Modelling Intraday Volatility in European Bond Market Hanyu Zhang ICMA Centre, Henley Business School Young Finance Scholars Conference 8th May,2014
Outline 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion
Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion
Volatility is a central issue Strong persistence in intraday bond yield volatility Fleming and Lopez (1999) Shift of yield volatility in Spanish market Diaz et al. (2006) Spillover Effects in European bond market Christiansen (2007) Sovereign rating effect Afonso et al. (2013) Deepening of sovereign bond crisis
Evidence from the Data Annualized daily return standard deviation
Stylised facts intraday volatility and high frequency data Intraday volatility periodicity Admati and Pfleiderer (1988), Andersen and Bollerslev (1997), Engle and Russell (1998) Macro news matters Bollerslev et al. (2000), Andersen et al. (2003) Interaction with lower frequency Andersen and Bollerslev (1998) Microstructure noise and its implication Roll (1984), Huang and Stoll (1996), Bandi and Russell (2008), Oomen (2006)
Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion
Institutional detail MTS(Mercato dei Titoli di Stato) tick-by-tick data Euro MTS and Local MTS parallel trading platforms for benchmark securities Trading 8:15-17:30 CET 1 Limit order market update when best 5 bid and asks changed 1 Detailed explanation:dufour and Skinner (2004)
Construction of return series Benchmark 10 year bonds Six Countries: Belgium, France, Germany, Italy, Netherlands, Spain Best bid and ask across all platforms Sample period: Daily log return series:january 2009-March 2012, April 2012-December 2013 10-min log return series: April 2012- December, 2013 Preserving liquidity and maturity Switching from off-the-run to on-the-run
Details of Switching Deciding switching date based on Pasquariello and Vega (2009) Maturity within 8.5-11.5 years implications on mean and variance modelling: inheritance Countries number of bonds average duration (unit:month) Belgium 6 10.84 France 9 6.66 Germany 14 4.28 Italy 11 5.45 Netherlands 6 11.73 Spain 9 6.66
Summary Statistics Country N Mean St.Dev Skewness Kurtosis Panel A: In-sample daily return Belgium 826 0.0082 0.498 0.234 5.541 France 827 0.0095 0.412 0.003 2.382 Germany 828 0.0151 0.463 0.174 1.599 Italy 829 0.0003 0.645 1.471 22.219 Netherlands 829 0.0162 0.402 0.197 1.689 Spain 828 0.0067 0.622 1.971 20.810 Panel B: 10-min return Belgium 23474 0.0005 0.040 0.031 17.453 France 23318 0.0004 0.041 0.281 12.054 Germany 23387 0.0002 0.045 0.149 7.835 Italy 23521 0.0010 0.085 2.319 109.67 Netherlands 23552 0.0003 0.046 0.284 12.473 Spain 22761 0.0004 0.096 1.073 48.832 a. Mean and standard deviation are in percentage terms. b. Number of observations of 10-minute returns may vary because of the late appearance of the first quote everyday.
Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion
The Model Engle and Sokalska (2012) Multiplicative form of intraday return r t,i = h t s i q t,i ɛ t,i and ɛ t,i D(0, 1) where h t daily variance forecast s i diurnal volatility (intraday periodicity) q t,i intraday variance with E(q t,i ) = 1 ɛ t,i error term
Daily volatility r k = a + φ(l)r k + ν k ν k F k 1 D(0, h k ) (1) h k = κ + ρν 2 k 1 + δh k 1 (2) Explicit account for Kurtosis: t-distribution Jumps because of Securities Market Programme(SMP) alternative way adding dummy variables
GARCH(-t) estimation Country a φ 1 φ 2 κ ρ δ df Belgium 0.0134 0.1285 0.0879 0.0070 0.1034 0.8614 (1.04) (3.33) ( 2.33) (3.00) (4.44) (29.16) France 0.0189 0.0956 0.0025 0.0653 0.9174 (1.58) ( 2.61) (2.08) (4.33) (49.07) Germany 0.0145 0.0783 0.1134 0.0034 0.0603 0.9235 (1.04) (2.21) ( 3.18) (1.84) (3.55) (42.58) Italy 0.0078 0.1516 0.1700 0.0029 0.0945 0.8400 5.1742 (0.70) (4.24) ( 4.65) (1.85) (2.77) (16.24) (6.19) Netherlands 0.0212 0.0836 0.0018 0.0533 0.9352 (1.74) ( 2.32) (1.72) (3.68) (52.40) Spain 0.0089 0.2077 0.1280 0.0207 0.1723 0.6328 4.9122 ( 0.63) (5.51) ( 3.54) (3.07) (4.11) (8.79) (5.67) t values are in parentheses
Transformation for Estimation rt,i 2 = h t s i q t,i ɛ 2 t,i (3) rt,i 2 = s i q t,i ɛ 2 t,i h t (4) E( r 2 t,i h t ) = s i E(q t,i ) = s i (5) ŝ i = 1 T T t=1 r 2 t,i h t (6) z t,i = r t,i / h t s i = q t,i ɛ t,i (7)
Intraday Periodicity Figure: Autocorrelograms(Italy) Dashed lines represent 2 times of standard errors of autocorrelations
Diurnal Pattern
Intraday volatility model I Three-step estimator Newey and McFadden (1994) z t,i = r t,i / h t s i (8) z t,i F t,i 1 D(0, q t,i ) (9) q t,i = ω + αz 2 t,i 1 + βq t,i 1 (10) Estimation strategy: Moment conditions implied by Maximum Likelihood Estimation
Intraday volatility model II Three-step estimator Newey and McFadden (1994) g(θ, s, φ, data) = g 3 (θ, ŝ, ˆφ, ɛ t,i ) g 2 (s, ˆφ, {rt,i 2 }, ν k ) g 1 (φ, ν k ) (11) [ ] θs The GMM estimator ψ = minimizes the objective function φ (12) g (θ, s, φ, data)w g(θ, s, φ, data) (13)
Intraday volatility model III Three-step estimator Newey and McFadden (1994) Theorem (6.1) If equations g1 g3 are satisfied with probability approaching one, ˆθ p θ 0, ŝ p s 0, ˆφ p φ 0, and g(θ, s, φ, data) satisfies certain conditions implied by Assumption 1 and 2 in Lumsdaine (1996), then the three estimators are all consistent and asymptotically normal and TN(ˆθ θ0 ) d N(0, V ) where V is the upperleft block of matrix G 1 E[ g(θ, s, φ, data) g (θ, s, φ, data)] G 1.
Intraday volatility model IV Three-step estimator Newey and McFadden (1994) G 3,θ G 3,s G 3,φ G = 0 G 2,s G 2,φ (14) 0 0 G 1,φ G 3,θ = E[ θ g 3 (θ, ŝ, ˆφ, ɛ)], (15) G 3,s = E[ s g 3 (θ, ŝ, ˆφ, ɛ)], (16) G 3,φ = E[ φ g 3 (θ, ŝ, ˆφ, ɛ)] (17) G 2,s = E[ s g 2 (s, ˆφ, {rt,i 2 }, ν)], (18) G 2,φ = E[ φ g 2 (s, ˆφ, {rt,i 2 }, ν)] (19) G 1,φ = E[ φ g 1 (φ, ν)] (20)
Intraday GARCH(-t) estimation Country c ω α β df Belgium 0.0137 0.0289 0.0455 0.9263 (2.27) (11.32) (17.51) (205.22) France 0.0098 0.0390 0.0613 0.8998 (1.64) (8.26) (14.21) (106.43) Germany 0.0065 0.0152 0.0316 0.9534 (1.04) (6.11) (10.72) (189.48) Italy 0.0120 0.0294 0.0740 0.8492 7.0834 (1.94) (9.19) (15.86) (77.81) (10.26) Netherlands 0.0062 0.0170 0.0288 0.9546 (0.98) (5.37) (10.05) (170.08) Spain 0.0075 0.0390 0.0771 0.6978 2.5796 (1.79) (9.83) (14.93) (33.74) (44.46) t values are in parentheses
Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion
Concluding Remarks High uncertainty-low beta Chou (1988) Periodicity at different frequency Andersen and Bollerslev (1997) Corsi (2004) Persistence does not decrease from daily to intraday. Relevance of ECB action Kurtosis Full specification for three parts
Thank You
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