
pti
mal
rep
lica
tin
g p
ort
foli
o f
rom
sce
nar
ios
for
futu
re
•M
ult
ista
ge
sto
chas
tic
pro
gra
mm
ing
mo
del
th
at d
eter
min
es
an o
pti
mal
rep
lica
tin
g p
ort
foli
o f
rom
sce
nar
ios
for
futu
re
an o
pti
mal
rep
lica
tin
g p
ort
foli
o f
rom
sce
nar
ios
for
futu
re
ou
tco
mes
of
the
rele
van
t ri
sk f
acto
rs:
ou
tco
mes
of
the
rele
van
t ri
sk f
acto
rs:
ou
tco
mes
of
the
rele
van
t ri
sk f
acto
rs:
−m
ark
et r
ates
−m
ark
et r
ates
−cl
ien
t ra
tes
−cl
ien
t ra
tes
−cl
ien
t ra
tes
−v
olu
mes
−
vo
lum
es
•R
eali
stic
cli
ent
rate
an
d v
olu
mes
mo
del
s ar
e re
qu
ired
•R
eali
stic
cli
ent
rate
an
d v
olu
mes
mo
del
s ar
e re
qu
ired
•R
eali
stic
cli
ent
rate
an
d v
olu
mes
mo
del
s ar
e re
qu
ired
: Mar
gin
Op
tim
izer
: Mar
gin
Op
tim
izer
: Mar
gin
Op
tim
izer
Dy
nam
ic m
od
elin
g a
nd
op
tim
izat
ion
of
NM
AD
yn
amic
mo
del
ing
an
d o
pti
miz
atio
n o
f N
MA
Dy
nam
ic m
od
elin
g a
nd
op
tim
izat
ion
of
NM
A
Mu
ltis
tag
e st
och
asti
c p
rog
ram
min
g m
od
el t
hat
det
erm
ines
M
ult
ista
ge
sto
chas
tic
pro
gra
mm
ing
mo
del
th
at d
eter
min
es
an o
pti
mal
rep
lica
tin
g p
ort
foli
o f
rom
sce
nar
ios
for
futu
re
Mu
ltis
tag
e st
och
asti
c p
rog
ram
min
g m
od
el t
hat
det
erm
ines
an
op
tim
al r
epli
cati
ng
po
rtfo
lio
fro
m s
cen
ario
s fo
r fu
ture
an
op
tim
al r
epli
cati
ng
po
rtfo
lio
fro
m s
cen
ario
s fo
r fu
ture
o
utc
om
es o
f th
e re
lev
ant
risk
fac
tors
:o
utc
om
es o
f th
e re
lev
ant
risk
fac
tors
:o
utc
om
es o
f th
e re
lev
ant
risk
fac
tors
:
Rea
list
ic c
lien
t ra
te a
nd
vo
lum
es m
od
els
are
req
uir
edR
eali
stic
cli
ent
rate
an
d v
olu
mes
mo
del
s ar
e re
qu
ired
Rea
list
ic c
lien
t ra
te a
nd
vo
lum
es m
od
els
are
req
uir
ed
Mo
del
ing
cli
ent
rate
Cli
ent
rate
an
d v
olu
mes
of
the
sav
ing
s ac
cou
nts
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
5C
lien
t ra
te a
nd
vo
lum
es o
f th
e sa
vin
gs
acco
un
tsan
dv
olu
mes
of
NM
AP
age
5C
lien
t ra
te a
nd
vo
lum
es o
f th
e sa
vin
gs
acco
un
ts
Av
era
ge
of
the
cli
en
t ra
te a
nd
vo
lum
es
of
the
swis
s b
ank
s' s
avin
gs
acco
un
ts
of
the
swis
s b
ank
s' s
avin
gs
acco
un
ts
1011 910 89 78
client rate
6
client rate
5
client rate
34 23 12 01
01.01.1988
01.08.1988
01.03.1989
01.10.1989
01.05.1990
01.12.1990
01.07.1991
01.02.1992
01.09.1992
01.04.1993
01.11.1993
01.06.1994
01.01.1995
01.01.1988
01.08.1988
01.03.1989
01.10.1989
01.05.1990
01.12.1990
01.07.1991
01.02.1992
01.09.1992
01.04.1993
01.11.1993
01.06.1994
01.01.1995
01.01.1988
01.08.1988
01.03.1989
01.10.1989
01.05.1990
01.12.1990
01.07.1991
01.02.1992
01.09.1992
01.04.1993
01.11.1993
01.06.1994
01.01.1995
BB
CH
F1
MB
BC
HF
3M
ICC
HF
4Y
ICC
HF
5Y
•C
lien
t ra
te:
•C
lien
t ra
te:
•C
lien
t ra
te:
−as
ym
met
ric
adju
stm
ent
to t
he
mar
ket
rat
es−
asy
mm
etri
c ad
just
men
t to
th
e m
ark
et r
ates
−ri
gid
ity
(d
elay
in
th
e cl
ien
t ra
te's
ad
just
men
t to
mar
ket
rat
es)
−ri
gid
ity
(d
elay
in
th
e cl
ien
t ra
te's
ad
just
men
t to
mar
ket
rat
es)
−ri
gid
ity
(d
elay
in
th
e cl
ien
t ra
te's
ad
just
men
t to
mar
ket
rat
es)
•V
olu
mes
: neg
ativ
e co
rrel
atio
n w
ith
th
e m
ark
et r
ates
•V
olu
mes
: neg
ativ
e co
rrel
atio
n w
ith
th
e m
ark
et r
ates
Cli
ent
rate
an
d v
olu
mes
of
the
sav
ing
s ac
cou
nts
Cli
ent
rate
an
d v
olu
mes
of
the
sav
ing
s ac
cou
nts
Cli
ent
rate
an
d v
olu
mes
of
the
sav
ing
s ac
cou
nts
Av
era
ge
of
the
cli
en
t ra
te a
nd
vo
lum
es
of
the
swis
s b
ank
s' s
avin
gs
acco
un
ts
of
the
swis
s b
ank
s' s
avin
gs
acco
un
ts
data
sou
rce:
Sw
iss
Nat
ion
al B
ank
250'
000
data
sou
rce:
Sw
iss
Nat
ion
al B
ank
200'
000
200'
000
(millions Francs)
150'
000
(millions Francs)
150'
000
(millions Francs)
100'
000
volumes (millions Francs)
100'
000
volumes
50'0
00
0
01.01.1995
01.08.1995
01.03.1996
01.10.1996
01.05.1997
01.12.1997
01.07.1998
01.02.1999
01.09.1999
01.04.2000
01.11.2000
01.06.2001
01.01.2002
01.08.2002
01.03.2003
01.10.2003
01.05.2004
01.12.2004
01.07.2005
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01.09.2006
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BB
CH
F6
MB
BC
HF
12
ICC
HF
2Y
ICC
HF
3Y
Cli
en
t ra
teV
olu
me
sIC
CH
F7
YIC
CH
F1
0C
lie
nt
rate
Vo
lum
es
asy
mm
etri
c ad
just
men
t to
th
e m
ark
et r
ates
asy
mm
etri
c ad
just
men
t to
th
e m
ark
et r
ates
rig
idit
y (
del
ay i
n t
he
clie
nt
rate
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dju
stm
ent
to m
ark
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ates
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gid
ity
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elay
in
th
e cl
ien
t ra
te's
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just
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t to
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ket
rat
es)
rig
idit
y (
del
ay i
n t
he
clie
nt
rate
's a
dju
stm
ent
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ark
et r
ates
)
Vo
lum
es: n
egat
ive
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elat
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wit
h t
he
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ket
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esV
olu
mes
: neg
ativ
e co
rrel
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n w
ith
th
e m
ark
et r
ates
Mo
del
ing
cli
ent
rate
Asy
mm
etry
in
th
e L
iter
atu
reM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 6
Asy
mm
etry
in
th
e L
iter
atu
rean
dv
olu
mes
of
NM
AP
age
6A
sym
met
ry i
n t
he
Lit
erat
ure
•H
ann
anan
d B
erge
r (1
991)
, Au
sube
l•
Han
nan
and
Ber
ger
(199
1), A
usu
bel
asy
mm
etri
c m
od
el f
or
dep
osi
t re
nts
bas
ed o
n c
on
sum
er s
earc
h
•H
ann
anan
d B
erge
r (1
991)
, Au
sube
las
ym
met
ric
mo
del
fo
r d
epo
sit
ren
ts b
ased
on
co
nsu
mer
sea
rch
as
ym
met
ric
mo
del
fo
r d
epo
sit
ren
ts b
ased
on
co
nsu
mer
sea
rch
co
sts
cost
s
•K
ahn
, Pen
nac
chi,
Sop
ran
zett
i•
Kah
n, P
enn
acch
i, S
opra
nze
tti
qu
anti
tati
ve
dis
cret
enes
s in
dep
osi
t ra
tes
adju
stm
ents
, bu
t th
ere'
s q
uan
tita
tiv
e d
iscr
eten
ess
in d
epo
sit
rate
s ad
just
men
ts, b
ut
ther
e's
no
ex
pla
nat
ion
fo
r th
e as
ym
met
ryq
uan
tita
tiv
e d
iscr
eten
ess
in d
epo
sit
rate
s ad
just
men
ts, b
ut
ther
e's
no
ex
pla
nat
ion
fo
r th
e as
ym
met
ryn
o e
xp
lan
atio
n f
or
the
asy
mm
etry
•D
uek
er(2
000)
: ex
pla
nat
ion
s fo
r as
ym
met
ric
adju
stm
ent
in t
he
•D
uek
er(2
000)
: ex
pla
nat
ion
s fo
r as
ym
met
ric
adju
stm
ent
in t
he
•D
uek
er(2
000)
: ex
pla
nat
ion
s fo
r as
ym
met
ric
adju
stm
ent
in t
he
con
tex
t o
f lo
an r
ates
con
tex
t o
f lo
an r
ates
•O
'Bri
en (
2000
): f
irst
wh
o d
eriv
es a
n i
nte
rest
ing
pro
per
ty o
f th
e •
O'B
rien
(20
00):
fir
st w
ho
der
ives
an
in
tere
stin
g p
rop
erty
of
the
•O
'Bri
en (
2000
): f
irst
wh
o d
eriv
es a
n i
nte
rest
ing
pro
per
ty o
f th
e as
ym
met
ry:
asy
mm
etry
:as
ym
met
ry:
[]
[]
1max
,0e
eER
ER
ER
R
=
−−
−
[
]1
max
,0t
rtt
rtR
tt
ER
ER
ER
R
=
−−
−
–
equ
ilib
riu
m d
epo
sit
rate
co
nd
itio
nal
on
a m
ark
et r
ate
–eq
uil
ibri
um
dep
osi
t ra
te c
on
dit
ion
al o
n a
mar
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ilib
riu
m d
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rate
co
nd
itio
nal
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ate
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etry
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th
e L
iter
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n t
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erat
ure
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mm
etry
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e L
iter
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re
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sube
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ficu
ltie
s in
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pla
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g
Au
sube
l(1
992)
:dif
ficu
ltie
s in
ex
pla
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asy
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etri
c m
od
el f
or
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osi
t re
nts
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ed o
n c
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er s
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h
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sube
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992)
:dif
ficu
ltie
s in
ex
pla
inin
g
asy
mm
etri
c m
od
el f
or
dep
osi
t re
nts
bas
ed o
n c
on
sum
er s
earc
h
asy
mm
etri
c m
od
el f
or
dep
osi
t re
nts
bas
ed o
n c
on
sum
er s
earc
h
Sop
ran
zett
i(1
999)
: ex
pla
in t
he
tem
po
ral
and
S
opra
nze
tti
(199
9): e
xp
lain
th
e te
mp
ora
l an
d
qu
anti
tati
ve
dis
cret
enes
s in
dep
osi
t ra
tes
adju
stm
ents
, bu
t th
ere'
s q
uan
tita
tiv
e d
iscr
eten
ess
in d
epo
sit
rate
s ad
just
men
ts, b
ut
ther
e's
no
ex
pla
nat
ion
fo
r th
e as
ym
met
ryq
uan
tita
tiv
e d
iscr
eten
ess
in d
epo
sit
rate
s ad
just
men
ts, b
ut
ther
e's
no
ex
pla
nat
ion
fo
r th
e as
ym
met
ryn
o e
xp
lan
atio
n f
or
the
asy
mm
etry
(200
0): e
xp
lan
atio
ns
for
asy
mm
etri
c ad
just
men
t in
th
e (2
000)
: ex
pla
nat
ion
s fo
r as
ym
met
ric
adju
stm
ent
in t
he
(200
0): e
xp
lan
atio
ns
for
asy
mm
etri
c ad
just
men
t in
th
e
(200
0): f
irst
wh
o d
eriv
es a
n i
nte
rest
ing
pro
per
ty o
f th
e (2
000)
: fir
st w
ho
der
ives
an
in
tere
stin
g p
rop
erty
of
the
(200
0): f
irst
wh
o d
eriv
es a
n i
nte
rest
ing
pro
per
ty o
f th
e
{}
λ+
{}
1max
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eER
ER
ER
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+
−
=−
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1max
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tt
ER
ER
ER
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−
=
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eq
uil
ibri
um
dep
osi
t ra
te c
on
dit
ion
al o
n a
mar
ket
rat
e
λ
eq
uil
ibri
um
dep
osi
t ra
te c
on
dit
ion
al o
n a
mar
ket
rat
eeq
uil
ibri
um
dep
osi
t ra
te c
on
dit
ion
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n a
mar
ket
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e
e=
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Mo
del
ing
cli
ent
rate
Eq
uil
ibri
um
dep
osi
t ra
tes
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
7E
qu
ilib
riu
m d
epo
sit
rate
san
dv
olu
mes
of
NM
AP
age
7E
qu
ilib
riu
m d
epo
sit
rate
s
•C
om
mo
n p
ract
ice:
rel
ate
the
dep
osi
t ra
tes
to a
sh
ort
ter
m i
nte
rest
•
Co
mm
on
pra
ctic
e: r
elat
e th
e d
epo
sit
rate
s to
a s
ho
rt t
erm
in
tere
st
rate
, ass
um
ing
dep
osi
tors
wer
e co
nce
rned
wit
h o
pp
ort
un
ity
co
sts
•C
om
mo
n p
ract
ice:
rel
ate
the
dep
osi
t ra
tes
to a
sh
ort
ter
m i
nte
rest
ra
te, a
ssu
min
g d
epo
sito
rs w
ere
con
cern
ed w
ith
op
po
rtu
nit
y c
ost
sra
te, a
ssu
min
g d
epo
sito
rs w
ere
con
cern
ed w
ith
op
po
rtu
nit
y c
ost
s
agai
nst
em
pir
ical
ev
iden
ceag
ain
st e
mp
iric
al e
vid
ence
•W
e re
late
th
e id
ea o
f eq
uil
ibri
um
to
th
e co
mm
on
tre
nd
of
dep
osi
t •
We
rela
te t
he
idea
of
equ
ilib
riu
m t
o t
he
com
mo
n t
ren
d o
f d
epo
sit
•W
e re
late
th
e id
ea o
f eq
uil
ibri
um
to
th
e co
mm
on
tre
nd
of
dep
osi
t ra
tes
and
mar
ket
rat
es (
incl
ud
ing
als
o a
lo
ng
er m
atu
rity
)ra
tes
and
mar
ket
rat
es (
incl
ud
ing
als
o a
lo
ng
er m
atu
rity
)
stu
dy
st
ud
y
Joh
an
sen
Jo
ha
nse
n
Sy
stem
Vect
or
Sy
stem
Vect
or
Cli
en
t C
lien
t
rate
1.0
00
rate
1.0
00
-0.2
95
Lib
or
3m
-0.2
95
(0.0
85)
(0.0
85)
Sw
ap
5y
-0.6
95
Sw
ap
5y
-0.6
95
(0.1
23)
Co
nst
an
t1
.37
8
(0.2
37)
Co
nst
an
t(0
.237
)
Eq
uil
ibri
um
dep
osi
t ra
tes
Eq
uil
ibri
um
dep
osi
t ra
tes
Eq
uil
ibri
um
dep
osi
t ra
tes
Co
mm
on
pra
ctic
e: r
elat
e th
e d
epo
sit
rate
s to
a s
ho
rt t
erm
in
tere
st
Co
mm
on
pra
ctic
e: r
elat
e th
e d
epo
sit
rate
s to
a s
ho
rt t
erm
in
tere
st
assu
min
g d
epo
sito
rs w
ere
con
cern
ed w
ith
op
po
rtu
nit
y c
ost
sC
om
mo
n p
ract
ice:
rel
ate
the
dep
osi
t ra
tes
to a
sh
ort
ter
m i
nte
rest
as
sum
ing
dep
osi
tors
wer
e co
nce
rned
wit
h o
pp
ort
un
ity
co
sts
assu
min
g d
epo
sito
rs w
ere
con
cern
ed w
ith
op
po
rtu
nit
y c
ost
s
agai
nst
em
pir
ical
ev
iden
ceag
ain
st e
mp
iric
al e
vid
ence
We
rela
te t
he
idea
of
equ
ilib
riu
m t
o t
he
com
mo
n t
ren
d o
f d
epo
sit
We
rela
te t
he
idea
of
equ
ilib
riu
m t
o t
he
com
mo
n t
ren
d o
f d
epo
sit
We
rela
te t
he
idea
of
equ
ilib
riu
m t
o t
he
com
mo
n t
ren
d o
f d
epo
sit
rate
s an
d m
ark
et r
ates
(in
clu
din
g a
lso
a l
on
ger
mat
uri
ty)
rate
s an
d m
ark
et r
ates
(in
clu
din
g a
lso
a l
on
ger
mat
uri
ty)
stu
dy
co
inte
gra
tio
nst
ud
y c
oin
teg
rati
on
Joh
an
sen
co
inte
gra
tio
nte
st r
esu
lts
Joh
an
sen
co
inte
gra
tio
nte
st r
esu
lts
Vect
or
Eig
en
valu
e
Tra
ce
stati
stic
Lag
sV
ect
or
valu
est
ati
stic
Lag
s
0.1
58
58
.47
74
0.1
58
58
.47
74
(0.0
85)
(0.0
85)
(0.1
23)
(0.2
37)
(0.2
37)
Mo
del
ing
cli
ent
rate
Th
resh
old
mo
del
in
err
or
corr
ecti
on
fo
rmM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 8
Th
resh
old
mo
del
in
err
or
corr
ecti
on
fo
rman
dv
olu
mes
of
NM
AP
age
8T
hre
sho
ld m
od
el i
n e
rro
r co
rrec
tio
n f
orm
•In
der
ivin
g t
he
clie
nt
rate
mo
del
, we
tak
e in
to a
cco
un
t it
s d
evia
tio
ns
•In
der
ivin
g t
he
clie
nt
rate
mo
del
, we
tak
e in
to a
cco
un
t it
s d
evia
tio
ns
fro
m t
he
equ
ilib
riu
m l
evel
(er
ror
corr
ecti
on
ter
m d
eriv
ed f
rom
th
e fr
om
th
e eq
uil
ibri
um
lev
el (
erro
r co
rrec
tio
n t
erm
der
ived
fro
m t
he
fro
m t
he
equ
ilib
riu
m l
evel
(er
ror
corr
ecti
on
ter
m d
eriv
ed f
rom
th
e co
inte
gra
tin
gv
ecto
r)co
inte
gra
tin
gv
ecto
r)
•W
e ch
eck
fo
r th
e as
ym
met
ry b
y a
llo
win
g t
he
par
amet
er f
or
the
mar
ket
•
We
chec
k f
or
the
asy
mm
etry
by
all
ow
ing
th
e p
aram
eter
fo
r th
e m
ark
et
rate
s to
dif
fer
wh
en t
hey
are
ab
ov
e o
r b
elo
w s
om
e es
tim
atin
g t
hre
sho
ld•
We
chec
k f
or
the
asy
mm
etry
by
all
ow
ing
th
e p
aram
eter
fo
r th
e m
ark
et
rate
s to
dif
fer
wh
en t
hey
are
ab
ov
e o
r b
elo
w s
om
e es
tim
atin
g t
hre
sho
ldra
tes
to d
iffe
r w
hen
th
ey a
re a
bo
ve
or
bel
ow
so
me
esti
mat
ing
th
resh
old
short
long
RR
rr
EC
αβ
ββ
δλϖ
ε∆
=+
∆+
∆+
∆+
++
11
21
31
11
short
long
tt
tt
tt
tR
Rr
rEC
αβ
ββ
δλϖ
ε−
−−
−−
∆=
+∆
+∆
+∆
++
+1
12
13
11
1t
tt
tt
tt
−−
−−
−
−ch
ang
e in
th
e d
epo
sit
rate
tR
∆−
chan
ge
in t
he
dep
osi
t ra
te
−la
gg
ed c
han
ge
in t
he
mar
ket
rat
e
tR
∆ r∆−
lag
ged
ch
ang
e in
th
e m
ark
et r
ate
−la
gg
ed e
rro
r-co
rrec
tio
n t
erm
1tr −∆ EC
−la
gg
ed e
rro
r-co
rrec
tio
n t
erm
−ra
nd
om
i.i
.d. d
istu
rban
ceε
1t
EC
−
−ra
nd
om
i.i
.d. d
istu
rban
cetε tε
•T
he
var
iab
le
c
aptu
res
the
thre
sho
ld e
ffec
t, w
her
e
is
the
[]
Iϖ
ωω
τ=
≤•
Th
e v
aria
ble
cap
ture
s th
e th
resh
old
eff
ect,
wh
ere
i
s th
e th
resh
old
var
iab
le,
i
s th
e u
nk
no
wn
th
resh
old
var
iab
le a
nd
th
e [
]1
11
tt
tI
ϖω
ωτ
−−
−=
≤
τth
resh
old
var
iab
le,
i
s th
e u
nk
no
wn
th
resh
old
var
iab
le a
nd
th
e in
dic
ato
r fu
nct
ion
is
def
ined
as:
τth
resh
old
var
iab
le,
i
s th
e u
nk
no
wn
th
resh
old
var
iab
le a
nd
th
e in
dic
ato
r fu
nct
ion
is
def
ined
as:
τin
dic
ato
r fu
nct
ion
is
def
ined
as:
[[1
tIω
τ−≤
=[
1t
Iω
τ−≤
=
Th
resh
old
mo
del
in
err
or
corr
ecti
on
fo
rmT
hre
sho
ld m
od
el i
n e
rro
r co
rrec
tio
n f
orm
Th
resh
old
mo
del
in
err
or
corr
ecti
on
fo
rm
In d
eriv
ing
th
e cl
ien
t ra
te m
od
el, w
e ta
ke
into
acc
ou
nt
its
dev
iati
on
s In
der
ivin
g t
he
clie
nt
rate
mo
del
, we
tak
e in
to a
cco
un
t it
s d
evia
tio
ns
fro
m t
he
equ
ilib
riu
m l
evel
(er
ror
corr
ecti
on
ter
m d
eriv
ed f
rom
th
e fr
om
th
e eq
uil
ibri
um
lev
el (
erro
r co
rrec
tio
n t
erm
der
ived
fro
m t
he
fro
m t
he
equ
ilib
riu
m l
evel
(er
ror
corr
ecti
on
ter
m d
eriv
ed f
rom
th
e
We
chec
k f
or
the
asy
mm
etry
by
all
ow
ing
th
e p
aram
eter
fo
r th
e m
ark
et
We
chec
k f
or
the
asy
mm
etry
by
all
ow
ing
th
e p
aram
eter
fo
r th
e m
ark
et
rate
s to
dif
fer
wh
en t
hey
are
ab
ov
e o
r b
elo
w s
om
e es
tim
atin
g t
hre
sho
ldW
e ch
eck
fo
r th
e as
ym
met
ry b
y a
llo
win
g t
he
par
amet
er f
or
the
mar
ket
ra
tes
to d
iffe
r w
hen
th
ey a
re a
bo
ve
or
bel
ow
so
me
esti
mat
ing
th
resh
old
rate
s to
dif
fer
wh
en t
hey
are
ab
ov
e o
r b
elo
w s
om
e es
tim
atin
g t
hre
sho
ld
short
long
RR
rr
EC
αβ
ββ
δλϖ
ε∆
=+
∆+
∆+
∆+
++
11
21
31
11
short
long
tt
tt
tt
tR
Rr
rEC
αβ
ββ
δλϖ
ε−
−−
−−
∆=
+∆
+∆
+∆
++
+1
12
13
11
1t
tt
tt
tt
−−
−−
−
lag
ged
ch
ang
e in
th
e m
ark
et r
ate
lag
ged
ch
ang
e in
th
e m
ark
et r
ate
corr
ecti
on
ter
mco
rrec
tio
n t
erm
Th
e v
aria
ble
cap
ture
s th
e th
resh
old
eff
ect,
wh
ere
i
s th
e ω
Th
e v
aria
ble
cap
ture
s th
e th
resh
old
eff
ect,
wh
ere
i
s th
e th
resh
old
var
iab
le,
i
s th
e u
nk
no
wn
th
resh
old
var
iab
le a
nd
th
e ωth
resh
old
var
iab
le,
i
s th
e u
nk
no
wn
th
resh
old
var
iab
le a
nd
th
e in
dic
ato
r fu
nct
ion
is
def
ined
as:
thre
sho
ld v
aria
ble
,
is
the
un
kn
ow
n t
hre
sho
ld v
aria
ble
an
d t
he
ind
icat
or
fun
ctio
n i
s d
efin
ed a
s:in
dic
ato
r fu
nct
ion
is
def
ined
as: ]
0 for ω
τ>
]1
1
0 for
tω
τω
τ−>
≤=
]
1
1
1 for
t
ωτ
ωτ
−
≤=
≤
11 for
tω
τ−≤
Mo
del
ing
cli
ent
rate
Th
resh
old
est
imat
ion
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
9T
hre
sho
ld e
stim
atio
nan
dv
olu
mes
of
NM
AP
age
9T
hre
sho
ld e
stim
atio
n
•W
e ap
ply
Han
sen
's g
rid
sea
rch
(19
96)
to l
oca
te t
he
mo
st l
ikel
y
•W
e ap
ply
Han
sen
's g
rid
sea
rch
(19
96)
to l
oca
te t
he
mo
st l
ikel
y
thre
sho
ld v
alu
e in
th
e m
ark
et r
ates
or
erro
r co
rrec
tio
n t
erm
•W
e ap
ply
Han
sen
's g
rid
sea
rch
(19
96)
to l
oca
te t
he
mo
st l
ikel
y
thre
sho
ld v
alu
e in
th
e m
ark
et r
ates
or
erro
r co
rrec
tio
n t
erm
thre
sho
ld v
alu
e in
th
e m
ark
et r
ates
or
erro
r co
rrec
tio
n t
erm
–M
od
el p
aram
eter
s ar
e es
tim
ated
by
–
Mo
del
par
amet
ers
are
esti
mat
ed b
y
–M
od
el p
aram
eter
s ar
e es
tim
ated
by
⌢
argmin
ττ
=⌢
argmin
ττ
=
–W
e ap
ply
th
e li
kel
iho
od
rat
io s
tati
stic
to
tes
t–
We
app
ly t
he
lik
elih
oo
d r
atio
sta
tist
ic t
o t
est
(LR
nτ (
nLR
nτ (
nLR
nτ
–p-
val
ues
are
der
ived
:–
p-v
alu
es a
re d
eriv
ed: p
LR
=−
−−
nn
pLR
=−
−−
nn
pLR
=−
−−
Sh
ort
ra
teS
ho
rt r
ate
(1
short
trω
−=
Th
resh
old
val
ue
0.46
8
(1
trω
−=
Th
resh
old
val
ue
0.46
8
p-v
alu
e0.
262
p-v
alu
e0.
262
Th
resh
old
est
imat
ion
Th
resh
old
est
imat
ion
Th
resh
old
est
imat
ion
We
app
ly H
anse
n's
gri
d s
earc
h (
1996
) to
lo
cate
th
e m
ost
lik
ely
W
e ap
ply
Han
sen
's g
rid
sea
rch
(19
96)
to l
oca
te t
he
mo
st l
ikel
y
thre
sho
ld v
alu
e in
th
e m
ark
et r
ates
or
erro
r co
rrec
tio
n t
erm
We
app
ly H
anse
n's
gri
d s
earc
h (
1996
) to
lo
cate
th
e m
ost
lik
ely
th
resh
old
val
ue
in t
he
mar
ket
rat
es o
r er
ror
corr
ecti
on
ter
mth
resh
old
val
ue
in t
he
mar
ket
rat
es o
r er
ror
corr
ecti
on
ter
m
Mo
del
par
amet
ers
are
esti
mat
ed b
y M
LE
(
)(
),,
Sβδτ
Mo
del
par
amet
ers
are
esti
mat
ed b
y M
LE
(
)(
),,
nS
βδτ
Mo
del
par
amet
ers
are
esti
mat
ed b
y M
LE
(
)(
)n
()
()
()
()
argmin
nS
ττ ()
()
argmin
nS
ττ
We
app
ly t
he
lik
elih
oo
d r
atio
sta
tist
ic t
o t
est
:H
ττ
=W
e ap
ply
th
e li
kel
iho
od
rat
io s
tati
stic
to
tes
t0
0:
Hτ
τ=
()
()ˆ
ττ
−)
()
()ˆ
nn
SS
LR
nτ
ττ
−= )
()
()
()ˆ
ˆ
nn
SS
LR
nSτ
ττ
τ−= )
()ˆ
n
LR
nS
ττ
=()ˆ
nS
τ2
()
2
21
11exp
pLR
τ
=
−−
−(
)20
11
1exp
2n
np
LR
τ
=
−−
−
()
01
1exp
2n
np
LR
τ=
−−
−
2
Sh
ort
ra
teL
on
g r
ate
E
C t
erm
Sh
ort
ra
teL
on
g r
ate
E
C t
erm
()
EC
ω=
()
1
long
trω
−=
)1
short
-0.5
201.
027
()
EC
ω=
()
1tr
ω−
=)
1
-0.5
201.
027
0.04
80.
016
0.04
80.
016
Mo
del
ing
cli
ent
rate
Est
imat
ion
res
ult
sM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 10
Est
imat
ion
res
ult
san
dv
olu
mes
of
NM
AP
age
10E
stim
atio
n r
esu
lts
αβ
ββ
δλϖ
ε∆
=+
∆+
∆+
∆+
++
11
21
31
11
tt
tt
tt
tR
Rr
rEC
αβ
ββ
δλϖ
ε−
−−
−−
∆=
+∆
+∆
+∆
++
+1
12
13
11
1t
tt
tt
tt
RR
rr
EC
αβ
ββ
δλϖ
ε−
−−
−−
∆=
+∆
+∆
+∆
++
+
Pa
ram
ete
rsL
ibo
r 3
mth
resh
old
Pa
ram
ete
rsL
ibo
r 3
mth
resh
old
0.0
56
0.0
56
(2.4
1)α
(2.4
1)0
.09
8β
0.0
98
(1.2
45)
1β(1
.245
)-0
.06
2(1
.216
)2β
-0.0
62
(1.2
16)
-0.0
43
2β
-0.0
43
(-3.
35)
3β(-
3.35
)-0
.05
3(-
7.35
)δ
-0.0
53
(-7.
35)
0.0
57
δ
0.0
57
(3.4
7)λ
(3.4
7)
0.5
92
λ
2R
0.5
92
2R D
urb
in-W
atso
n s
tat.
2.01
Du
rbin
-Wat
son
sta
t.2.
01
Th
resh
old
0.4
68
Th
resh
old
0.4
68
Su
p-L
M10
.53
Su
p-L
M10
.53
p-v
alu
e0
.26
2p
-val
ue
0.2
62
t S
tati
stic
s ar
e in
par
enth
esis
.T
hres
hold
is
the
val
ue
of
the
nu
isan
ce p
aram
eter
ass
oci
ated
wit
h t
he
t S
tati
stic
s ar
e in
par
enth
esis
.T
hres
hold
is
the
val
ue
of
the
nu
isan
ce p
aram
eter
ass
oci
ated
wit
h t
he
loca
te t
he
mo
st l
ikel
y t
hre
sho
ld.
the
P v
alu
e as
soci
ated
wit
h s
up
loca
te t
he
mo
st l
ikel
y t
hre
sho
ld.
the
P v
alu
e as
soci
ated
wit
h s
up
the
asy
mp
toti
c d
istr
ibu
tio
n (
1000
rep
lica
tio
ns)
of
the
test
sta
tist
ic u
sin
g t
he
met
ho
d p
rop
ose
d b
y H
anse
n (
1996
).
the
asy
mp
toti
c d
istr
ibu
tio
n (
1000
rep
lica
tio
ns)
of
the
test
sta
tist
ic u
sin
g t
he
met
ho
d p
rop
ose
d b
y H
anse
n (
1996
).
short
long
αβ
ββ
δλϖ
ε∆
=+
∆+
∆+
∆+
++
11
21
31
11
short
long
tt
tt
tt
tR
Rr
rEC
αβ
ββ
δλϖ
ε−
−−
−−
∆=
+∆
+∆
+∆
++
+1
12
13
11
1t
tt
tt
tt
RR
rr
EC
αβ
ββ
δλϖ
ε−
−−
−−
∆=
+∆
+∆
+∆
++
+
Err
or-
corr
ect
ion
thre
sho
ldS
wap
5Y
thre
sho
ldE
rro
r-co
rre
ctio
nth
resh
old
thre
sho
ldS
wap
5Y
thre
sho
ldE
rro
r-co
rre
ctio
nth
resh
old
0.0
00
8-0
.02
70
.00
08
(0.2
75)
-0.0
27
(-3.
028)
(0.2
75)
(-3.
028)
0.1
01
0.0
70
0.1
01
(1.2
87)
0.0
70
(0.8
87)
(1.2
87)
(0.8
87)
0.0
20
(1.6
79)
0.0
20
(1.7
85)
0.0
20
(1.6
79)
0.0
20
(1.7
85)
0.0
34
0.0
42
0.0
34
(2.2
7)0
.04
2(3
.328
)(2
.27)
(3.3
28)
-0.0
53
(-6.
799)
-0.1
40
(2.5
92)
-0.0
53
(-6.
799)
-0.1
40
(2.5
92)
0.7
56
0.1
01
0.7
56
(7.6
3)0
.10
1(1
.983
)(7
.63)
(1.9
83)
0.5
51
0.5
63
0.5
51
0.5
63
1.98
2.00
051.
982.
0005
-0.5
20
1.0
27
-0.5
20
1.0
27
8.95
813
.78
8.95
813
.78
0.0
48
0.0
16
0.0
48
0.0
16
is t
he
val
ue
of
the
nu
isan
ce p
aram
eter
ass
oci
ated
wit
h t
he
sup-
LM
stat
isti
c to
is
th
e v
alu
e o
f th
e n
uis
ance
par
amet
er a
sso
ciat
ed w
ith
th
e su
p-L
Mst
atis
tic
to
loca
te t
he
mo
st l
ikel
y t
hre
sho
ld.
the
P v
alu
e as
soci
ated
wit
h s
up
-LM
is
also
pre
sen
ted
, an
d i
s o
bta
ined
by
sim
ula
tin
g
loca
te t
he
mo
st l
ikel
y t
hre
sho
ld.
the
P v
alu
e as
soci
ated
wit
h s
up
-LM
is
also
pre
sen
ted
, an
d i
s o
bta
ined
by
sim
ula
tin
g
the
asy
mp
toti
c d
istr
ibu
tio
n (
1000
rep
lica
tio
ns)
of
the
test
sta
tist
ic u
sin
g t
he
met
ho
d p
rop
ose
d b
y H
anse
n (
1996
).
the
asy
mp
toti
c d
istr
ibu
tio
n (
1000
rep
lica
tio
ns)
of
the
test
sta
tist
ic u
sin
g t
he
met
ho
d p
rop
ose
d b
y H
anse
n (
1996
).
Mo
del
ing
cli
ent
rate
Mo
del
per
form
ance
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
11M
od
el p
erfo
rman
cean
dv
olu
mes
of
NM
AP
age
11M
od
el p
erfo
rman
ce
•B
est
fit
to t
he
ob
serv
ed d
ata
is o
bta
ined
by
th
e m
od
el w
ith
EC
•
Bes
t fi
t to
th
e o
bse
rved
dat
a is
ob
tain
ed b
y t
he
mo
del
wit
h E
C
term
as
thre
sho
ld v
aria
ble
:•
Bes
t fi
t to
th
e o
bse
rved
dat
a is
ob
tain
ed b
y t
he
mo
del
wit
h E
C
term
as
thre
sho
ld v
aria
ble
:te
rm a
s th
resh
old
var
iab
le:
Cli
en
t ra
te m
od
el
pe
rfo
rma
nce
Cli
en
t ra
te m
od
el
pe
rfo
rma
nce
0.4
00
0
0.3
00
0
0.4
00
0
0.3
00
0
0.2
00
0
0.1
00
0
0.2
00
0
0.0
00
0
0.1
00
0
0.0
00
0
01.02.1988
01.11.1988
01.08.1989
01.05.1990
01.02.1991
01.11.1991
01.08.1992
01.05.1993
01.02.1994
01.11.1994
-0.1
00
0
01.02.1988
01.11.1988
01.08.1989
01.05.1990
01.02.1991
01.11.1991
01.08.1992
01.05.1993
01.02.1994
01.11.1994
-0.2
00
0
-0.1
00
0
01.02.1988
01.11.1988
01.08.1989
01.05.1990
01.02.1991
01.11.1991
01.08.1992
01.05.1993
01.02.1994
01.11.1994
-0.2
00
0
01.02.1988
01.11.1988
01.08.1989
01.05.1990
01.02.1991
01.11.1991
01.08.1992
01.05.1993
01.02.1994
01.11.1994
-0.3
00
0
-0.4
00
0
-0.5
00
0
-0.4
00
0
-0.5
00
0
ob
serv
edfi
tted
wh
ile
EC
=th
resh
old
ob
serv
edfi
tted
wh
ile
EC
=th
resh
old
Bes
t fi
t to
th
e o
bse
rved
dat
a is
ob
tain
ed b
y t
he
mo
del
wit
h E
C
Bes
t fi
t to
th
e o
bse
rved
dat
a is
ob
tain
ed b
y t
he
mo
del
wit
h E
C
term
as
thre
sho
ld v
aria
ble
:B
est
fit
to t
he
ob
serv
ed d
ata
is o
bta
ined
by
th
e m
od
el w
ith
EC
te
rm a
s th
resh
old
var
iab
le:
term
as
thre
sho
ld v
aria
ble
:
Cli
en
t ra
te m
od
el
pe
rfo
rma
nce
Cli
en
t ra
te m
od
el
pe
rfo
rma
nce
01.08.1995
01.05.1996
01.02.1997
01.11.1997
01.08.1998
01.05.1999
01.02.2000
01.11.2000
01.08.2001
01.05.2002
01.02.2003
01.11.2003
01.08.2004
01.05.2005
01.02.2006
01.11.2006
01.08.2007
01.05.2008
01.08.1995
01.05.1996
01.02.1997
01.11.1997
01.08.1998
01.05.1999
01.02.2000
01.11.2000
01.08.2001
01.05.2002
01.02.2003
01.11.2003
01.08.2004
01.05.2005
01.02.2006
01.11.2006
01.08.2007
01.05.2008
01.08.1995
01.05.1996
01.02.1997
01.11.1997
01.08.1998
01.05.1999
01.02.2000
01.11.2000
01.08.2001
01.05.2002
01.02.2003
01.11.2003
01.08.2004
01.05.2005
01.02.2006
01.11.2006
01.08.2007
01.05.2008
01.08.1995
01.05.1996
01.02.1997
01.11.1997
01.08.1998
01.05.1999
01.02.2000
01.11.2000
01.08.2001
01.05.2002
01.02.2003
01.11.2003
01.08.2004
01.05.2005
01.02.2006
01.11.2006
01.08.2007
01.05.2008
fitt
ed w
hil
e E
C=
thre
sho
ldfi
tted
wh
ile
S5
y=
thre
sho
ldfi
tted
wh
ile
EC
=th
resh
old
fitt
ed w
hil
e S
5y
=th
resh
old
Mo
del
ing
cli
ent
rate
Inte
rpre
tati
on
of
resu
lts
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
12In
terp
reta
tio
n o
f re
sult
san
dv
olu
mes
of
NM
AP
age
12In
terp
reta
tio
n o
f re
sult
s
•T
her
e is
a s
tro
ng
asy
mm
etri
c re
lati
on
ship
bet
wee
n t
he
clie
nt
rate
•
Th
ere
is a
str
on
g a
sym
met
ric
rela
tio
nsh
ip b
etw
een
th
e cl
ien
t ra
te
and
th
e ch
ang
es i
n t
he
lon
g r
ate
mat
uri
ty:
•T
her
e is
a s
tro
ng
asy
mm
etri
c re
lati
on
ship
bet
wee
n t
he
clie
nt
rate
an
d t
he
chan
ges
in
th
e lo
ng
rat
e m
atu
rity
:an
d t
he
chan
ges
in
th
e lo
ng
rat
e m
atu
rity
:–
a si
gn
ific
ant
thre
sho
ld e
xis
ts a
t –
a si
gn
ific
ant
thre
sho
ld e
xis
ts a
t
–fo
r ev
ery
neg
ativ
e sh
ock
of
100
–fo
r ev
ery
neg
ativ
e sh
ock
of
100
rate
wil
l b
e ad
just
ed, o
n a
ver
age,
by
a 7
9 –
for
ever
y n
egat
ive
sho
ck o
f 10
0 ra
te w
ill
be
adju
sted
, on
av
erag
e, b
y a
79
rate
wil
l b
e ad
just
ed, o
n a
ver
age,
by
a 7
9
–fo
r ev
ery
100
b.p
. ch
ang
e in
th
e S
wap
rat
e ab
ov
e –
for
ever
y 1
00 b
.p.
chan
ge
in t
he
Sw
ap r
ate
abo
ve
chan
ge,
on
av
erag
e, w
ith
on
ly 3
.4
chan
ge,
on
av
erag
e, w
ith
on
ly 3
.4
•T
he
gre
ater
th
e m
agn
itu
de
of
the
dis
equ
ilib
riu
m, t
he
gre
ater
th
e •
Th
e g
reat
er t
he
mag
nit
ud
e o
f th
e d
iseq
uil
ibri
um
, th
e g
reat
er t
he
•T
he
gre
ater
th
e m
agn
itu
de
of
the
dis
equ
ilib
riu
m, t
he
gre
ater
th
e sp
eed
of
adju
stm
ent
tow
ard
s eq
uil
ibri
um
spee
d o
f ad
just
men
t to
war
ds
equ
ilib
riu
msp
eed
of
adju
stm
ent
tow
ard
s eq
uil
ibri
um
–a
sig
nif
ican
t th
resh
old
ex
ists
wh
en t
he
clie
nt
rate
is
1.02
7% (
102.
7 –
a si
gn
ific
ant
thre
sho
ld e
xis
ts w
hen
th
e cl
ien
t ra
te i
s 1.
027%
(10
2.7
equ
ilib
riu
m l
evel
;eq
uil
ibri
um
lev
el;
–fo
r ev
ery
100
b.p
. ab
ov
e th
is d
epar
ture
fro
m e
qu
ilib
riu
m, w
e ex
pec
t th
e co
nv
erg
ence
–
for
ever
y 1
00 b
.p.
abo
ve
this
dep
artu
re f
rom
eq
uil
ibri
um
, we
exp
ect
the
con
ver
gen
ce
bac
k t
o e
qu
ilib
riu
m t
o b
e o
f 14
b.p
bac
k t
o e
qu
ilib
riu
m t
o b
e o
f 14
b.p
–b
elo
w t
he
dis
equ
ilib
riu
m t
hre
sho
ld, t
he
con
ver
gen
ce t
o e
qu
ilib
riu
m o
nly
occ
urs
wit
h
–b
elo
w t
he
dis
equ
ilib
riu
m t
hre
sho
ld, t
he
con
ver
gen
ce t
o e
qu
ilib
riu
m o
nly
occ
urs
wit
h
3.9
b.p
. d
rop
.3.
9 b
.p.
dro
p.
3.9
b.p
. d
rop
.
Inte
rpre
tati
on
of
resu
lts
Inte
rpre
tati
on
of
resu
lts
Inte
rpre
tati
on
of
resu
lts
Th
ere
is a
str
on
g a
sym
met
ric
rela
tio
nsh
ip b
etw
een
th
e cl
ien
t ra
te
Th
ere
is a
str
on
g a
sym
met
ric
rela
tio
nsh
ip b
etw
een
th
e cl
ien
t ra
te
and
th
e ch
ang
es i
n t
he
lon
g r
ate
mat
uri
ty:
Th
ere
is a
str
on
g a
sym
met
ric
rela
tio
nsh
ip b
etw
een
th
e cl
ien
t ra
te
and
th
e ch
ang
es i
n t
he
lon
g r
ate
mat
uri
ty:
and
th
e ch
ang
es i
n t
he
lon
g r
ate
mat
uri
ty:
a si
gn
ific
ant
thre
sho
ld e
xis
ts a
t -5
2 b
.p.
chan
ge
in t
he
Sw
ap 5
yea
rs r
ate;
a si
gn
ific
ant
thre
sho
ld e
xis
ts a
t -5
2 b
.p.
chan
ge
in t
he
Sw
ap 5
yea
rs r
ate;
for
ever
y n
egat
ive
sho
ck o
f 10
0 b
.p.
bel
ow
-52
b.p
. in
th
e S
wap
5 y
ears
rat
e, t
he
clie
nt
for
ever
y n
egat
ive
sho
ck o
f 10
0 b
.p.
bel
ow
-52
b.p
. in
th
e S
wap
5 y
ears
rat
e, t
he
clie
nt
rate
wil
l b
e ad
just
ed, o
n a
ver
age,
by
a 7
9 b
.p.
dro
p p
er m
on
th;
for
ever
y n
egat
ive
sho
ck o
f 10
0 b
.p.
bel
ow
-52
b.p
. in
th
e S
wap
5 y
ears
rat
e, t
he
clie
nt
rate
wil
l b
e ad
just
ed, o
n a
ver
age,
by
a 7
9 b
.p.
dro
p p
er m
on
th;
rate
wil
l b
e ad
just
ed, o
n a
ver
age,
by
a 7
9 b
.p.
dro
p p
er m
on
th;
. ch
ang
e in
th
e S
wap
rat
e ab
ov
e -5
2 b
.p.
lev
el, t
he
clie
nt
rate
wil
l .
chan
ge
in t
he
Sw
ap r
ate
abo
ve
-52
b.p
. le
vel
, th
e cl
ien
t ra
te w
ill
chan
ge,
on
av
erag
e, w
ith
on
ly 3
.4 b
.p.
per
mo
nth
.ch
ang
e, o
n a
ver
age,
wit
h o
nly
3.4
b.p
. p
er m
on
th.
Th
e g
reat
er t
he
mag
nit
ud
e o
f th
e d
iseq
uil
ibri
um
, th
e g
reat
er t
he
Th
e g
reat
er t
he
mag
nit
ud
e o
f th
e d
iseq
uil
ibri
um
, th
e g
reat
er t
he
Th
e g
reat
er t
he
mag
nit
ud
e o
f th
e d
iseq
uil
ibri
um
, th
e g
reat
er t
he
spee
d o
f ad
just
men
t to
war
ds
equ
ilib
riu
m:
spee
d o
f ad
just
men
t to
war
ds
equ
ilib
riu
m:
spee
d o
f ad
just
men
t to
war
ds
equ
ilib
riu
m:
a si
gn
ific
ant
thre
sho
ld e
xis
ts w
hen
th
e cl
ien
t ra
te i
s 1.
027%
(10
2.7
b.p
.) a
bo
ve
its
a si
gn
ific
ant
thre
sho
ld e
xis
ts w
hen
th
e cl
ien
t ra
te i
s 1.
027%
(10
2.7
b.p
.) a
bo
ve
its
. ab
ov
e th
is d
epar
ture
fro
m e
qu
ilib
riu
m, w
e ex
pec
t th
e co
nv
erg
ence
.
abo
ve
this
dep
artu
re f
rom
eq
uil
ibri
um
, we
exp
ect
the
con
ver
gen
ce
b.p
. d
rop
in
th
e cl
ien
t ra
te p
er m
on
th;
b.p
. d
rop
in
th
e cl
ien
t ra
te p
er m
on
th;
bel
ow
th
e d
iseq
uil
ibri
um
th
resh
old
, th
e co
nv
erg
ence
to
eq
uil
ibri
um
on
ly o
ccu
rs w
ith
b
elo
w t
he
dis
equ
ilib
riu
m t
hre
sho
ld, t
he
con
ver
gen
ce t
o e
qu
ilib
riu
m o
nly
occ
urs
wit
h
Mo
del
ing
cli
ent
rate
Mo
del
ing
vo
lum
es o
f N
MA
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
13M
od
elin
g v
olu
mes
of
NM
Aan
dv
olu
mes
of
NM
AP
age
13M
od
elin
g v
olu
mes
of
NM
A
Co
mm
on
pra
ctic
e:C
om
mo
n p
ract
ice:
Co
mm
on
pra
ctic
e:
–fo
rmu
lati
on
of
vo
lum
e m
od
els
as a
uto
reg
ress
ive
dis
trib
ute
d l
ag
–fo
rmu
lati
on
of
vo
lum
e m
od
els
as a
uto
reg
ress
ive
dis
trib
ute
d l
ag
–fo
rmu
lati
on
of
vo
lum
e m
od
els
as a
uto
reg
ress
ive
dis
trib
ute
d l
ag
mo
del
s: S
elv
agg
io(1
996)
, O'B
rien
(20
00),
de
mo
del
s: S
elv
agg
io(1
996)
, O'B
rien
(20
00),
de
(200
1), D
ewac
hte
r, L
yri
oan
d
(200
1), D
ewac
hte
r, L
yri
oan
d
(200
1), D
ewac
hte
r, L
yri
oan
d
–ex
pla
inin
g t
he
vo
lum
es b
y a
pro
xy
fo
r th
e m
ark
et r
ates
(le
vel
or
–ex
pla
inin
g t
he
vo
lum
es b
y a
pro
xy
fo
r th
e m
ark
et r
ates
(le
vel
or
–ex
pla
inin
g t
he
vo
lum
es b
y a
pro
xy
fo
r th
e m
ark
et r
ates
(le
vel
or
spre
ad b
etw
een
cli
ent
rate
an
d m
ark
et r
ates
): H
utc
his
on
an
d
spre
ad b
etw
een
cli
ent
rate
an
d m
ark
et r
ates
): H
utc
his
on
an
d
Pen
acch
i(1
996)
, Bar
den
hew
erP
enac
chi
(199
6), B
ard
enh
ewer
Wie
lho
uw
er(2
007)
Wie
lho
uw
er(2
007)
Wie
lho
uw
er(2
007)
NM
A. L
iter
atu
re o
ver
vie
wN
MA
. Lit
erat
ure
ov
erv
iew
NM
A. L
iter
atu
re o
ver
vie
w
form
ula
tio
n o
f v
olu
me
mo
del
s as
au
tore
gre
ssiv
e d
istr
ibu
ted
lag
fo
rmu
lati
on
of
vo
lum
e m
od
els
as a
uto
reg
ress
ive
dis
trib
ute
d l
ag
form
ula
tio
n o
f v
olu
me
mo
del
s as
au
tore
gre
ssiv
e d
istr
ibu
ted
lag
(1
996)
, O'B
rien
(20
00),
de
Jon
gan
d W
ielh
ou
ver
(199
6), O
'Bri
en (
2000
), d
e Jo
ng
and
Wie
lho
uv
eran
d M
aes
(200
6)an
d M
aes
(200
6)an
d M
aes
(200
6)
exp
lain
ing
th
e v
olu
mes
by
a p
rox
y f
or
the
mar
ket
rat
es (
lev
el o
r ex
pla
inin
g t
he
vo
lum
es b
y a
pro
xy
fo
r th
e m
ark
et r
ates
(le
vel
or
exp
lain
ing
th
e v
olu
mes
by
a p
rox
y f
or
the
mar
ket
rat
es (
lev
el o
r sp
read
bet
wee
n c
lien
t ra
te a
nd
mar
ket
rat
es):
Hu
tch
iso
n a
nd
sp
read
bet
wee
n c
lien
t ra
te a
nd
mar
ket
rat
es):
Hu
tch
iso
n a
nd
B
ard
enh
ewer
(200
7), O
'Bri
en (
2000
), d
e Jo
ng
and
B
ard
enh
ewer
(200
7), O
'Bri
en (
2000
), d
e Jo
ng
and
Mo
del
ing
cli
ent
rate
Mo
del
ing
NM
Av
olu
mes
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
14M
od
elin
g N
MA
vo
lum
esan
dv
olu
mes
of
NM
AP
age
14M
od
elin
g N
MA
vo
lum
es
•d
epen
den
t v
aria
ble
s:•
dep
end
ent
var
iab
les:
–ti
me
tren
d a
s p
rox
y f
or
the
un
spec
ific
mac
ro v
aria
ble
s–
tim
e tr
end
as
pro
xy
fo
r th
e u
nsp
ecif
ic m
acro
var
iab
les
–la
gg
ed v
alu
e o
f d
epo
sit
vo
lum
es–
lag
ged
val
ue
of
dep
osi
t v
olu
mes
–sp
read
bet
wee
n c
lien
t ra
te a
nd
mar
ket
rat
es–
spre
ad b
etw
een
cli
ent
rate
an
d m
ark
et r
ates
–sp
read
bet
wee
n c
lien
t ra
te a
nd
mar
ket
rat
es
Dt
DR
rr
ββ
ββ
δδ
ε
=
++
+−
+−
+1
23
14
33
3t
tt
tt
tD
tD
Rr
rβ
ββ
βδ
δε
−−
−−
=+
++
−+
−+
12
31
43
33
tt
tt
tt
−−
−−
•as
pro
xy
fo
r th
e m
ark
et r
ates
we
incl
ud
e a
mix
of
a sh
ort
er a
nd
a
•as
pro
xy
fo
r th
e m
ark
et r
ates
we
incl
ud
e a
mix
of
a sh
ort
er a
nd
a
lon
ger
mat
uri
tylo
ng
er m
atu
rity
lon
ger
mat
uri
ty
•w
hen
sig
nif
ican
t ch
ang
es i
n t
he
less
vo
lati
le m
ark
et r
ates
(in
ou
r •
wh
en s
ign
ific
ant
chan
ges
in
th
e le
ss v
ola
tile
mar
ket
rat
es (
in o
ur
case
5 y
ears
Sw
ap)
occ
ur,
dep
osi
tors
bec
om
e m
ore
sen
siti
ve
and
•
wh
en s
ign
ific
ant
chan
ges
in
th
e le
ss v
ola
tile
mar
ket
rat
es (
in o
ur
case
5 y
ears
Sw
ap)
occ
ur,
dep
osi
tors
bec
om
e m
ore
sen
siti
ve
and
ca
se 5
yea
rs S
wap
) o
ccu
r, d
epo
sito
rs b
eco
me
mo
re s
ensi
tiv
e an
d
we
exp
ect
chan
ges
in
th
e v
olu
mes
dy
nam
ics
(
)
we
exp
ect
chan
ges
in
th
e v
olu
mes
dy
nam
ics
(
)
vo
lum
esv
olu
mes
vo
lum
es
tim
e tr
end
as
pro
xy
fo
r th
e u
nsp
ecif
ic m
acro
var
iab
les
tim
e tr
end
as
pro
xy
fo
r th
e u
nsp
ecif
ic m
acro
var
iab
les
lag
ged
val
ue
of
dep
osi
t v
olu
mes
lag
ged
val
ue
of
dep
osi
t v
olu
mes
spre
ad b
etw
een
cli
ent
rate
an
d m
ark
et r
ates
spre
ad b
etw
een
cli
ent
rate
an
d m
ark
et r
ates
spre
ad b
etw
een
cli
ent
rate
an
d m
ark
et r
ates (
){
}1
short
long
Dt
DR
rr
ββ
ββ
δδ
ε
=
++
+−
+−
+(
){
}1
23
14
33
31
short
long
tt
tt
tt
Dt
DR
rr
ββ
ββ
δδ
ε−
−−
−
=
++
+−
+−
+
(
){
}1
23
14
33
3t
tt
tt
t−
−−
−
as p
rox
y f
or
the
mar
ket
rat
es w
e in
clu
de
a m
ix o
f a
sho
rter
an
d a
as
pro
xy
fo
r th
e m
ark
et r
ates
we
incl
ud
e a
mix
of
a sh
ort
er a
nd
a
wh
en s
ign
ific
ant
chan
ges
in
th
e le
ss v
ola
tile
mar
ket
rat
es (
in o
ur
wh
en s
ign
ific
ant
chan
ges
in
th
e le
ss v
ola
tile
mar
ket
rat
es (
in o
ur
case
5 y
ears
Sw
ap)
occ
ur,
dep
osi
tors
bec
om
e m
ore
sen
siti
ve
and
w
hen
sig
nif
ican
t ch
ang
es i
n t
he
less
vo
lati
le m
ark
et r
ates
(in
ou
r ca
se 5
yea
rs S
wap
) o
ccu
r, d
epo
sito
rs b
eco
me
mo
re s
ensi
tiv
e an
d
case
5 y
ears
Sw
ap)
occ
ur,
dep
osi
tors
bec
om
e m
ore
sen
siti
ve
and
w
e ex
pec
t ch
ang
es i
n t
he
vo
lum
es d
yn
amic
s (
)33%
δ=
we
exp
ect
chan
ges
in
th
e v
olu
mes
dy
nam
ics
(
)
33%
δ=
Mo
del
ing
cli
ent
rate
Est
imat
ion
res
ult
sM
od
elin
g c
lien
tra
te
and
vo
lum
eso
f N
MA
Pag
e 15
Est
imat
ion
res
ult
san
dv
olu
mes
of
NM
AP
age
15E
stim
atio
n r
esu
lts
ββ
ββ
δδ
ε
=
++
+−
+−
+1
23
14
33
3t
tt
tt
tD
tD
Rr
rβ
ββ
βδ
δε
−−
−−
=+
++
−+
−+
12
31
43
33
tt
tt
tt
Dt
DR
rr
ββ
ββ
δδ
ε−
−−
−
=
++
+−
+−
+
Tab
le 3
: Ste
p on
e: O
LS
cova
rian
ce m
atri
x ob
tain
ed w
ith
Va
ria
ble
Co
eff
icie
nt
Tab
le 3
: Ste
p on
e: O
LS
cova
rian
ce m
atri
x ob
tain
ed w
ith
Va
ria
ble
Co
eff
icie
nt
8850
8850
1β
4.60
1 2β4.
60
0.96
2β
3β0.
96
1486
3β β14
86
0.99
71
4β
2R
0.99
71
Du
rbin
-Wat
son
1.17
40
2R D
urb
in-W
atso
n1.
1740
Ta
ble
4:R
esu
lts
esti
mat
ing
the
volu
mes
mod
el i
n A
R(1
) fo
rm
tren
dfr
omth
ees
tim
atio
n:
Ta
ble
4:R
esu
lts
esti
mat
ing
the
volu
mes
mod
el i
n A
R(1
) fo
rm
tren
dfr
omth
ees
tim
atio
n:
Va
ria
ble
Co
eff
icie
nt
Va
ria
ble
Co
eff
icie
nt
7884
β78
84
0.96
1β β0.
96
1360
3β β13
60
0.42
4β AR
(1)
0.42
0.99
2R
0.99
Du
rbin
-Wat
son
2.04
R Du
rbin
-Wat
son
2.04
()
{}
ββ
ββ
δδ
ε
=
++
+−
+−
+(
){
}1
23
14
33
31
short
long
tt
tt
tt
Dt
DR
rr
ββ
ββ
δδ
ε−
−−
−
=
++
+−
+−
+
(
){
}1
23
14
33
31
tt
tt
tt
Dt
DR
rr
ββ
ββ
δδ
ε−
−−
−
=
++
+−
+−
+
cova
rian
ce m
atri
x ob
tain
ed w
ith
New
eyW
est
esti
mat
or
t-st
atis
tic
p-v
alu
es
cova
rian
ce m
atri
x ob
tain
ed w
ith
New
eyW
est
esti
mat
or
t-st
atis
tic
p-v
alu
es
5.00
0.00
005.
000.
0000
1.20
0.23
11*
!! n
ot
sig
nif
ican
t1.
200.
2311
*
100.
120.
0000
!! n
ot
sig
nif
ican
t
100.
120.
0000
5.81
0.00
005.
810.
0000
mod
el i
n A
R(1
) fo
rm e
xclu
din
gth
eti
me
mod
el i
n A
R(1
) fo
rm e
xclu
din
gth
eti
me
t-st
atis
tic
p-v
alu
est-
stat
isti
cp
-val
ues
4.17
9615
0.00
004.
1796
150.
0000
115.
3435
0.00
0011
5.34
350.
0000
4.89
5730
0.00
00
7.01
6911
0.00
007.
0169
110.
0000
Mo
del
ing
cli
ent
rate
Inte
rpre
tati
on
of
resu
lts
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
16In
terp
reta
tio
n o
f re
sult
san
dv
olu
mes
of
NM
AP
age
16In
terp
reta
tio
n o
f re
sult
s
•T
he
lag
ged
dep
osi
ts a
nd
th
e sp
read
bet
wee
n d
epo
sits
an
d m
ark
et
•T
he
lag
ged
dep
osi
ts a
nd
th
e sp
read
bet
wee
n d
epo
sits
an
d m
ark
et
rate
s h
ave
imp
ort
ant
exp
lan
ato
ry p
ow
er f
or
dep
osi
t b
alan
ces
•T
he
lag
ged
dep
osi
ts a
nd
th
e sp
read
bet
wee
n d
epo
sits
an
d m
ark
et
rate
s h
ave
imp
ort
ant
exp
lan
ato
ry p
ow
er f
or
dep
osi
t b
alan
ces
rate
s h
ave
imp
ort
ant
exp
lan
ato
ry p
ow
er f
or
dep
osi
t b
alan
ces
•D
epo
sito
rs a
re s
ensi
tiv
e to
mar
ket
rat
es i
ncr
ease
: If
mar
ket
rat
es
•D
epo
sito
rs a
re s
ensi
tiv
e to
mar
ket
rat
es i
ncr
ease
: If
mar
ket
rat
es
•D
epo
sito
rs a
re s
ensi
tiv
e to
mar
ket
rat
es i
ncr
ease
: If
mar
ket
rat
es
are
100
b.p
. ab
ov
e cl
ien
t ra
te, t
his
wo
uld
det
erm
ine
1360
mil
lio
ns
are
100
b.p
. ab
ov
e cl
ien
t ra
te, t
his
wo
uld
det
erm
ine
1360
mil
lio
ns
CH
Fd
rop
in
th
e v
olu
mes
val
ue.
C
HF
dro
p i
n t
he
vo
lum
es v
alu
e.
CH
Fd
rop
in
th
e v
olu
mes
val
ue.
6000
4000
6000
2000
4000 0
2000
-2000
-6000
-4000
-6000
25
50
75
100
Residual
Residual
Inte
rpre
tati
on
of
resu
lts
Inte
rpre
tati
on
of
resu
lts
Inte
rpre
tati
on
of
resu
lts
Th
e la
gg
ed d
epo
sits
an
d t
he
spre
ad b
etw
een
dep
osi
ts a
nd
mar
ket
T
he
lag
ged
dep
osi
ts a
nd
th
e sp
read
bet
wee
n d
epo
sits
an
d m
ark
et
rate
s h
ave
imp
ort
ant
exp
lan
ato
ry p
ow
er f
or
dep
osi
t b
alan
ces
Th
e la
gg
ed d
epo
sits
an
d t
he
spre
ad b
etw
een
dep
osi
ts a
nd
mar
ket
ra
tes
hav
e im
po
rtan
t ex
pla
nat
ory
po
wer
fo
r d
epo
sit
bal
ance
s ra
tes
hav
e im
po
rtan
t ex
pla
nat
ory
po
wer
fo
r d
epo
sit
bal
ance
s
Dep
osi
tors
are
sen
siti
ve
to m
ark
et r
ates
in
crea
se: I
f m
ark
et r
ates
D
epo
sito
rs a
re s
ensi
tiv
e to
mar
ket
rat
es i
ncr
ease
: If
mar
ket
rat
es
Dep
osi
tors
are
sen
siti
ve
to m
ark
et r
ates
in
crea
se: I
f m
ark
et r
ates
. a
bo
ve
clie
nt
rate
, th
is w
ou
ld d
eter
min
e 13
60 m
illi
on
s . a
bo
ve
clie
nt
rate
, th
is w
ou
ld d
eter
min
e 13
60 m
illi
on
s d
rop
in
th
e v
olu
mes
val
ue.
d
rop
in
th
e v
olu
mes
val
ue.
d
rop
in
th
e v
olu
mes
val
ue.
200000
220000
180000
200000
160000
180000
140000
160000
120000
140000
100000
100125150175200225
Actual
Fitted
Actual
Fitted
Mo
del
ing
cli
ent
rate
Cas
e st
ud
y –
clie
nt
rate
mo
del
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
17C
ase
stu
dy
–cl
ien
t ra
te m
od
elan
dv
olu
mes
of
NM
AP
age
17C
ase
stu
dy
–cl
ien
t ra
te m
od
el
We
rees
tim
ate
the
coef
fici
ents
of
the
clie
nt
rate
mo
del
usi
ng
dat
a fr
om
th
e W
e re
esti
mat
eth
e co
effi
cien
ts o
f th
e cl
ien
t ra
te m
od
el u
sin
g d
ata
fro
m t
he
beg
inn
ing
of
the
dat
a sa
mp
le u
p t
o J
anu
ary
199
8 an
d w
e ca
lcu
late
th
e o
ut
of
beg
inn
ing
of
the
dat
a sa
mp
le u
p t
o J
anu
ary
199
8 an
d w
e ca
lcu
late
th
e o
ut
of
sam
ple
fit
ted
val
ue
(fo
r th
e re
st o
f th
e d
ata
sam
ple
)b
egin
nin
g o
f th
e d
ata
sam
ple
up
to
Jan
uar
y 1
998
and
we
calc
ula
te t
he
ou
t o
f sa
mp
le f
itte
d v
alu
e (f
or
the
rest
of
the
dat
a sa
mp
le)
sam
ple
fit
ted
val
ue
(fo
r th
e re
st o
f th
e d
ata
sam
ple
)
Ou
t o
f S
am
ple
te
st
0.4
00
0
0.3
00
0
0.4
00
0
0.2
00
0
0.0
00
0
0.1
00
0
-0.1
00
0
0.0
00
0
01.02.1988
01.12.1988
01.10.1989
01.08.1990
01.06.1991
01.04.1992
01.02.1993
01.12.1993
-0.2
00
0
-0.1
00
0
01.02.1988
01.12.1988
01.10.1989
01.08.1990
01.06.1991
01.04.1992
01.02.1993
01.12.1993
-0.3
00
0
01.02.1988
01.12.1988
01.10.1989
01.08.1990
01.06.1991
01.04.1992
01.02.1993
01.12.1993
-0.5
00
0
-0.4
00
0
-0.5
00
0
Ob
serv
edO
bse
rved
Ou
t o
f sa
mp
le t
est
35
0'0
00
.00
Ou
t o
f sa
mp
le t
est
30
0'0
00
.00
35
0'0
00
.00
25
0'0
00
.00
15
0'0
00
.00
20
0'0
00
.00
10
0'0
00
.00
15
0'0
00
.00
50
'00
0.0
0
10
0'0
00
.00
0.0
0
ob
serv
edo
bse
rved
clie
nt
rate
mo
del
clie
nt
rate
mo
del
clie
nt
rate
mo
del
the
coef
fici
ents
of
the
clie
nt
rate
mo
del
usi
ng
dat
a fr
om
th
e th
e co
effi
cien
ts o
f th
e cl
ien
t ra
te m
od
el u
sin
g d
ata
fro
m t
he
beg
inn
ing
of
the
dat
a sa
mp
le u
p t
o J
anu
ary
199
8 an
d w
e ca
lcu
late
th
e o
ut
of
beg
inn
ing
of
the
dat
a sa
mp
le u
p t
o J
anu
ary
199
8 an
d w
e ca
lcu
late
th
e o
ut
of
sam
ple
fit
ted
val
ue
(fo
r th
e re
st o
f th
e d
ata
sam
ple
)b
egin
nin
g o
f th
e d
ata
sam
ple
up
to
Jan
uar
y 1
998
and
we
calc
ula
te t
he
ou
t o
f sa
mp
le f
itte
d v
alu
e (f
or
the
rest
of
the
dat
a sa
mp
le)
sam
ple
fit
ted
val
ue
(fo
r th
e re
st o
f th
e d
ata
sam
ple
)
Ou
t o
f S
am
ple
te
st -
Cli
en
t ra
te
01.12.1993
01.10.1994
01.08.1995
01.06.1996
01.04.1997
01.02.1998
01.12.1998
01.10.1999
01.08.2000
01.06.2001
01.04.2002
01.02.2003
01.12.2003
01.10.2004
01.08.2005
01.06.2006
01.04.2007
01.02.2008
01.12.1993
01.10.1994
01.08.1995
01.06.1996
01.04.1997
01.02.1998
01.12.1998
01.10.1999
01.08.2000
01.06.2001
01.04.2002
01.02.2003
01.12.2003
01.10.2004
01.08.2005
01.06.2006
01.04.2007
01.02.2008
01.12.1993
01.10.1994
01.08.1995
01.06.1996
01.04.1997
01.02.1998
01.12.1998
01.10.1999
01.08.2000
01.06.2001
01.04.2002
01.02.2003
01.12.2003
01.10.2004
01.08.2005
01.06.2006
01.04.2007
01.02.2008
Ob
serv
edin
+o
ut o
f sa
mp
le f
itte
d v
alu
esO
bse
rved
in+
ou
t of
sam
ple
fit
ted
va
lues
Ou
t o
f sa
mp
le t
est
-V
olu
me
s O
ut
of
sam
ple
te
st -
Vo
lum
es
ob
serv
edin
+o
ut o
f sa
mp
le f
itte
d v
alu
eso
bse
rved
in+
ou
t of
sam
ple
fit
ted
va
lues
Mo
del
ing
cli
ent
rate
Co
ncl
usi
on
Mo
del
ing
cli
ent
rate
an
dv
olu
mes
of
NM
AP
age
18C
on
clu
sio
nan
dv
olu
mes
of
NM
AP
age
18C
on
clu
sio
n
•C
han
ges
in
th
e d
epo
sit
rate
s re
spo
nd
to
ch
ang
es i
n t
he
5 y
ear
•C
han
ges
in
th
e d
epo
sit
rate
s re
spo
nd
to
ch
ang
es i
n t
he
5 y
ear
Sw
ap r
ate
in a
n a
sym
met
ric
man
ner
•C
han
ges
in
th
e d
epo
sit
rate
s re
spo
nd
to
ch
ang
es i
n t
he
5 y
ear
Sw
ap r
ate
in a
n a
sym
met
ric
man
ner
Sw
ap r
ate
in a
n a
sym
met
ric
man
ner
•A
dju
stm
ent
of
the
clie
nt
rate
to
a d
iseq
uil
ibri
um
is
mo
re
•A
dju
stm
ent
of
the
clie
nt
rate
to
a d
iseq
uil
ibri
um
is
mo
re
•A
dju
stm
ent
of
the
clie
nt
rate
to
a d
iseq
uil
ibri
um
is
mo
re
pro
no
un
ced
wh
en t
he
dis
equ
ilib
riu
m w
iden
s n
oti
ceab
ly: l
arg
e p
ron
ou
nce
d w
hen
th
e d
iseq
uil
ibri
um
wid
ens
no
tice
ably
: lar
ge
dis
equ
ilib
ria
cau
sed
by
sh
ock
s to
mo
ney
mar
ket
rat
es w
ill
imp
ly
dis
equ
ilib
ria
cau
sed
by
sh
ock
s to
mo
ney
mar
ket
rat
es w
ill
imp
ly
pro
po
rtio
nal
ly m
ore
rap
id r
esp
on
ses
fro
m c
lien
t ra
tes
dis
equ
ilib
ria
cau
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nt
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ates
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ates
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apid
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om
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ark
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ates
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ply
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rop
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re r
apid
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om
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rop
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re r
apid
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s fr
om
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ent
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s
Th
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lum
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od
els
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ve
a re
alis
tic
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t-o
f-T
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clie
nt
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d v
olu
mes
mo
del
s p
rov
e a
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of-
Th
e cl
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te a
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els
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ve
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mp
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it a
nd
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ou
ld b
e in
teg
rate
d i
n t
he
gen
eral
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mew
ork
sa
mp
le f
it a
nd
th
ey c
ou
ld b
e in
teg
rate
d i
n t
he
gen
eral
fra
mew
ork
o
pti
miz
atio
n t
oo
lso
pti
miz
atio
n t
oo
lso
pti
miz
atio
n t
oo
ls
