jumps and information asymmetry in the us treasury market · jumps and information asymmetry in the...
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Jumps and information asymmetry in the USTreasury market
Ana-Maria H. DumitruGiovanni Urga
University of SurreyCass Business School, City University
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Background and objectives
Background and objectives
Jumps=big unexpected changes in the prices of financialsecuritiesrecent statistical tools to identify jumps
literature in high frequency econometrics
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Background and objectives
Background and objectives
unanticipative nature: bring new info to the market
mark the incorporation of new info in prices
Hypothesis: no private info after the jump
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Background and objectives
Background and objectives
Research objectives
MAIN OBJECTIVE: investigate the role of jumps in dissipatinginformational asymmetry in the US Treasury bond market
identify jumps in the US Treasury market
determinants of jumps: the liquidity puzzle
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Background and objectives
Outline
1 Background and objectives
2 Other research work in the area
3 Data and methodology
4 Jumps and determinants
5 Jumps and informativeness of the order flow
6 Conclusion and further developments
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Other research work in the area
Other research work in the area
Jiang et al (2011) and Dungey et al (2009): US-Treasury bonds
Lahaye et al (2011): 8 different financial assets
Boudt and Petitjean (2014): Dow Jones Industrial Average indexconstituents
Gilder et al (2014): portfolio of US stocks
Common findings
identify jumps, co-jumps
most frequent jump determinants: public info, liquidity shocks
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Data and methodology
Data
Brokertec trading platform
order book and trade data for the 2-, 5-, 10- and 30- year bondsand covering a period between January 2003 and March 2004
the 30-year- less liquid
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Data and methodology
Data
7:30 a.m. EST and 5:00 p.m. EST
sampling: every 5 and 15 minutes
mid-quotes for jump testing
trade data
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Data and methodology
Methodology- Jump identification
Dumitru and Urga (2012): thorough comparison between differentjump detection procedures:
evidence that combining different tests and different samplingfrequencies through reunions and intersections can lead to betterpower and size properties
final jumps: the ones identified on 15 minutes data by theLee-Mykland (2008) test corrected for periodicity in the volatilityfactor if they were also detected by the Barndorff-Nielsen andShephard (2006) procedure on either 5 or 15 minutes data
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Data and methodology
Working hypotheses: data generating process
semimartingale (Brownian semimartingale + jump)
µ drift; σ diffusion
usually µ, σ cadlag; µ predictable
dpt = µtdt +σtdWt +dJt ,
J(t) =Nt
∑j=1
c j,
where
Nt counting process, λt
c j size of the jump
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Data and methodology
Working hypotheses: what is to estimate?
quadratic variation of the process:
QVt =∫ t
0σ2
s ds+Nt
∑j=1
c2t j,
integrated volatility (variance)
IVt =∫ t
0σ2
s ds
interval [0, t] is split into n equal subintervals of length δj-th intraday return
r j = pt−1+ jδ − pt−1+( j−1)δ
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Data and methodology
Barndorff-Nielsen and Shephard (2006) test for jumps
H0: no jumps in the sample path in the interval [0, t]
RVt =n
∑j=1
r2j
p→ QVt ,
BVt =π2
n
∑j=1
|r j||r j+1|p→ IVt
1− BVtRVt√
0.61δ max(
1, T Qt
BV 2t
)
where T Qt = n1.74(
nn−2
)∑n
j=3 |r j−2|4/3|r j−1|
4/3|r j|4/3 consistent for
integrated quarticity
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Data and methodology
Lee-Mykland (2008) test for jumps
H0: no jumps in the sample path at time t j
z j = |r j|/√
V̂j,
where V̂j = BVt j/(K −2), with K the window size on which BVt j iscalculated
(max(z j)−Cn)/SnL→ ξ , P(ξ ) = exp(−e−x)
Nonparametric correction for periodicity based on Boudt et al. (2011).
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Jumps and determinants
Detected jumps
the 2-year bonds jump in 14.5% of the days, the 5-year in 10.6%,the 10-year in 9.6% and finally, the 30-year in 17.91% of the days
jump size: increasing with the maturity
Average Y2 Y5 Y10 Y30size 0.081% 0.24% 0.4% 0.77%
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Jumps and determinants
Jumps and macroeconomic announcements
Y2 Y5 Y10 Y30Match 94 92.16% 79 100.00% 60 93.75% 72 83.72%
No match 8 7.84% 4 6.25% 14 16.28%Total 102 100.00% 79 100.00% 64 100.00% 86 100.00%
Table: Number and percentages of jumps matched with macroeconomicannouncements
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Jumps and determinants
The liquidity around jump times puzzle
−25 −20 −15 −10 −5 0 5 10 15 20 250
20
40
60
80
100
120
140Depth on the ask side
minutes−25 −20 −15 −10 −5 0 5 10 15 20 25
0
20
40
60
80
100
120
140
160Depth on the bid side
minutes
−25 −20 −15 −10 −5 0 5 10 15 20 250
5
10
15Spread
minutes−25 −20 −15 −10 −5 0 5 10 15 20 25
0
2
4
6
8
10
12x 10
6 Trading volume
minutes
Figure: Various liquidity measures around the time of jump for the 2-YearbondDumitru and Urga (2014) Jumps US Treasury 05/09/2014 16 / 27
Jumps and determinants
The liquidity around jump times puzzle
most jumps occur as a result of macroeconomic announcements
before jumps, a severe liquidity withdrawal is observed
before announcements- market awaits
simultaneity of jumps and liquidity withdrawal= both caused byannouncements
endogeneity issue
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Jumps and determinants
Regression explaining jump occurrence
Pr{I jump = 1|X}= f (Surprise,BVt) ,
where f is extreme value
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Jumps and determinants
Determinants of jump occurrence
Coefficient p-value Goodness of fitY2 C -2.53 0.0000 H-L Statistic 5.74
Surprise 0.29 0.0021 Prob. Chi-Sq(8) 0.68Volatility (BV) 1881.19 0.0000
Y5 C -2.37 0.0000 H-L Statistic 4.36Surprise 0.40 0.0002 Prob. Chi-Sq(8) 0.82
Volatility (BV) 432.54 0.0002
Y10 C -1.62 0.0000 H-L Statistic 8.28Surprise 0.30 0.0014 Prob. Chi-Sq(8) 0.41
Volatility (BV) 107.26 0.0262
Y30 C -1.33 0.0000 H-L Statistic 11.91Surprise 0.18 0.0284 Prob. Chi-Sq(8) 0.16
Volatility (BV) 88.96 0.0066
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in theproximity of jumps
starting point: Madhavan, Richardson and Roomans (1997)’model of price formation:
pti − pti−1 = (φ +θ)xti − (φ +ρθ)xti−1 + eti
Green(2004) uses this model to explore the informativeness of theorderflow when news impact the market
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in the proximity of jumps
Estimated models:Model 1
pti − pti−1 =(φJ +θJ)IJ,ti xt − (φJ +ρθJ)IJ,ti xti−1 +(φNJ +θNJ)INJ,ti xt−
(φNJ +ρθNJ)INJ,ti xti−1 + eti ,
Model 2
pti − pti−1 =(φJ0+θJ0)IJ,ti IJ0,ti xti − (φJ0+ρθJ0)IJ,ti IJ0,ti xti−1 +(φB +θB)IJ,ti IB,ti xti−
(φB +ρθB)IJ,ti IB,ti xti−1 +(φA +θA)IJ,ti IA,ti xti − (φA +ρθA)IJ,ti IA,ti xti−1+
(φNJ +θNJ)INJ,ti xti − (φNJ +ρθNJ)INJ,ti xti−1+ eti ,
Model 3
pti − pti−1 =(φJ0+θJ0)IJ,ti IJ0,ti xti − (φJ0+ρθJ0)IJ,ti IJ0,ti xti−1+
(φB5+θB5)IJ,ti IB5,ti xti − (φB5+ρθB5)IJ,ti IB5,ti xti−1+
(φA5+θA5)IJ,ti IA5,ti xti − (φA5+ρθA5)IJ,ti IA5,ti xti−1+
(φother +θother)Iother,ti xti − (φother +ρθother)Iother,ti xti−1 + eti
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in the proximity of jumps
Estimated models:Model 4
pti − pti−1 =(φJ0+θJ0)IJ,ti IJ0,ti xti − (φJ0+ρθJ0)IJ,ti IJ0,ti xti−1+
(φB10+θB10)IJ,ti IB10,ti xti − (φB10+ρθB10)IJ,ti IB10,ti xti−1+
(φA10+θA10)IJ,ti IA10,ti xti − (φA10+ρθA10)IJ,ti IA10,ti xti−1+
(φother +θother)Iother,ti xti − (φother +ρθother)Iother,ti xti−1 + eti ,
Model 5
pti − pti−1 =(φJ0+θJ0)IJ,ti IJ0,ti xti − (φJ0+ρθJ0)IJ,ti IJ0,ti xti−1+
(φB20+θB20)IJ,ti IB20,ti xti − (φB20+ρθB20)IJ,ti IB20,ti xti−1+
(φA20+θA20)IJ,ti IA20,ti xti − (φA20+ρθA20)IJ,ti IA20,ti xti−1+
(φother +θother)Iother,ti xti − (φother +ρθother)Iother,ti xti−1 + eti ,
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in theproximity of jumps
estimation method:GMM
for Model 1,
E
xtixti−1 − x2tiρ
eti −α(eti −α)IJ,tixti(eti −α)IJ,tixti−1
(eti −α)INJ,tixti(eti −α)INJ,tixti−1
= 0
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in the proximity of jumps.
Results
Model 1 Model 2 Model 3Coef Prob. Coef Prob. Coef Prob.
α 0.003 0.003 α 0.003 0.004 α 0.003 0.004φJ 0.031 0.028 φJ0 -0.852 0.114 φJ0 -0.842 0.118θJ 0.376 0.000 θJ0 1.378 0.001 θJ0 1.527 0.000
φNJ 0.046 0.000 φB 0.065 0.008 φB5 0.191 0.172θNJ 0.326 0.000 θB 0.286 0.000 θB5 0.345 0.000
φA 0.032 0.011 φA5 -0.135 0.286θA 0.360 0.000 θA5 0.667 0.000
φNJ 0.046 0.000 φother 0.046 0.000θNJ 0.326 0.000 θother 0.329 0.000
Model 4 Model 5Coef Prob. Coef Prob.
α 0.003 0.004 α 0.003 0.004φJ0 -0.842 0.118 φJ0 -0.842 0.119θJ0 1.528 0.000 θJ0 1.419 0.001
φB10 0.154 0.054 φB20 0.124 0.046θB10 0.246 0.000 θB20 0.266 0.000φA10 -0.083 0.279 φA20 -0.056 0.236θA10 0.573 0.000 θA20 0.506 0.000
φother 0.047 0.000 φother 0.047 0.000θother 0.328 0.000 θother 0.326 0.000
Estimated coefficients and p-values for Models 1-5 for the 2-Year bond. Throughout all the models, we use a unique correlation
coefficient for the order flow: ρ̂ = 0.661
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in the proximity of jumps.
Results
Model 1 Model 2 Model 3Coef Prob. Coef Prob. Coef Prob.
α 0.004 0.010 α 0.004 0.011 α 0.004 0.011φJ -0.171 0.000 φJ0 -1.618 0.076 φJ0 -1.671 0.067θJ 0.858 0.000 θJ0 2.958 0.001 θJ0 3.277 0.000
φNJ -0.177 0.000 φB -0.175 0.000 φB5 -0.216 0.144θNJ 0.845 0.000 θB 0.761 0.000 θB5 0.773 0.000
φA -0.130 0.000 φA5 -0.017 0.953θA 0.788 0.000 θA5 1.144 0.000
φNJ -0.177 0.000 φother -0.173 0.000θNJ 0.845 0.000 θother 0.841 0.000
Model 4 Model 5Coef Prob. Coef Prob.
α 0.004 0.011 α 0.004 0.011φJ0 -1.670 0.068 φJ0 -1.607 0.078θJ0 3.277 0.000 θJ0 3.032 0.001
φB10 -0.263 0.012 φB20 -0.315 0.036θB10 0.729 0.000 θB20 0.805 0.000φA10 -0.181 0.281 φA20 -0.120 0.237θA10 0.944 0.000 θA20 0.841 0.000
φother -0.172 0.000 φother -0.172 0.000θother 0.840 0.000 θother 0.840 0.000
Estimated coefficients and p-values for Models 1-5 for the 5-Year bond. Throughout all the models, we use a unique correlation
coefficient for the order flow: ρ̂ = 0.693
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Jumps and informativeness of the order flow
Analysis of the informativeness of the order flow in the proximity of jumps.
Results
Model 1 Model 2 Model 3Coef Prob. Coef Prob. Coef Prob.
α 0.003 0.310 α 0.003 0.299 α 0.003 0.306φJ -0.104 0.016 φJ0 -0.836 0.637 φJ0 -0.910 0.608θJ 1.322 0.000 θJ0 0.000 1.000 θJ0 0.517 0.739
φNJ -0.202 0.000 φB -0.030 0.707 φB5 0.516 0.677θNJ 1.365 0.000 θB 1.037 0.000 θB5 2.312 0.017
φA -0.088 0.035 φA5 0.153 0.606θA 1.263 0.000 θA5 1.715 0.000
φNJ -0.202 0.000 φother -0.190 0.000θNJ 1.365 0.000 θother 1.357 0.000
Model 4 Model 5Coef Prob. Coef Prob.
α 0.003 0.305 α 0.004 0.286φJ0 -0.910 0.608 φJ0 -0.873 0.624θJ0 0.520 0.737 θJ0 -0.053 0.973
φB10 0.279 0.574 φB20 -0.308 0.448θB10 1.567 0.018 θB20 1.932 0.000φA10 -0.020 0.943 φA20 0.154 0.350θA10 1.509 0.000 θA20 1.363 0.000
φother -0.191 0.000 φother -0.195 0.000θother 1.356 0.000 θother 1.359 0.000
Estimated coefficients and p-values for Models 1-5 for the 10-Year bond. Throughout all the models, we use a unique correlation
coefficient for the order flow: ρ̂ = 0.672
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Conclusion
Conclusions
the paper analyzes the occurrence of jumps and role in reducingthe informational asymmetry in the US Treasury market.
we detect and estimate jumps in the US Treasury 2-,5-,10- and30-year bondsthe release of macroeconomic news is found to be the major causeof jumps in the bond prices
2- and 5- year maturities: the level of information asymmetryincreases immediately after jumps occur and remains high up to20 minutes after the jump
before a jump: low degree of informational asymmetry, consistentwith a low extent of information leakage
10- year maturity behaves differently (different explanations)
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