The Kyle Model
Week 3
FPR Ch3
Introduction
This is a framework for analysing determinants of market depth (how and why transaction prices
react to order size). In a deep market larger orders do not have a much greater impact on prices
than small orders.
Determinants:
• Asymmetric information
◦ Large orders re ect more private information than small orders, so induce larger price
movements
◦ Sensitivity of price to trade size is determined by the degree of asymmetric information
◦ Greater asymmetry —> Shallower market
• Risk aversion of liquidity providers
◦ Filling a large order exposes them to greater inventory risk , so the more risk averse they are,
the large price concessions they require to execute trades
◦ As orders may be absorbed by multiple providers, market depth depends on their aggregate
risk bearing capacity and their number
• Rents due to imperfect competition among market makers
◦ Liquidity provider’s market power is inversely related to their number
◦ ↑ no. providers —> ↑ maket depth
Vs. Glosten and Milgrom
• Under the Milgrom model the spread is due to adverse selection or equivalently gaining
information
• It’s assumptions are that informed traders are
◦ Myopic, they are only allowed to trade once
◦ Can only buy/ sell one unit of the asset
◦ Informationally large, they know the security value payo but do not realise the impact of
their orders on the price
• Assumptions shared
◦ Informed and uninformed traders
‣ G and M- trader faced either informed or uninformed
‣ Kyle- orders from both types are batched together
One period Kyle model
traderdoesn'tsee
neededasinformed
ASSUMPTIONS
realisedorder trader
noise
from
I
Riskysecurity w terminalvalue v u NIi o
Xv ofsingleriskneutralstrategicspeculatorwhoknows v
marketo rder
UnNlo o marketo rder noisetradersystematicallyonthewrongsideofthemarket NPmarketordersonlynotlimit
of
w Xlvto o rder
aggregate
uItv
marketmakers
areriskneutral
setasin
price GAM
Week 3
FPR Ch3
Introduction
This is a framework for analysing determinants of market depth (how and why transaction prices
react to order size). In a deep market larger orders do not have a much greater impact on prices
than small orders.
Determinants:
• Asymmetric information
◦ Large orders re ect more private information than small orders, so induce larger price
movements
◦ Sensitivity of price to trade size is determined by the degree of asymmetric information
◦ Greater asymmetry —> Shallower market
• Risk aversion of liquidity providers
◦ Filling a large order exposes them to greater inventory risk , so the more risk averse they are,
the large price concessions they require to execute trades
◦ As orders may be absorbed by multiple providers, market depth depends on their aggregate
risk bearing capacity and their number
• Rents due to imperfect competition among market makers
◦ Liquidity provider’s market power is inversely related to their number
◦ ↑ no. providers —> ↑ maket depth
Vs. Glosten and Milgrom
• Under the Milgrom model the spread is due to adverse selection or equivalently gaining
information
• It’s assumptions are that informed traders are
◦ Myopic, they are only allowed to trade once
◦ Can only buy/ sell one unit of the asset
◦ Informationally large, they know the security value payo but do not realise the impact of
their orders on the price
• Assumptions shared
◦ Informed and uninformed traders
‣ G and M- trader faced either informed or uninformed
‣ Kyle- orders from both types are batched together
One period Kyle model
traderdoesn'tsee
neededasinformed
ASSUMPTIONS
realisedorder trader
noise
from
I
Riskysecurity w terminalvalue v u NIi o
Xv ofsingleriskneutralstrategicspeculatorwhoknows v
marketo rder
UnNlo o marketo rder noisetradersystematicallyonthewrongsideofthemarket NPmarketordersonlynotlimit
of
w Xlvto o rder
aggregate
uItv
marketmakers
areriskneutral
setasin
price GAM
