High-frequency trading model for a complex trading hierarchy

References

• Admati , AR and Pfleiderer , P . 1988 . A theory of intraday trading patterns: Volume and price variability . Rev. Financ. Stud. , 1 : 3 – 40 .
   Web of Science ®Google Scholar
• Bagehot , W . 1971 . The only game in town . Financ. Anal. J. , 22 : 12 – 14 .
   Google Scholar
• Bak , P , Paczuski , M and Shubik , M . 1997 . Price variations in a stock market with many agents . Physica A , 246 : 430 – 453 .
   Web of Science ®Google Scholar
• Brock , WA and Kleidon , AW . 1992 . Periodic market closure and trading volume: A model of intraday bids and asks . J. Econ. Dynam. Control , 16 : 451 – 489 .
   Web of Science ®Google Scholar
• Caldarelli , G , Marsili , M and Zhang , Y-C . 1997 . A prototype model of stock exchange . Europhys. Lett. , 40 : 479 – 484 .
   Google Scholar
• Challet , D and Zhang , Y-C . 1997 . Emergence of cooperation and organization in an evolutionary game . Physica A , 246 : 407 – 418 .
   Web of Science ®Google Scholar
• Chandrasekhar , S . 1943 . Stochastic problems in physics and astronomy . Rev. Mod. Phys. , 15 : 1 – 89 .
   Google Scholar
• Chung , KH and Charoenwong , C . 1998 . Insider trading and the bid–ask spread . Financ. Rev. , 33 : 1 – 20 .
   Google Scholar
• Cizeau , P , Liu , Y , Meyer , M , Peng , C-K and Stanley , HE . 1997 . Volatility distribution in the S&P500 stock index . Physica A , 245 : 441 – 445 .
   Web of Science ®Google Scholar
• Clark , P . 1973 . A subordinated stochastic process model with finite variance for speculative prices . Econometrica , 41 : 135 – 155 .
   Web of Science ®Google Scholar
• Cohen , KJ , Maier , SF , Schwartz , RA and Whitcomb , D . 1981 . Transaction costs, order placement strategy, and existence of the bid–ask spread . J. Polit. Econ. , 89 : 287 – 305 .
   Web of Science ®Google Scholar
• Cont , R and Bouchaud , J-P . 2000 . Herd behavior and aggregate fluctuations in financial markets . Macroecon. Dynam. , 4 : 170 – 196 .
   Web of Science ®Google Scholar
• Diamond , DW and Verrecchia , RE . 1987 . Constraints on short-selling and asset price adjustment to private information . J. Financ. Econ. , 18 : 277 – 311 .
   Web of Science ®Google Scholar
• Ding , Z , Granger , CWJ and Engle , RF . 1993 . A long memory property of stock market returns and a new model . J. Empir. Finance , 1 : 83 – 106 .
   Google Scholar
• Easley , D and O'Hara , M . 1987 . Price, trade size, and information in securities markets . J. Financ. Econ. , 19 : 69 – 90 .
   Web of Science ®Google Scholar
• Eisler , Z , Kertész , J , Lillo , F and Mantegna , RN . 2009 . Diffusive behavior and the modeling of characteristic times in limit order executions . Quantit. Finance , 9 : 547 – 563 .
   Web of Science ®Google Scholar
• Engle , RF . 2000 . The econometrics of ultra-high frequency data . Econometrica , 68 : 1 – 22 .
   Web of Science ®Google Scholar
• Engle , RF and Russell , JR . 1998 . Autoregressive conditional duration: A new model for irregularly spaced transaction data . Econometrica , 66 : 1127 – 1162 .
   Web of Science ®Google Scholar
• Farmer , JD , Gillemot , L , Lillo , F , Mike , S and Sen , A . 2004 . What really causes large price changes? . Quantit. Finance , 4 : 383 – 397 .
   Web of Science ®Google Scholar
• Fu , D , Pammolli , F , Buldyrev , SV , Riccaboni , M , Matia , K , Yamasaki , K and Stanley , HE . 2005 . The growth of business firms: Theoretical framework and empirical evidence . Proc. Natl. Acad. Sci. U.S.A. , 102 : 18801 – 18806 .
   PubMed Web of Science ®Google Scholar
• George , TJ , Kaul , G and Nimalendran , M . 1991 . Estimation of the bid–ask spread and its components: A new approach . Rev. Financ. Stud. , 4 : 623 – 656 .
   Web of Science ®Google Scholar
• Gillemot , L , Farmer , JD and Lillo , F . 2006 . There's more to volatility than volume . Quantit. Finance , 6 : 371 – 384 .
   Web of Science ®Google Scholar
• Glosten , LR and Milgrom , PR . 1985 . Bid, ask and transaction prices in a specialist market with heterogeneously informed traders . J. Financ. Econ. , 14 : 71 – 100 .
   Web of Science ®Google Scholar
• Gopikrishnan , P , Plerou , V , Amaral , LAN , Meyer , M and Stanley , HE . 1999 . Scaling of the distributions of fluctuations of financial market indices . Phys. Rev. , 60 : 5305 – 5316 .
   Google Scholar
• Gopikrishnan , P , Plerou , V , Gabaix , X and Stanley , HE . 2000 . Statistical properties of share volume traded in financial markets . Phys. Rev. E , 62 : R4493
   PubMed Web of Science ®Google Scholar
• Horvatic , D , Stanley , HE and Podobnik , B . 2011 . Detrended cross-correlation analysis for non-stationary time series with periodic trends . EPL , 94 : 18007
   Web of Science ®Google Scholar
• Ivanov , PC , Yuen , A , Podobnik , B and Lee , Y . 2004 . Common scaling patterns in intratrade times of U.S. stocks . Phys. Rev. E , 69 : 056107
   PubMed Web of Science ®Google Scholar
• Jasiak , J . 1998 . Persistence in intertrade durations . Finance , 19 : 166 – 195 .
   Google Scholar
• Kullmann , L and Kertész , J . 2001 . Preferential growth: Solution and application to modeling stock market . Physica A , 299 : 121 – 126 .
   Web of Science ®Google Scholar
• Levy , M , Levy , H and Solomon , S . 1994 . A microscopic model of the stock market . Econ. Lett. , 45 : 103 – 111 .
   Web of Science ®Google Scholar
• Lillo , F , Mike , S and Farmer , JD . 2005 . Theory for long-memory of supply and demand . Phys. Rev. E , 7106 : 287 – 297 .
   Google Scholar
• Liu , Y , Cizeau , P , Meyer , M , Peng , C-K and Stanley , HE . 1997 . Quantification of correlations in economic time series . Physica A , 245 : 437 – 440 .
   Web of Science ®Google Scholar
• Liu , Y , Gopikrishnan , P , Cizeau , P , Meyer , M , Peng , C-K and Stanley , HE . 1999 . The statistical properties of the volatility of price fluctuations . Phys. Rev. , 60 : 1390 – 1400 .
   Google Scholar
• Lux , T . 1996 . Long-term stochastic dependence in financial prices: Evidence from the German stock market . Appl. Econ. Lett. , 3 : 701 – 706 .
   Web of Science ®Google Scholar
• Lux , T and Marchesi , M . 1999 . Scaling and criticality in a stochastic multi-agent model of a financial market . Nature , 397 : 498 – 500 .
   Web of Science ®Google Scholar
• Maslov , S . 2000 . Simple model of a limit order-driven market . Physica A , 278 : 571 – 578 .
   Web of Science ®Google Scholar
• Maslov , S and Mills , M . 2000 . Price fluctuations from the order book perspective: Empirical facts and a simple model . Physica A , 299 : 234 – 246 .
   Web of Science ®Google Scholar
• McInish , TH and Wood , RA . 1992 . An analysis of intraday patterns in bid/ask spreads for NYSE stocks . J. Finance , 47 : 753 – 764 .
   Web of Science ®Google Scholar
• Palmer , RG , Arthur , WB , Holland , JH , LeBaron , BD and Tayler , D . 1994 . Artificial economic life: A simple model of a stockmarket . Physica D , 75 : 264 – 274 .
   Web of Science ®Google Scholar
• Peng , C-K , Buldyrev , SV , Havlin , S , Simons , M , Stanley , HE and Goldberger , AL . 1994 . Mosaic organization of DNA nucleotides . Phys. Rev. E , 49 : 1685 – 1689 .
   PubMed Web of Science ®Google Scholar
• Plerou , V , Gopikrishnan , P , Amaral , LAN , Gabaix , X and Stanley , HE . 2000 . Economic fluctuations and anomalous diffusion . Phys. Rev. E , 62 : R3023
   PubMed Web of Science ®Google Scholar
• Plerou , V , Gopikrishnan , P , Amaral , LAN , Meyer , M and Stanley , HE . 1999 . Scaling of the distribution of price fluctuations of individual companies . Phys. Rev. E , 60 : 6519 – 6529 .
   PubMed Web of Science ®Google Scholar
• Plerou , V , Gopikrishnan , P , Gabaix , X , Amaral , LAN and Stanley , HE . 2001 . Price fluctuations, market activity, and trading volume . Quantit. Finance , 1 : 262 – 269 .
   Web of Science ®Google Scholar
• Plerou , V , Gopikrishnan , P and Stanley , HE . 2005 . Quantifying fluctuations in market liquidity: Analysis of the bid–ask spread . Phys. Rev. E , 71 : 046131
   Web of Science ®Google Scholar
• Podobnik , B and Stanley , HE . 2008 . Detrended cross-correlation analysis: A new method for analyzing two non-stationary time series . Phys. Rev. Lett. , 100 : 084102
   PubMed Web of Science ®Google Scholar
• Podobnik , B , Grosse , I , Horvatic , D , Ilic , S , Ivanov , PCh and Stanley , HE . 2009a . Quantifying cross-correlations using local and global detrending approaches . Eur. Phys. J. B , 71 : 243 – 250 .
   Web of Science ®Google Scholar
• Podobnik , B , Horvatic , D , Petersen , AM and Stanley , HE . 2009b . Cross-correlations between volume change and price change . Proc. Natl. Acad. Sci. U.S.A. , 106 : 22079 – 22084 .
   PubMed Web of Science ®Google Scholar
• Podobnik , B , Wang , D , Horvatic , D , Grosse , I and Stanley , HE . 2010a . Time-lag cross-correlations in collective phenomena . EPL , 90 : 68001
   Web of Science ®Google Scholar
• Podobnik , B , Horvatic , D , Petersen , A , Urosevic , B and Stanley , HE . 2010b . Bankruptcy risk model and empirical tests . Proc. Natl. Acad. Sci. U.S.A. , 107 : 18325 – 18330 .
   Web of Science ®Google Scholar
• Podobnik , B , Valentincic , A , Horvatic , D and Stanley , HE . 2011 . Asymmetric Levy flight in financial ratios . Proc. Natl. Acad. Sci. U.S.A. , 108 : 17883 – 17888 .
   Web of Science ®Google Scholar
• Ponta , L , Raberto , M and Cincotti , S . 2011 . A multi-assets artificial stock market with zero-intelligence traders . EPL , 93 : 28002
   Web of Science ®Google Scholar
• Ponzi , A , Lillo , F and Mantegna , RN . 2009 . Market reaction to a bid–ask spread change: A power-law relaxation dynamics . Phys. Rev. E , 80 : 016112
   Web of Science ®Google Scholar
• Raberto , M , Cincotti , S , Focardi , SM and Marchesi , M . 2001 . Agent-based simulation of a financial market . Physica A , 299 : 319 – 327 .
   Web of Science ®Google Scholar
• Riccaboni , M , Pammolli , F , Buldyrev , SV , Ponta , L and Stanley , HE . 2008 . The size variance relationship of business firm growth rates . Proc. Natl. Acad. Sci. U.S.A. , 105 : 19595 – 19600 .
   Web of Science ®Google Scholar
• Scalas , E . 2006 . The application of continuous-time random walks in finance and economics . Physica A , 362 : 225 – 239 .
   Web of Science ®Google Scholar
• Scalas , E , Kaizoji , T , Kirchler , M , Huber , J and Tedeschi , A . 2006 . Waiting times between orders and trades in double-auction markets . Physica A , 366 : 463 – 471 .
   Web of Science ®Google Scholar
• Schwartz , RA . 1988 . Equity Markets , New York : Harper and Row .
   Google Scholar
• Schwert , GW . 1989 . Why does stock market volatility change over time? . J. Finance , 44 : 1115 – 1153 .
   Web of Science ®Google Scholar
• Simon , HA . 1955 . On a class of skew distribution functions . Biometrika , 42 : 425 – 440 .
   Web of Science ®Google Scholar
• Slanina , F . 2001 . Mean-field approximation for a limit order driven market model . Phys. Rev. E , 64 : 0561136
   Web of Science ®Google Scholar
• Stanley , MHR , Buldyrev , SV , Havlin , S , Mantegna , R , Salinger , MA and Stanley , HE . 1995 . Zipf plots and the size distribution of firms . Econ. Lett. , 49 : 453 – 457 .
   Web of Science ®Google Scholar
• Takayasu , H , Miura , H , Hirabayashi , T and Hamada , K . 1992 . Statistical properties of deterministic threshold elements: The case of market price . Physica A , 184 : 127 – 134 .
   Web of Science ®Google Scholar
• Wang , D , Podobnik , B , Horvatic , D and Stanley , HE . 2011 . Quantifying and modeling long-range cross-correlations in multiple time series with applications to world stock indices . Phys. Rev. E , 83 : 046121
   Web of Science ®Google Scholar
• Wyart , M , Bouchaud , J-P , Kockelkoren , J , Potters , M and Vettorazzo , M . 2008 . Relation between bid–ask spread, impact and volatility in double auction markets . Quantit. Finance , 8 : 41 – 57 .
   Web of Science ®Google Scholar