Amati Pfleiderer 1988

7/30/2019 Amati Pfleiderer 1988

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Siraprapa Watakit

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Overview and Contribution Theoretical Background and Model Conclusion

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Overview

The paper develop a theory around trading patterns which arises as aresult ofinformed traderand strategic liquidity trader.

The results provide some empirical explanation about tradingpatterns ofvolume andprice variability.

Contribution

New models which accounted for strategic behavior of liquidity trader

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Typical observation: Trading patterns of a day a U shape. Tradingvolume is intense at the beginning and endof the day,

Such empirical finding leads to the following question

Why does trading tend to be concentrated in particular time?

Why are returns more variable in some periods and less variable inothers?

Why do the periods of higher trading volume also tend to be theperiods of higher return variability?

To answer these question, we had better look at the trader behaviors

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Traders

Big assumption

Previous studies assumed that all un-informed or liquidity trader are

just noises e.g. ordinary or individual trader This is a too big assumption if we consider that large financial

institutions are also, many times, considered as liquidity traders ,whose trades reflects client liquidity needs

Minimizing transaction costs is obviously in order

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Traders

Informed

Liquidity

No

strategiesWith

Strategies


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Developing models: Based on Glosten Milgrom(1985) and*Kyle(1984,1985)

Market maker: Risk neutral, setting prices based on aggregated flows

Traders:

informed traders act on private information

non-discretionary traders just trade, no timing model

discretionary traders trade with strategic timing model

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Model of informed traders

The trading time is divided into T period

F is value of asset, tis mean zero i.i.d. random variable of public

information

In each period t, there assumed to be nt

trader who observe private

information at t+1

+twhere var(

t)=

t

If informed traders received noisy signal att, the information will bepublic at the beginning oft+1

Assumed that informed trader will act on it att+1. ( This is a one-period model, no linkage between period, information is short-lived), he needs to decide how much to trade

Order flows of informed traders is

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Model of non-discretionary trader

He needs to trade immediately, with a specific amount at 1 period(no split trade)

Order flows of non-discretionary trader is Model of discretionary trader

He needs not to trade immediately but he must trade before the endof day, so he choose carefully when to trade. He can also split trade

Suppose there is m discretionary traders, order flows is

Hence, all aggregated order flows from all 3 traders type is

Note that variance of uninformed order, , affects the equilibrium price

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The market maker determine the price from aggregated order flow

Where is a Kyle market depth parameter(price impact from orderflows)

Notice that market maker strategy include both public and privateinformation in his model

Main result in this section: for discretionarytrader, there aretendency that they will trade in the same period.

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Given that market maker follow the pricing rule, optimal strategiesfor informed traderand discretionary tradercan be determined

Xdepends on

no. of other informed, nt

variance of order, variance of private info.

is decreasing in nt

, .

Since (total variance of uninformed trader) is endogenous, thestrategic behavior of discretionary trader affect the prices

This is a significant departure from a passive role as in other studies

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For discretionary traders

In Admati and Pfleiderer model, discretionary traders are assumed totake as given.

If it werent, there will be many and many equillibrium since everyaction will affect

Hence, the problem is reduced to justchoose to transact at thelowest cost period offered by market maker

That lowest cost period is the one with highest

It follows that, all discretionary traders will select the same periodto transactinducing price patterns

Since the optimal strategy for informed traders depends on ,the informed trader patterns will follow discretionary patternsas well

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The model take strategic behavior of discretionary un-informedtrader into account which results in the following findings

discretionary trader chooses the optimal time to transact

his action affect the total variance of uninformed trade, Market maker price rules depend on aggregated order flow which is

also depends on ,

Since discretionary trader takes as given, all discretuinary traderwill transact at the lowest cost periodinducing patterns

discretionary trader pattern will causes informed trader pattern aswell

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Amati Pfleiderer 1988