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China-EU Summer School on Complexity Sciences

Universal price impact functions of Universal price impact functions of individual trades in an order-driven individual trades in an order-driven

marketmarketWei-Xing ZHOUWei-Xing ZHOU

East China University of Science and East China University of Science and TechnologyTechnology

14 August 201014 August 2010

Shanghai University for Science and Shanghai University for Science and TechnologyTechnology

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OutlinesOutlines

1. Order-driven markets1. Order-driven markets

2. LFM scaling with NYSE data2. LFM scaling with NYSE data

3. LC scaling with ASE data3. LC scaling with ASE data

4. New scaling with Chinese data4. New scaling with Chinese data

5. Summary5. Summary

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Order-driven marketOrder-driven market

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Cancelation of all orders at the best ask Cancelation of all orders at the best ask or bidor bid

Submission of an order inside the Submission of an order inside the spreadspread

All partially filled orders (market orders)All partially filled orders (market orders)Some filled orders (market orders)Some filled orders (market orders)

Which events move the price?Which events move the price?

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Market orders vs. Limit ordersMarket orders vs. Limit orders

Buy orders vs. Sell ordersBuy orders vs. Sell orders

Filled orders vs. Partially filled orderFilled orders vs. Partially filled order

Classification of ordersClassification of orders

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• Mid-price at time t:Mid-price at time t:

• Immediate price impact is defined as Immediate price impact is defined as the relative change of mid-price right the relative change of mid-price right before and after the transaction:before and after the transaction:

Immediate price impactImmediate price impact

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• Volume-volatility relation:Volume-volatility relation: vs. vs. • Volume-return relation:Volume-return relation: vs.vs.

Volume-price relationshipVolume-price relationship

Karpoff, J. Fin. Quant. Analysis 22 (1987) 109-126.

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New York Stock ExchangeNew York Stock Exchange

Lillo, Farmer & Mantegna, Master curve for price-Lillo, Farmer & Mantegna, Master curve for price-impact function, impact function, NatureNature 321 (2003) 129-130. 321 (2003) 129-130.

TAQ of 1000 largest stocks on NYSE (1995-1998)TAQ of 1000 largest stocks on NYSE (1995-1998)

vs.vs.

SourceSource

Date setsDate sets

VariablesVariables

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20 Portfolios grouped with Cap20 Portfolios grouped with Cap

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LFM scalingLFM scaling

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LFM scaling in Chinese data?LFM scaling in Chinese data?

NOT satisfactory!!!

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Australian Stock ExchangeAustralian Stock Exchange

Lim & Coggins, The immediate price impact of trades Lim & Coggins, The immediate price impact of trades on the Australian Stock Exchange, on the Australian Stock Exchange, Quantitative FinancQuantitative Financee (2005) 365-377. (2005) 365-377.

300 constituent stocks of S&P asx 300 index traded on 300 constituent stocks of S&P asx 300 index traded on the ASE (2001-2004)the ASE (2001-2004)

vs.vs.

Normalized daily-normalized trade sizeNormalized daily-normalized trade size

SourceSource

Date setsDate sets

VariablesVariables

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10 Portfolios grouped with Cap10 Portfolios grouped with Cap

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LC scalingLC scaling

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LC scalingLC scaling

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LC scalingLC scaling

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LC scalingLC scaling

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LC scaling in Chinese data?LC scaling in Chinese data?

NOT satisfactory!!!

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Shenzhen Stock ExchangeShenzhen Stock Exchange

Zhou, Universal price impact functions of Zhou, Universal price impact functions of individual trades in an order-driven market, individual trades in an order-driven market, Quantitative FinanceQuantitative Finance (2010) to appear. (2010) to appear.

23 constituent stocks of SZSE component index 23 constituent stocks of SZSE component index traded on the SZSE (2003)traded on the SZSE (2003)

vs.vs.

SourceSource

Date setsDate sets

VariablesVariables

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23 SZSE stocks23 SZSE stocks

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LFM scaling in Chinese data?LFM scaling in Chinese data?

NOT satisfactory!!!

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LC scaling in Chinese data?LC scaling in Chinese data?

NOT satisfactory!!!

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Simple scaling for buy ordersSimple scaling for buy orders

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Simple scaling for sell ordersSimple scaling for sell orders

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No buy-sell asymmetryNo buy-sell asymmetry

Slope = 2/3

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Anomalous hook explainedAnomalous hook explained

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SummarySummary

Simpler scaling form without additional variableSimpler scaling form without additional variable

Partially filled orders have greater price impactPartially filled orders have greater price impact

No buy-sell asymmetry at the transaction levelNo buy-sell asymmetry at the transaction level

Anomalous volume-return relation explainedAnomalous volume-return relation explained

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Thank you for your attention!