Estimating The Dynamics of Price Discovery

byBingcheng Yan

Numeric Investorsand

Eric ZivotRobert Richards Chaired Professor of Economics

Adjunct Professor of Finance, Statistics and Applied Mathematics

University of WashingtonMay11, 2012

Presentation Outline

BackgroundObjectives and ContributionsReduced Form Cointegration Model and Price

Discovery MeasuresStructural Cointegration ModelDynamic Price Discovery MeasuresEmpirical Example Using Fx DataConcluding Remarks

Background: Definitions

Price discovery “The search for an equilibrium price” (Schreiber and

Schwartz, JPM, 1986) “The dynamic process by which markets impound new

information” (Hasbrouck, JF, 1995) The incorporation of the information implicit in investor

trading into market prices (Lehmann, JFM, 2002) One of the most important functions of financial markets

Background: Questions

Research questions Does the proliferation of alternative trading venues and the

resulting market fragmentation adversely affect price discovery?

How do the dynamics of price discovery depend on market characteristics such as trading costs, liquidity?

What institutional factors and trading protocols facilitate information aggregation and price discovery?

Which markets move first in incorporating new information?

Answers require econometric methodology for measuring the dynamics of price discovery

Background: Methodology

Institutional trend of financial markets Trading of identical or closely related assets in multiple

markets; cross-listed stocksstock index and index futures, stock and stock options, direct and implied exchange rates

Provides a mechanism to measure price discovery

Background: Methodology

A common implicit efficient price shared by multiple market prices – cointegration framework

Hasbrouck (1995) proposed a reduced form cointegration model for arbitrage linked multiple market prices and defined the information share measure of price discovery

Booth et al. (1999) used Granger-Gonzalo permanent-transitory decomposition and defined the component share measure of price discovery.

There exists substantial confusion regarding the interpretation of existing price discovery measures because they are based on reduced form residuals

Existing measures of price discovery are static in nature

Objectives and Contributions of This Paper

Propose structural cointegration model with identified permanent and transitory shocks Borrow SVAR methodology from empirical

macroeconomics Propose a new methodology for measuring the

dynamic price discovery process Price discovery impulse response functions Price discovery efficiency loss measures

Illustrate the new approach with an empirical application to Fx markets Price discovery between the US dollar implied JPY/EUR

and the direct JPY/EUR rates Investigate impact of trading costs and liquidity on price

discovery dynamics

Reduced Form Cointegration Model

Same asset trading in two arbitrage linked markets

Note: time index represents high frequency intra-day data

0

11 12

12 22

( ) , ( ) (1-summable)

0[ ] , [ ]

t t s ss

t t s

L L L

t sE E

t s

p Ψ e Ψ Ψ

e 0 e e

1 2( , ) ~ (1)t t tp p Ip

1 2 ~ (0) (1, 1)t t tp p I β p β

MA (Wold) Representation

Reduced form Cointegration Model

0 01

0

1 2

0 0

(1) , ( )

(1) has rank 1

(1) 1, 1 (1) 0

(1) , ( , )

t

t j t t tj

ss

t

t s ts

L

p p Ψ e e e e Ψ e

Ψ Ψ

Ψ Ψ

Ψ 1

p p 1 e e e

Common Trends Representation:

Reduced Form Cointegration Model

0

1

0

Define: permanent shock

1

1

common efficient price

transitory shocks

Pt t

t t t

Pt t t

t t

m

m m

e

p p s

s e e

Common Efficient Price Representation:

Reduced Form Cointegration Model

1

11

,

s.t. (1) , (1)

K

t t j t j tj

p αβ p Γ p e

0 β 0

Assume approximating VEC(K-1) model implied by infinite order cointegrated VAR

Note: Johansen (1991) factorization

0

)1()1( 1

ββαα

αβΓαβΨ

Empirical Model: Reduced Form VEC Model:

Structural Cointegration Model

0 1 1 2 1

10 2 0

0

2

2

1 1

2 2

( )

( ) , , exists

, ~ serially and mutually uncorrelated

0var( )

0

( ) ( )( ) ( ( ) ( ))

( ) ( )

t t t t t

kk

k

Pt

t tTt

Pt

T

P TP T

P T

L

L L

d L d LL L L

d L d L

p D D D D

D D D I D

D D D

Permanent and Transitory Shocks

0

[ ] [ ]lim lim (1)

kPt t k t t l

P Pk klt t

E E

p pD 1

0

[ ] [ ]lim lim (1)

kTt t k t t l

T Tk klt t

E E

p pD 0

Long-run impact of transitory shock

Long-run impact of permanent shock

Long-run impact matrix

1 0(1)

1 0

D

Normalization imposed by common fundamental value

Common Efficient Price Representation

01

0

1

(1)

1

1

common efficient price

( ) ~ (0)

t

t j tj

t t t

Pt t t

t t

m

m m

L I

p p D s

p p s

s D

Pricing error contains reactions to both permanent and transitory shocks

Identification of Structural Cointegration

Parameters of structural model can be uniquely identified using a modification of the P-T decomposition of Gonzalo and Ng (2001, JEDC)

Identification does not depend on the ordering of the variables in the VAR

New Dynamic Measures of Price Discovery

Price Discovery Impulse Response Function (PDIRF): New information → market price response

permanently moves the efficient price, mt, and drives multiple market prices to mt in the long run

A direct characterization of how market prices discover the new efficient price

Pt

, ,, ,

0 0

[ ] [ ]k kt i t k t i t l P

i k i lP Pl lt t

E p E pf d

Dynamic Measures of Price Discovery

Price Discovery Efficiency Loss (PDEL)

fik – 1 = pricing error w.r.t. new information

L( ) = non-negative loss function

K* = truncation lag

*

*,

0

( ) ( 1), 1,2K

i i kk

PDEL K L f i

PDIRF and PDEL from Partial Adjustment Model

0.2

1.0

1.6

0 2 4 6 8 10 12 14 16 18 20Steps

Delta = 0.2

0.2

1.0

1.6Delta = 0.8

0.2

1.0

1.6 Delta = 1.6

Pri

ce L

eve

l Re

spo

nse

PDEL = 1.5

PDEL = 0.25

PDEL = 4.0

L(∙) = abs(∙)

Empirical Example: Price Discovery in Fx Markets

Empirical analysis of price discovery dynamics of the direct JPY/EUR rate and the US dollar implied rate (from JPY/USD and USD/EUR)

US dollar, major vehicle currency in Fx markets, has trillions of dollar daily turnover

Any news regarding JPY(EUR) may first or

Does liquidity and high trading volume imply more efficient price discovery in US dollar markets? Who moves first?

JPY/USD (USD/EUR)

JPY/EUR

Data Set and Variables Bid-ask quotes on spot Fx rates: USD/EUR, JPY/USD, and

JPY/EUR, time stamped up to milliseconds in GMT EBS (Electronic Brokerage Service) Quotes are firm (tradable)

Sample: 12 business weeks, July 6 – September 26, 2003 One business week: 22:00 Sunday – 22:00 Friday, GMT

Prices = log of mid quotes * 10000 (price changes in basis points)

Irregularly spaced quotes for all rates aligned to common time clock using “previous tick” method.

Data Set and Variables

Dollar implied rate for JPY/EURlog mid quote (JPY/USD) + log mid quote

(USD/EUR) Spreads (measures of transaction costs & liquidity)

Bid/Ask spreadBid/Ask spread ratio:

/ /

/

USD EUR JPY USD

JPY EUR

Intraday Trading Sessions

Asian European American Post-American

Hours in GMT

22:00 - 06:00

06:00 - 12:00

12:00 - 18:00

18:00 - 22:00

One Episode in Foreign Exchange Markets

At 23:50 on Aug. 11, 2003, Japan released the first GDP estimates for the second quarter of 2003

23:30 23:35 23:40 23:45 23:50 23:55 00:00Aug 11 2003, GMT Aug 12 2003, GMT

134.4

8134.5

0134.5

2134.5

4134.5

6134.5

8134.6

0134.6

2134.6

4134.6

6

USD/EUR * JPY/USDJPY/EUR

200

1000

1800

2600

3200

23:00 1:00 3:00 5:00 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00GMT

JPY/EUR

200

1000

1800

2600

3200JPY/USD

200

1000

1800

2600

3200USD/EUR

Ave

rag

e H

ou

rly

Tic

k F

req

ue

ncy

Asian European American Post-American

45

67

89

1113

23:00 1:00 3:00 5:00 7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00GMT

JPY/EUR

1.6

2.0

2.4

2.8

3.2

JPY/USD

1.3

1.7

2.1

2.5 USD/EUR

Hou

rly M

ean

Spr

eads

(P

ips)

Asian European American Post American

Figure 3 – 6. Price Discovery IRFs (15 – second resolution)Asian European

American Post-American

Dollar implied JPY/EUR

Direct JPY/EUR

0.6

0.8

1.0

1.2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00Time (Minutes:Seconds)

Panel B. Direct JPY/EUR

0.6

0.8

1.0

1.2

Panel A. Dollar Implied JPY/EUR

Price

Le

ve

l Re

sp

on

se

0.8

0.9

1.0

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00Time (Minutes:Seconds)

Panel B. Direct JPY/EUR

0.8

0.9

1.0

Panel A. Dollar Implied JPY/EUR

Price

Le

ve

l Re

sp

on

se

0.8

0.9

1.0

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00Time (Minutes:Seconds)

Panel B. Direct JPY/EUR

0.8

0.9

1.0

Panel A. Dollar Implied JPY/EUR

Price

Le

ve

l R

esp

on

se

0.6

0.8

1.0

1.2

00:00 01:00 02:00 03:00 04:00 05:00 06:00 07:00Time (Minutes:Seconds)

Panel B. Direct JPY/EUR

0.6

0.8

1.0

1.2

Panel A. Dollar Implied JPY/EUR

Price

Le

ve

l R

esp

on

se

Figure 7 – 10. Price Discovery IRFs (5 – minute resolution)Asian European

American Post-American

Dollar implied JPY/EUR

Direct JPY/EUR

0.8

0.9

1.0

1.1

00:00 05:00 10:00 15:00 20:00 25:00 30:00 35:00 40:00 45:00 50:00 55:00Time (Minutes:Seconds)

Resp. of Direct JPY/EUR Level

0.8

0.9

1.0

1.1

Resp. of Implied JPY/EUR Level

Price

Le

ve

l Re

sp

on

se

0.8

50.9

00.9

51.0

01.0

5

00:00 05:00 10:00 15:00 20:00 25:00 30:00 35:00 40:00 45:00 50:00 55:00Time (Minutes:Seconds)

Resp. of Direct JPY/EUR Level

0.8

50.9

00.9

51.0

01.0

5Resp. of Implied JPY/EUR Level

Price

Le

ve

l Re

sp

on

se

0.9

00.9

51.0

01.0

5

00:00 05:00 10:00 15:00 20:00 25:00 30:00 35:00 40:00 45:00 50:00 55:00Time (Minutes:Seconds)

Resp. of Direct JPY/EUR Level

0.9

00.9

51.0

01.0

5

Resp. of Implied JPY/EUR Level

Price

Le

ve

l R

esp

on

se

0.6

0.8

1.0

00:00 05:00 10:00 15:00 20:00 25:00 30:00 35:00 40:00 45:00 50:00 55:00Time (Minutes:Seconds)

Resp. of Direct JPY/EUR Level

0.6

0.8

1.0

Resp. of Implied JPY/EUR Level

Price

Le

ve

l R

esp

on

se

Asian

European

American

Post American

23:00 01:00 03:00 05:00 07:00 09:00 11:00 13:00 15:00 17:00 19:00 21:00GMT

0.1

0.2

0.3

0.4

0.5

0.6

0.7

PDEL RatioSpread Ratio

Conclusions

Propose new approach for the econometric analysis of price discovery dynamics based on structural cointegration model

Propose new measures of the dynamics of price discovery: PDIRF, PDEL

In application to Fx markets, show implied dollar JPY/EUR rate incorporates new information faster than direct JPY/EUR rate