4 ( ) NATURE SCIENCE [Battiston 16] 2008 ( ) 5 JPX [ 13] [ 15a, 15b] [ 15,Mizuta 16c] [ 15a, 15b] δt (δt =1) (δt > 1) 4 [ 09, 12] 5 [LeBaron 06,Chen 1

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1 1 Takanobu Mizuta 2 Kiyoshi Izumi 1 SPARX Asset Management Co., Ltd. 2 School of Engineering, The University of Tokyo () ( ) [Farmer 12, Budish 15] [Budish 15] ( ) [Budish 15] : mizutata@gmail.com JPX [ 16a] 1 [ 13] [ 12] [Fricke 15] ( ) [Manahov 16] 2 [ 14] 3 [Budish 15, Fricke 15] [ 14] [Bellia 15] [Bellia 15] 2 [ 14] 3 [ 14] 1

2 4 ( ) NATURE SCIENCE [Battiston 16] 2008 ( ) 5 JPX [ 13] [ 15a, 15b] [ 15,Mizuta 16c] [ 15a, 15b] δt (δt =1) (δt > 1) 4 [ 09, 12] 5 [LeBaron 06,Chen 12, 12,Cristelli 14,Mizuta 16b] 2. [Chiarella 02] (stylized fact) [ 13] [Chiarella 02] [Chiarella 02] 1 ( ) [ 15a, 15b] [ 13] [Nakajima 04] [ 15a, 15b] δt (δt =1) (δt > 1) 2.1 δt (δt =1) (δt > 1) (NA) t 1 δt δt =1 t ( ) P t t ( ) P t δt t ( )P t 1 1 δt =1( ) δt =4( ) t =0, 1, 2, 3, 4 t =0δt =4 t =1 99 () δt =1 99 δt =4 t =2, δt =1 δt =4 t =4 98 δt =1 δt =4t =

3 1: 2: (MM) t =4 δt =1 δt =4 4 δt =1 4 δt =4 2 δt n (NA) 1 (MM) NA j =1 j =2, 3, 4,... MM NA 2 MM NA t c NA j = n NA j =1 t 1 NA 1 1 () () ( ) δp (NA) NA stylized fact NA Po,j t t NA j ()re,j t ( re,j t 1 = w 1,j log P ) f w 1,j + w 2,j + u j P + w 2,jr t t h,j + u j ɛ t j (1) w i,j t NA j i 3

4 3: (MM) PMM3 PMM4 PMM3 PMM4 4: (MM) 0 w i,max u j NA j 3 0 u max log P f P t ( ) ɛ t j t j 0 σ ɛ r t h,j t NA j r t h,j =log(p t /P t τ j ) 6 τ j 1 τ max NA (1) 1 () () r t e,j P t e,j P t e,j = P t exp (r t e,j) (2) Po,j t Pe,j t P σ P σ Pe,j t Po,j t Pe,j t >Po,j1 t Pe,j t <Po,j1 t (3) 7 6 t <τ j rh,j t =0 7 t <t c P f > (MM) [ 15a, 15b] (MM) 2 MM P fair P spread (P fair + P spread ) 1 P spread (P fair P spread ) 1 MM NA δt MM MM 4 1 MM(SMM) P fair = P t 2 MM(PMM) P fair =(1 ks 3 )P t (4) k S MM ( ) (S >0) P fair P t S (S <0) P fair P t S PMM SMM Po,j t 1 P f <Po,j t 1 P t = P f 4

5 ( ) [ 15a, 15b] PMM 2 3 ΔT ΔT end PMM 1 PMM3 4 (S >0) (S <0) PMM4 4 (S >0) P fair P spread ( ) (S <0) P fair + P spread ( ) PMM4 PMM3 0 NA S S PMM3 δt PMM3 0 PMM4 3. [ 13] [ 15a, 15b], n =1, 000 w 1,max =1 w 2,max =10 u max =1 τ max =10, 000 σ ɛ = 0.06 P σ =30 t c =20, 000 δp =0.02,P f =10, 000 k = ΔT =20, 000 ΔT end =2, 000 t = t e =10, 000, MM P spread /P f =0.03%, 0.1%, 0.3%, 1% δt =1, 2, 5, 10, 20, 50, 100, 200, 500, P spread 1 δt, MM P spread /P f MM /MM PMM4 δt MM MM NA () MM δt MM MM 8 [ 14] 9 4 MM 4 P spread 10 δt 160(= ) P spread /P f MM P spread /P f =0.1% δt =1 δt 50 MM δt 50 P spread /P f =0.03% 3.2 MM 2 δt MM S P spread /P f =0.03% ( ) S 1 S SMM PMM 0 PMM3 δt 0 δt 20 S =0 δt S δt S =0 PMM4 S δt 20 S 0 PMM4 NA S S δt 20 S 0 δt S =0 δt PMM4 S 0 PMM δt MM /P f S MM NA MM PMM4 P spread /P f =0.03% δt =2, 5, 10 MM MM δt =20, 50, 100, 200 δt =1 δt δt =1 5

6 1: δt, MM P spread /P f MM (PMM4) δt MM P spread /P f 0.03% 0.10% 0.30% 1.00% 1( ) 8.06% 1.53% 0.00% 0.00% % 0.88% 0.00% 0.00% % 0.37% 0.00% 0.00% % 0.14% 0.00% 0.00% % 0.02% 0.00% 0.00% % 0.00% 0.00% 0.00% % 0.00% 0.00% 0.00% % 0.00% 0.00% 0.00% % 0.00% 0.00% 0.00% % 0.00% 0.00% 0.00% 2: δt MM S (P spread /P f = 0.03%) δt SMM PMM PMM3 PMM4 S 1( ) 12,357 12, ,42 17, ,409 4, ,744 1, δt =1 4. [ 15a, 15b] δt (δt =1) (δt > 1) δt MM MM δt δt =1 δt > 1 [ 14] 6

7 3: δt MM S MM NA (PMM4 P spread /P f = 0.03%) δt S MM 1 MM NA /P f 1( ) % 39.1% % 39.1% % 37.6% % 36.3% % 34.9% % 33.4% % 32.5% % 31.8% % 31.0% % 30.5% [LeBaron 06, Chen 12, 12, Cristelli 14, Mizuta 16b] [Chen 12],, fat-tail volatilityclustering stylized fact 4: (δt =1) MM 32.3% 26.1% / % 1 (ΔT = 20000) 0.562% [LeBaron 06, Chen 12, 12, Cristelli 14, Mizuta 16b] 2 [Sewell 11] [Sewell 11] 4 (δt =1) MM (ΔT ) = / = /( + )

8 JST CREST JSPS 15H02745 [Battiston 16] Battiston, S., Farmer, J. D., Flache, A., Garlaschelli, D., Haldane, A. G., Heesterbeek, H., Hommes, C., Jaeger, C., May, R., and Scheffer, M.: Complexity theory and financial regulation, Science, Vol. 351, No. 6275, pp (2016), [Bellia 15] Bellia, M., Pelizzon, L., Subrahmanyam, M. G., Uno, J., and Yuferova, D.: Low-Latency Trading and Price Discovery Without Trading: Evidence from The Tokyo Stock Exchange Pre- Opening Period, SSRN Working Paper Series (2015), [Budish 15] Budish, E., Cramton, P., and Shim, J.: The High- Frequency Trading Arms Race: Frequent Batch Auctions as a Market Design Response, The Quarterly Journal of Economics, Vol. 130, No. 4, pp (2015), [Chen 12] Chen, S.-H., Chang, C.-L., and Du, Y.-R.: Agent-based economic models and econometrics, Knowledge Engineering Review, Vol. 27, No. 2, pp (2012), [Chiarella 02] Chiarella, C. and Iori, G.: A simulation analysis of the microstructure of double auction markets, Quantitative Finance, Vol. 2, No. 5, pp (2002), [Cristelli 14] Cristelli, M.: Complexity in Financial Markets, Modeling Psychological Behavior in Agent-Based Models and Order Book Models, Springer (2014), [ 09],, (2009), [Farmer 12] Farmer, D. and Skouras, S.: Review of the Benefits of a Continuous Market Vs. Randomised Stop Auctions and of Alternative Priority Rules (policy Options 7 and 12), Manuscript, Foresight, Government Office for Science, UK (2012), computer-trading-continuous-market-vs-randomised -stop-auctions-and-alternative-priority-rules [Fricke 15] Fricke, D. and Gerig, A.: Too fast or too slow? Determining the optimal speed of financial markets, SSRN Working Paper Series (2015), [ 12] 3,, ( 6 ), (2012), [ 12], (2012), IEEJ-GH1262-PRT [ 15a],,,, JPX, No. 8, (2015), [ 15b],,, :,, Vol. 30, No. 5, pp (2015), [LeBaron 06] LeBaron, B.: Agent-based computational finance, Handbook of computational economics, Vol. 2, pp (2006), [Manahov 16] Manahov, V.: A note on the relationship between high-frequency trading and latency arbitrage, International Review of Financial Analysis (2016), [ 12] 1. --,, Vol. 53, No. 9, pp (2012), [ 13],,,, JPX, No. 2, (2013), [ 14], PhD thesis, (2014), [ 15],,,, JPX, No. 9, (2015), [ 16a],, JPX, No. 17, (2016), [Mizuta 16b] Mizuta, T.: A Brief Review of Recent Artificial Market Simulation (Multi-Agent Simulation) Studies for Financial Market Regulations and/or Rules, SSRN Working Paper Series (2016), [Mizuta 16c] Mizuta, T., Noritake, Y., Hayakawa, S., and Izumi, K.: Affecting Market Efficiency by Increasing Speed of Order Matching Systems on Financial Exchanges Investigation using Agent Based Model, in Computational Intelligence for Financial Engineering Economics (CIFEr), 2016 IEEE Conference on, 2016 IEEE Symposium Series on Computational Intelligence on (2016), [Nakajima 04] Nakajima, Y. and Shiozawa, Y.: Usefulness and feasibility of market maker in a thin market, in ICEES (International Conference Experiments in Economic Sciences), Vol. 47 (2004), 47.pdf [ 14] HFT, JPX,, (2014), [Sewell 11] Sewell, M.: Characterization of financial time series, Research Note, University College London, Department of Computer Science, No. RN/11/01 (2011), [ 13] HFT PTS, (2013), 8

SIG-FIN Nature Science [Farmer 9,Battiston 16] 4 5 [Cremers 16] (Patient) (Impatient) 2. [Cremers 16] (Patient) (Impatient) 2 [ 9, 12a] 3 [ 3,

SIG-FIN Nature Science [Farmer 9,Battiston 16] 4 5 [Cremers 16] (Patient) (Impatient) 2. [Cremers 16] (Patient) (Impatient) 2 [ 9, 12a] 3 [ 3, SIG-FIN-19 (Patient) 1 Takanobu Mizuta 2 Sadayuki Horie 1 SPARX Asset Management Co., Ltd. 2 Nomura Research Institute, Ltd. (Patient) (Impatient) 1 1. [French 8, Bogle 14] 1 [A.T.Kearney 16, 17] ( ) (