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1 c Hawkes 10 Hawkes 1. HFT arrowhead 40% UFJ

89 2. 2.1 2010 1 arrowhead 2015 9 24 arrowhead 1 arrowhead 4.7 260 2 1 2.

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4 URL: 3 URL: statistics-derivatives/sector/ % 1%

5 peg Gomber et al. 2011

6 ID NASDAQ ID 2014 Bellia et al ID Hasbrouck and Saar 2013 strategic runs strategic runs strategic runs Latza et al fast fast aggressive trade fast trade fast trade 2015 Hasbrouck 1991 VAR 1 Eisler et al Cont et al Taranto et al. 2016a, 2016b Hawkes

7 93 Bacry and Muzy 2014 Bacry et al Hawkes Toke and Pomponio 2012 trades-through Hawkes Rambaldi et al Hawkes Martins and Hendricks 2016 Hawkes Hawkes FLEX Full arrowhead Pre Post Pre Post Pre 1 Post ID TOPIX500

8 TOPIX Post Post Pre Post

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11 t * * 10% 5% 1% % 10 90% Pre Post Pre Post

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14 Pre Post Post Post Post 2 9 Bacry and Muzy Pre Post 0.01 Post Pre 1 1 Hawkes

15 Pre Post Post Hawkes 3 Bacry and Muzy 2014 Bacry et al Hawkes D N t =(Nt i ) 1 i D λ t i(1 i D) N t D Hawkes D (5.1) λ i t = μ i + φ ij (t s)dns j. j=1 (,t) μ =(μ i ) 1 i D φ =(φ ij ) 1 i,j D Hawkes μ i 0,φ ij (t) > 0 D λ i t t i φ ij j i i λ i t i Hawkes conditional law g =(g ij ) 1 i,j D (5.2) g ij (t)dt =E[dN i t dn j 0 =1] 1 {i=j} δ(t) Λ i dt. Λ i =E[λ i t] δ(t) g 5 conditional law g Hawkes φ t>0 Wiener-Hopf (5.3) g(t) =φ(t)+(g φ)(t) Bacry and Muzy 2014 φ ij

16 L 1 φ ij 1 = φ ij (t)dt (5.4) φ =( φ ij 1) 1 i,j D 1 Hawkes N t φ, μ (5.5) Λ=(I D φ ) 1 μ Λ =(Λ i ) 1 i D I D D Bacry and Muzy 2014 Bacry et al t 1 (5.6) {t k } 1 k K = {0,δT 1, 2δT 1,...,T 1,T 1e δ,t 1e 2δ,...,T 2}. T 1,T 2,δ K {t k } 0 T 1 T 1 T 2 2 {Tl i } l ni (1 i D) n i i (i, j) g ( ) g ij tk + t k+1 1 tk+1 (5.7) g ij (t)dt 2 t k+1 t k 1 1 t k+1 t k n j t k n i n j l=1 m=1 (k =1, 2,...,K 1) 1 T i l T j m [t k,t k+1 ) Λi. Λ i i 1 n i g ij (t) φ t n φ D n 1 tn tk (5.8) g ij (t n)=φ ij (t n)+ φ mj (t k ) g im (s)ds t n t k+1 + D n 1 m=1 k=1 D n 1 m=1 k=1 m=1 k=1 (n =1,...,K) (φ mj (t k+1 ) φ mj (t k ))(t n t k ) t k+1 t k φ mj (t k+1 ) φ mj (t k ) t k+1 t k tn t k t n φ ij (t) φ, Λ μ tn t k t n t k+1 sg im (s)ds. t n t k+1 g im (s)ds Hawkes Hawkes φ

17 103 φ t Hawkes 5.1 Bacry and Muzy 2014 Bacry and Muzy ( D ) (5.9) λ i t = μ i + φ ij (t s)dns j. j=1 (,t) (c) + c c D {t k } T 1 = T 2 = T 1 e 6 2 δ δ =0.04 {t k } + (5.10) {t k } = {0, , ,..., , , e 0.04,..., e 6 } L 1 φ ij 1 = T K 0 φ ij (t)dt φ ij (t) φ ij (t) φ ij (t) 9 9=81 φ ij (t) j t i j i Φ ij (t) = t 0 φij (t)dt Φ ij (t) i Φ ij (t) j t i 6 8 Φ ij (t) Pre Pre Post

18 (a) 6(b) 6(b) 0.01

19 Pre Post Post 6(a) (b) Pre 0.02 Post (b) 2 Post (f) Φ ij (t) (b) 2 7(b) (c) 8(d) 1

20 (a) 8(b) 8(a) 2 8(b)

21 % 10% 9 9(c) 9(d) 2 2 Pre 9(b) 2 9(a) 2 9(c) 9(d) 9(c) (d) (c) 9(c) 9(d) Pre Post Post Pre 6(b) 8(c) 8(d) 9(c) 9(d) 9 1

22 % 10% 1 6. Hawkes 10

23 109 Rambaldi et al (2012).,, 50, Bacry, E. and Muzy, J. F. (2014). Second order statistics characterization of Hawkes processes and non-parametric estimation, Preprint, Bacry, E., Jaisson, T. and Muzy, J. F. (2016). Estimation of slowly decreasing Hawkes kernels: Application to high-frequency order book dynamics, Quantitative Finance, 16, Bellia, M., Pelizzon, L., Subrahmanyam, M.G., Uno, J. and Yuferova, D. (2016). Low-latency trading and price discovery: Evidence from the Tokyo Stock Exchange in the pre-opening and opening periods, Preprint, Cont, R., Arseniy, K. and Sasha, S. (2014). Price impact of order book events, Journal of Financial Econometrics, 12, Eisler, Z., Bouchaud, J. P. and Kockelkoren, J. (2012). The price impact of order book events: Market orders, limit orders and cancellations, Quantitative Finance, 12, Gomber, P., Arndt, B., Lutat, M. and Uhle, T. (2011). High-frequency trading, Preprint, com/abstract= Hasbrouck, J. (1991). Measuring the information content of stock trades, Journal of Finance, 46, Hasbrouck, J. and Saar, G. (2013). Low-latency trading, Journal of Financial Markets, 16, (2014). High-Frequency Trading, JPX, Vol.04,,. (2015).,, 8, Latza, T., Marsh, I. and Payne, R. (2014). Fast aggressive trading, Preprint, abstract= Martins, R. and Hendricks, D. (2016). The statistical significance of multivariate Hawkes processes fitted to limit order book data, Preprint, (2013).,, 2013-J-2,,. Rambaldi, M., Bacry, E. and Lilio, F. (2016). The role of volume in order book dynamics: A multivariate

24 Hawkes process analysis, Preprint, (2011).,, 30(2), Taranto, D.E., Bormetti, G., Bouchaud, J.P., Lillo, F. and Toth, B. (2016a). Linear models for the impact of order flow on prices I. Propagators: Transient vs. history dependent impact, Preprint, Taranto, D.E., Bormetti, G., Bouchaud, J.P., Lillo, F. and Toth, B. (2016b). Linear models for the impact of order flow on prices II. The mixture transition distribution model, Preprint, Toke, I. M. and Pomponio, F. (2012). Modelling trades-through in a limit order book using hawkes processes, Economics: The Open-access, Open-assessment E-journal, 6, 1 23., (2012).,, 31,

25 Proceedings of the Institute of Statistical Mathematics Vol. 65, No. 1, (2017) 111 Analysis of High Frequency Reactions on Tokyo Stock Exchange Yusuke Tashiro and Muneki Kawaguchi Mitsubishi UFJ Trust Investment Technology Institute Co., Ltd. In recent stock markets, the presence of high-frequency trading (HFT) has globally increased. In the Tokyo Stock Exchange (TSE), the market share of high-frequency trading increases year after year and market players can trade stocks faster than before due to the renewal of the trading system in September In this paper, we analyze the high-frequency order book dynamics on TSE. For this purpose, we focus on the short interval order, which is submitted immediately after an order submission, and discuss its characteristics. We also analyze whether the highfrequency reaction to the order changes or not with the renewal. We find that short interval order is likely to be submitted continuously after the submission of an order that has a large impact, such as market order, and continuity is more remarkable after the renewal on TSE. Moreover, we estimate multivariate Hawkes models that represent order interval among the different order types, and we observe two kinds of players: one that immediately reacts to an order and the other that reacts about 10 milliseconds behind. We then find that the latter players increase the aggressiveness of the order submission of the specific order type after the renewal and change their order activity depending on the characteristics of limit order books. Key words: Market microstructure, high-frequency trading, order book dynamics, multivariate Hawkes process.

Vol.57 No.4 March 2008 : () 1 () () (1 ) (2 ) ( ) 1 Takagi (1989)Hamao (1992) (1998)

Vol.57 No.4 March 2008 : () 1 () () (1 ) (2 ) ( ) 1 Takagi (1989)Hamao (1992) (1998) Title Author(s) 東京証券取引所における株式取引 : 2001 年から 2003 年太田, 亘 Citation 大阪大学経済学. 57(4) P.242-P.262 Issue Date 2008-03 Text Version publisher URL https://doi.org/10.18910/15995 DOI 10.18910/15995 rights Vol.57