Modelling Intraday Volatility in European Bond Market

Transcription

1 Modelling Intraday Volatility in European Bond Market Hanyu Zhang ICMA Centre, Henley Business School Young Finance Scholars Conference 8th May,2014

2 Outline 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion

3 Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion

4 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

5 Evidence from the Data Annualized daily return standard deviation

6 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)

7 Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion

8 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)

9 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 min log return series: April December, 2013 Preserving liquidity and maturity Switching from off-the-run to on-the-run

10 Details of Switching Deciding switching date based on Pasquariello and Vega (2009) Maturity within years implications on mean and variance modelling: inheritance Countries number of bonds average duration (unit:month) Belgium France Germany Italy Netherlands Spain

11 Summary Statistics Country N Mean St.Dev Skewness Kurtosis Panel A: In-sample daily return Belgium France Germany Italy Netherlands Spain Panel B: 10-min return Belgium France Germany Italy Netherlands Spain 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.

12 Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion

13 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

14 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

15 GARCH(-t) estimation Country a φ 1 φ 2 κ ρ δ df Belgium (1.04) (3.33) ( 2.33) (3.00) (4.44) (29.16) France (1.58) ( 2.61) (2.08) (4.33) (49.07) Germany (1.04) (2.21) ( 3.18) (1.84) (3.55) (42.58) Italy (0.70) (4.24) ( 4.65) (1.85) (2.77) (16.24) (6.19) Netherlands (1.74) ( 2.32) (1.72) (3.68) (52.40) Spain ( 0.63) (5.51) ( 3.54) (3.07) (4.11) (8.79) (5.67) t values are in parentheses

16 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)

17 Intraday Periodicity Figure: Autocorrelograms(Italy) Dashed lines represent 2 times of standard errors of autocorrelations

18 Diurnal Pattern

19 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

20 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)

21 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.

22 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)

23 Intraday GARCH(-t) estimation Country c ω α β df Belgium (2.27) (11.32) (17.51) (205.22) France (1.64) (8.26) (14.21) (106.43) Germany (1.04) (6.11) (10.72) (189.48) Italy (1.94) (9.19) (15.86) (77.81) (10.26) Netherlands (0.98) (5.37) (10.05) (170.08) Spain (1.79) (9.83) (14.93) (33.74) (44.46) t values are in parentheses

24 Table of Contents 1 Introduction and Literature Review 2 Data 3 Model and Three-step Estimator 4 Conclusion

25 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

26 Thank You

27 Reference I Admati, A. R. and Pfleiderer, P. (1988). A theory of intraday patterns: Volume and price variability. Review of Financial Studies, 1(1):3 40. Afonso, A., Gomes, P., and Taamouti, A. (2013). Sovereign credit ratings, market volatility, and financial gains. Computational Statistics & Data Analysis, pages. Andersen, T. G. and Bollerslev, T. (1997). Intraday periodicity and volatility persistence in financial markets. Journal of empirical finance, 4(2): Andersen, T. G. and Bollerslev, T. (1998). Deutsche mark-dollar volatility: intraday activity patterns, macroeconomic announcements, and longer run dependencies. the Journal of Finance, 53(1): Andersen, T. G., Bollerslev, T., Diebold, F. X., and Vega, C. (2003). Micro effects of macro announcements: Real-time price discovery in foreign exchange. The American Economic Review, 93(1): Bandi, F. M. and Russell, J. R. (2008). Microstructure noise, realized variance, and optimal sampling. The Review of Economic Studies, 75(2):

28 Reference II Bollerslev, T., Cai, J., and Song, F. M. (2000). Intraday periodicity, long memory volatility, and macroeconomic announcement effects in the us treasury bond market. Journal of Empirical Finance, 7(1): Chou, R. Y. (1988). Volatility persistence and stock valuations: Some empirical evidence using garch. Journal of Applied Econometrics, 3(4): Christiansen, C. (2007). Volatility-spillover effects in european bond markets. European Financial Management, 13(5): Corsi, F. (2004). A simple long memory model of realized volatility. Manuscript, University of Southern Switzerland, pages. Diaz, A., Merrick Jr., J. J., and Navarro, E. (2006). Spanish treasury bond market liquidity and volatility pre- and post-european monetary union. Journal of Banking & Finance, 30(4): Dufour, A. and Skinner, F. (2004). Mts time series: Market and data description for the european bond and repo database. Technical report, Henley Business School, ICMA Centre.

29 Reference III Engle, R. F. and Russell, J. R. (1998). Autoregressive conditional duration: a new model for irregularly spaced transaction data. Econometrica, pages Engle, R. F. and Sokalska, M. E. (2012). Forecasting intraday volatility in the us equity market. multiplicative component garch. Journal of Financial Econometrics, 10(1): Fleming, M. and Lopez, J. (1999). Heat waves, meteor showers, and trading volume: An analysis of volatility spillovers in the us treasury market. FRB of New York Staff Report, (82). Huang, R. D. and Stoll, H. R. (1996). Dealer versus auction markets: A paired comparison of execution costs on nasdaq and the nyse. Journal of Financial economics, 41(3): Lumsdaine, R. L. (1996). Consistency and asymptotic normality of the quasi-maximum likelihood estimator in igarch (1, 1) and covariance stationary garch (1, 1) models. Econometrica: Journal of the Econometric Society, pages

30 Reference IV Newey, W. K. and McFadden, D. (1994). Large sample estimation and hypothesis testing. Handbook of econometrics, 4: Oomen, R. C. A. (2006). Properties of realized variance under alternative sampling schemes. Journal of Business & Economic Statistics, 24(2): Pasquariello, P. and Vega, C. (2009). The on-the-run liquidity phenomenon. Journal of Financial Economics, 92(1):1 24. Roll, R. (1984). A simple implicit measure of the effective bid-ask spread in an efficient market. The Journal of Finance, 39(4):