Estimating The Dynamics of Price Discovery by Bingcheng Yan Numeric Investors and Eric Zivot Robert Richards Chaired Professor of Economics Adjunct Professor.
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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
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