Estimating The Dynamics of Price
Discovery
by
Bingcheng Yan
Numeric Investors
and
Eric Zivot
Robert Richards Chaired Professor of Economics
Adjunct Professor of Finance, Statistics and Applied
Mathematics
University of Washington
May11, 2012
Presentation Outline
Background
Objectives and Contributions
Reduced Form Cointegration Model and Price
Discovery Measures
Structural Cointegration Model
Dynamic Price Discovery Measures
Empirical Example Using Fx Data
Concluding 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 stocks
stock 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 permanenttransitory 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
 p t  ( p1 t , p 2 t )  ~ I (1)
 β p t  p1 t  p 2 t ~ I (0)  β  (1,  1) 
Note: time index represents high frequency intra-day data
MA (Wold) Representation

 p t  Ψ ( L )e t , Ψ ( L ) 
Ψ
s
L s (1-sum m able)
s0
0
E [ e t ]  0 , E [ e t e s ]  

  11
 
  12
 12 
 22 
t s
t s
Reduced form Cointegration Model
Common Trends Representation:
t
p t  p 0  Ψ (1)  e j  e t  e 0 , e t  Ψ ( L ) e t
j 1

Ψ (1) 
Ψ
s
h as ran k 1
s0
  Ψ (1)   1,  1   Ψ (1)  0
 Ψ (1)  1  ,    ( 1 , 2 ) 
t
p t  p 0  1    e s  e t  e 0
s
Reduced Form Cointegration Model
Common Efficient Price Representation:
P
D efin e:  t   e t  p erm an en t sh ock
1 
p t  p 0    mt  st
1 
m t  m t  1   t  com m on efficien t p rice
P
s t  e t  e 0  tran sitory sh ocks
Reduced Form Cointegration Model
Empirical Model: Reduced Form VEC Model:
Assume approximating VEC(K-1) model implied by infinite
order cointegrated VAR
K 1
 p t  α β p t  1 
Γ
j
p t j  e t ,
j 1
s.t.
 (1)  0 , β  (1)  0
Note: Johansen (1991) factorization
Ψ (1)  β  α  Γ (1) β 
α  α  β  β  0
  1 α 
Structural Cointegration Model
 p t  D ( L )  t  D 0  t  D 1  t 1  D 2  t 1 

D(L) 

1
D k L , D 0  I 2 , D 0 exists
k
k 0
t
t   T
t
P

 ,  t ~ serially and m utually uncorrelated

 P
var(  t )  
 0
2
0 
2 
T 
 d1 ( L)
P
T
D ( L )  ( D ( L ) D ( L ))   P
 d2 (L)
P
d1 ( L) 

T
d2 (L) 
T
Permanent and Transitory Shocks
Long-run impact of transitory shock
lim
k
E t [p tk ]

T
t
k

 lim
k
l0
E t [ p tl ]
 t
T
 D (1)  0
T
Long-run impact of permanent shock
lim
k
E t [p tk ]
 t
P
k
 lim
k

E t [ p tl ]
l0
t
P
P
Normalization imposed by
common fundamental value
Long-run impact matrix
1
D (1)  
1
 D (1)  1
0

0
Common Efficient Price Representation
t
p t  p 0  D (1)   j  s t
j 1
1 
p t  p 0    mt  st
1 
m t  m t 1  
P
t
Pricing error contains
reactions to both permanent
and transitory shocks
 c om m on e ffic ie n t p ric e
s t  D ( L )  t ~ I (0 )
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
f i ,k 
 E t [ p i ,t  k ]

P
t
k


l0
 E t [  p i ,t  l ]

P
t
k


P
d i ,l
l0
  tP 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
Dynamic Measures of Price Discovery
Price Discovery Efficiency Loss (PDEL)
K
P D E Li ( K ) 
*
*
 L( f
i ,k
 1), i  1, 2
k 0
fik – 1 = pricing error w.r.t. new information
L( ) = non-negative loss function
K* = truncation lag
PDIRF and PDEL from Partial
Adjustment Model
L(∙) = abs(∙)
0 .2
PDEL = 1.5
PDEL = 0.25
0 .2
1 .0
1 .6
Delta = 0.8
1 .0
1 .6
Delta = 0.2
PDEL = 4.0
0 .2
P ric e L e v e l R e s p o n s e
1 .0
1 .6
Delta = 1.6
0
2
4
6
8
10
Steps
12
14
16
18
20
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
JPY/USD (USD/EUR)
 Any news regarding JPY(EUR) may first
or
JPY/EUR
 Does liquidity and high trading volume imply more efficient
price discovery in US dollar markets?
 Who moves first?
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/EUR
log mid quote (JPY/USD) + log mid quote
(USD/EUR)
Spreads (measures of transaction costs & liquidity)
Bid/Ask spread
Bid/Ask spread ratio:
U SD / E U R  JP Y / U SD
JP Y / E U R
Intraday Trading Sessions
Hours in
GMT
Asian
European
American
PostAmerican
22:00 06:00
06:00 12:00
12:00 18:00
18:00 22:00
134.56
134.58
134.60
134.62
134.64
134.66
JP
G
D
P
One Episode in Foreign Exchange Markets
134.48
134.50
134.52
134.54
USD/EUR * JPY/USD
JPY/EUR
23:30
23:35
23:40
23:45
Aug 11 2003, GMT
23:50
23:55
00:00
Aug 12 2003, GMT
At 23:50 on Aug. 11, 2003, Japan released the first GDP estimates for the second quarter of
2003
Asian
European
American
Post-American
USD/EUR
3200
2600
A v e ra g e H o u rly T ic k F re q u e n c y
1800
1000
200
JPY/USD
3200
2600
1800
1000
200
JPY/EUR
3200
2600
1800
1000
200
23:00
1:00
3:00
5:00
7:00
9:00
11:00
GMT
13:00
15:00
17:00
19:00
21:00
Asian
European
American
Post American
1 .3
1 .6
2 .0
2 .4
2 .8
3 .2
JPY/USD
11
13
JPY/EUR
4 5 6 7 8 9
H o u rly M e a n S p re a d s (P ip s )
1 .7
2 .1
2 .5
USD/EUR
23:00
1:00
3:00
5:00
7:00
9:00
11:00
GMT
13:00
15:00
17:00
19:00
21:00
Figure 3 – 6. Price Discovery IRFs (15 – second resolution)
Asian
Panel A. Dollar Implied JPY/EUR
0.8
Panel B. Direct JPY/EUR
1.0
P ric e L e v e l R e s p o n s e
0.8
0.6
1.2
Panel B. Direct JPY/EUR
Dollar implied JPY/EUR
0.9
1.0
P ric e L e v e l R e s p o n s e
0.9
1.0
1.0
1.2
Panel A. Dollar Implied JPY/EUR
European
0.6
0.8
0.8
Direct JPY/EUR
00:00
01:00
02:00
03:00
04:00
Time (Minutes:Seconds)
05:00
06:00
07:00
00:00
01:00
02:00
03:00
04:00
Time (Minutes:Seconds)
05:00
American
06:00
07:00
Post-American
Panel A. Dollar Implied JPY/EUR
0.8
0.6
1.2
Panel B. Direct JPY/EUR
0.6
0.8
0.9
1.0
P ric e Le v el R e sp on s e
0.8
1.0
Panel B. Direct JPY/EUR
0.8
P ric e Le v el R e sp on s e
0.9
1.0
1.0
1.2
Panel A. Dollar Implied JPY/EUR
00:00
01:00
02:00
03:00
04:00
Time (Minutes:Seconds)
05:00
06:00
07:00
00:00
01:00
02:00
03:00
04:00
Time (Minutes:Seconds)
05:00
06:00
07:00
Figure 7 – 10. Price Discovery IRFs (5 – minute resolution)
1.05
Resp. of Implied JPY/EUR Level
1.0
1.00
1.1
Resp. of Implied JPY/EUR Level
European
0.90
0.85
1.05
P ric e L e v e l R e sp o n s e
Resp. of Direct JPY/EUR Level
Direct JPY/EUR
0.85
0.8
0.90
0.9
0.95
1.00
0.9
0.8
1.1
Resp. of Direct JPY/EUR Level
1.0
P ric e L e v e l R e sp o n s e
Dollar implied JPY/EUR
0.95
Asian
00:00
05:00
10:00
15:00
20:00
25:00
30:00
Time (Minutes:Seconds)
35:00
40:00
45:00
50:00
55:00
00:00
05:00
10:00
15:00
20:00
25:00
30:00
Time (Minutes:Seconds)
35:00
American
40:00
45:00
50:00
55:00
Post-American
Resp. of Implied JPY/EUR Level
0.8
0.6
0.8
P ric e L e v e l R e sp o n s e
Resp. of Direct JPY/EUR Level
1.0
0.90
0.95
1.00
1.05
Resp. of Direct JPY/EUR Level
0.6
0.90
P ric e L e v e l R e sp o n s e
0.95
1.00
1.0
1.05
Resp. of Implied JPY/EUR Level
00:00
05:00
10:00
15:00
20:00
25:00
30:00
Time (Minutes:Seconds)
35:00
40:00
45:00
50:00
55:00
00:00
05:00
10:00
15:00
20:00
25:00
30:00
Time (Minutes:Seconds)
35:00
40:00
45:00
50:00
55:00
Asian
European
American
Post
American
an
ic
er
P
A
E
m
os
er
tA
ic
m
an
n
ea
op
ur
an
si
A
0 .7
0 .1
0 .2
0 .3
0 .4
0 .5
0 .6
PDEL Ratio
Spread Ratio
23:00
01:00
03:00
05:00
07:00
09:00
11:00
GMT
13:00
15:00
17:00
19:00
21:00
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