Week 9
Aggregate Liquidity Shock
Ch 4.1-4.4
Aggregate liquidity uncertainty
λ is unknown
Model
State Prstate Prlearly Pilate
H t th Ha IA did
L 1y 1 p
Stateunknown
attobutknownattt
marketopensatt1
Asset
arketclearing Dsl's.y 5 Psy stil Different dependentons
prices
Assume
sayo
Early consumer at t=1:
• Exchange x unit of long asset for short asset at t=1
Late consumer with y:
• Repurchase y unit of the short asset Return
y
• Exchange y unit of the short asset to y/Ps unit of the long asset RyPs
Late consumer with x:
• Keep x until t=2 R
• Exchange x for Psx of the short asset p
Buyer
ifPak
seller
iiPsR
5,11s
lift is
i R Ps s.mnR.Y.y
H
L
dust in
s upply
more Pack
AslongasBakPinew y ieastheamountofliquidassetincreas
111314
g
11 I themarketp rices
Cashin
PsMy cR when
t hereisnot
iiPsRy enoughcash
S.PscRS.BR
PcannotbeR
forexchangeto IfyislageenoughPfundamentalvalue
occur
Isevenwhenthereisno
uncert
to
in
Priceisvolatiledue liquidityuncertainty
Cash-in-the market price is when price depends on the R
thefundamentalassetvalue
amount of y that late consumers have Index price
of
volatility
I ifnovolatility
Under it P<R, means that rather than the early consumer
being on the back foot (they must sell x of the long asset at www.nnm.mn yyyyyyy
t=1 even if P is very low), late consumers are also restricted 2OnlyPakRlcashinthe
11Yyc1tastItor
market
price.PE
as they do not have an unlimited amount of cash, y
Aggregate Liquidity Shock
Ch 4.1-4.4
Aggregate liquidity uncertainty
λ is unknown
Model
State Prstate Prlearly Pilate
H t th Ha IA did
L 1y 1 p
Stateunknown
attobutknownattt
marketopensatt1
Asset
arketclearing Dsl's.y 5 Psy stil Different dependentons
prices
Assume
sayo
Early consumer at t=1:
• Exchange x unit of long asset for short asset at t=1
Late consumer with y:
• Repurchase y unit of the short asset Return
y
• Exchange y unit of the short asset to y/Ps unit of the long asset RyPs
Late consumer with x:
• Keep x until t=2 R
• Exchange x for Psx of the short asset p
Buyer
ifPak
seller
iiPsR
5,11s
lift is
i R Ps s.mnR.Y.y
H
L
dust in
s upply
more Pack
AslongasBakPinew y ieastheamountofliquidassetincreas
111314
g
11 I themarketp rices
Cashin
PsMy cR when
t hereisnot
iiPsRy enoughcash
S.PscRS.BR
PcannotbeR
forexchangeto IfyislageenoughPfundamentalvalue
occur
Isevenwhenthereisno
uncert
to
in
Priceisvolatiledue liquidityuncertainty
Cash-in-the market price is when price depends on the R
thefundamentalassetvalue
amount of y that late consumers have Index price
of
volatility
I ifnovolatility
Under it P<R, means that rather than the early consumer
being on the back foot (they must sell x of the long asset at www.nnm.mn yyyyyyy
t=1 even if P is very low), late consumers are also restricted 2OnlyPakRlcashinthe
11Yyc1tastItor
market
price.PE
as they do not have an unlimited amount of cash, y
