2019/10/31 PRIMA2019: Comparison of Behaviors of Actual and Simulated HFT Traders for Agent Design
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This document compares the behaviors of actual high-frequency trading (HFT) traders and simulated HFT traders in an artificial stock market simulation. It finds that while the ordering prices of the simulated and actual traders are similar near the best price, the simulation lacks some features of the actual data, such as long tails in the ordering price distribution. The document concludes that building a more realistic simulation and using a data-driven approach could help address these limitations and better capture features of real HFT trader behavior.
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2019/10/31 PRIMA2019: Comparison of Behaviors of Actual and Simulated HFT Traders for Agent Design
- 1. Comparison of Behaviors of Actual and Simulated HFT Traders for Agent Design Masanori HIRANO, Kiyoshi IZUMI, Hiroyasu MATSUSHIMA, Hiroki SAKAJI Izumi Lab. School of Engineering, The University of Tokyo hirano@g.ecc.u-tokyo.ac.jp https://mhirano.jp/
- 2. Increasing Uncertainty in Financial Market • The 2007-2008 financial crisis • Flash crashes • happened in stock market, currency, etc.… • The causes: Auto trading, Auto news analysis… • DJIA on May 6, 2010 <-- One big sell order 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 2
- 3. Artificial Financial Market • Simulations on computer using virtual markets • We can test hypothetical situations! • Promising approach for financial market analysis • But… 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 3
- 4. Artificial Financial Market • Simulations on computer using virtual markets • We can test hypothetical situations! • Promising approach for financial market analysis • But… 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 4 Are the simulations trustable?
- 5. Our work • Comparing Real data Outcomes from simulations • Only focus on HFT-MM Specific trader & strategy • Target: Tokyo Stock Exchange • Collaborative Research w/ Japan Exchange Group (JPX) • We analyzed a special data provided by JPX 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 5 Tokyo Stock Exchange
- 6. What’s the HFT-MM? • High-Frequency-Trader Market-Making strategy • Market-making strategy: • (Basically) order near the best price • Get profit by the spread (1001-999=2) • Do repeatedly • Risk-hedge by high-frequency-trade: • Always have price move risk (Price move >> spread) • Do action faster & hedge risk by setting off their inventory 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 6 Sell Buy
- 7. Study Outline 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 7 Data Simulation HFT-MM Order Data HFT-MM Order Data in Simulation Comparison Processing, VS merging, Clustering
- 8. Study Outline 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 8 Data Simulation HFT-MM Order Data HFT-MM Order Data in Simulation Comparison Processing, VS merging, Clustering
- 9. Simulation outline • We used “PlhamJ” as a simulation platform. PlhamJ: Platform for Large-scale and High-frequency Artificial Market (Java version) 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 9 Market (Only one) Continuous Double Auction HFT-MM Traders ・・・ Stylized Traders ・・・ Order Information Order Information 100 Stpes Delay Only Every 100 Steps
- 10. Stylized Trader Agents [Chiarella et al. 02] • Logarithmic return prediction for bid/ask price 𝑟 = 1 𝑤 𝐹+𝑤 𝐶+𝑤 𝑁 𝑤 𝐹 ⋅ 𝐹 + 𝑤 𝐶 ⋅ 𝐶 + 𝑤 𝑁 ⋅ 𝑁 • Fundamentals 𝐹 = 1 mean reversion time ln current market price current fundamental price • Chartist (trend) 𝐶 = logarithm averaged return in the past • Noise 𝑁 ~ 𝑁 0, 𝜎 𝑁 • + margin => decide price • Every 100 step they make a buy or sell order 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 10
- 11. HFT-MM Trader Agents [Avellaneda et al. 02] • Trader’s price interval: 𝛾 𝑖 𝜎 𝑖 2 + 2 𝛾 𝑖 ln 1 + 𝛾 𝑖 𝑘 • Trader’s mid-price 𝑝𝑡 ∗ − 𝛾 𝑖 𝜎 𝑖 2 𝑞𝑡 𝑖 • Note: 𝛾 𝑖: risk-hedge level 𝜎 𝑖: SD in price 𝑘: a parameter for order arrival 𝑝𝑡 ∗ : fundamental price 𝑞𝑡 𝑖 :inventory 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 11 Price Sell Buy Fundamental Price Trader’s mid-price Trader’s price interval
- 12. Simulation settings • 1,000 stylized agents vs. 10 HFT-MM trader agents • 100 steps before market opening + 500 dummy steps for stabilization + 10,000 steps for test • Fundamental price: • Start at 400 • Geometric Brownian motion with SD of 0.0001 • Run 21 times (The same as the business day in real data in Aug. 2015) 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 12
- 13. Ordering Price Distribution (Simulation) • HFT-MM ordering price distribution = How many ticks far from the best price 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 13 − 5 0 5 10 15 0.0e+0 5.0e+3 1.0e+4 1.5e+4 2.0e+4 Order Executed Order Ticks Freq.
- 14. Study Outline 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 15 Data Simulation HFT-MM Order Data HFT-MM Order Data in Simulation Comparison Processing, VS merging, Clustering
- 15. Data • “Order-book reproduction data” provided by Japan Exchange Group (JPX) • Containing masked trader information <- Called “Virtual Server (VS)” 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 16 Time Ticker Kind Buy/sell VS Price 11:11:50.702813 A Limit Order sell VS1 2570 11:11:50.703600 B Executed buy VS4 Market Order 11:11:50.704001 A Cancel sell VS1 2570 Sample Some columns are not shown such as volume
- 16. Data: VS merging • Virtual Server: Gateway to the order system for brokers 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 17 Limit: 60,20,10 orders/s (depends on contract)
- 17. Data: VS merging • Merging VS as many as possible • Focus on each continuous actions 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 18 Order01 Limit Order
- 18. Data: VS merging • Merging VS as many as possible • Focus on each continuous actions 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 19 Order01 Cancel
- 19. Data: VS merging • Merging VS as many as possible • Focus on each continuous actions 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 20 Used by the same trader!
- 20. Indices for clustering (extracting HFT-MM) • The logarithm of action per ticker ActionsPerTicker = newOrders + changeOrders + (cancelOrders) (numTicker) ActionsPerTickerLOG = ln ActionsPerTicker • Inventory Ratio InventoryRatioABS = 𝑀𝑒𝑑𝑖𝑎𝑛ticker soldVolume ticker − boughtVolume ticker soldVolume ticker + boughtVolume ticker • Cancel ratio CanceledVolumeRatio = (cancelVolume) (newVolume) • The logarithm of ticker per VS TickerPerVSLOG = ln (numTicker) (numVS) 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 21 Many order Low inventory Many VS usage High cancel ratio
- 21. Indices for clustering (extracting HFT-MM) • The logarithm of action per ticker ActionsPerTicker = newOrders + changeOrders + (cancelOrders) (numTicker) ActionsPerTickerLOG = ln ActionsPerTicker • Inventory Ratio InventoryRatioABS = 𝑀𝑒𝑑𝑖𝑎𝑛ticker soldVolume ticker − boughtVolume ticker soldVolume ticker + boughtVolume ticker • Cancel ratio CanceledVolumeRatio = (cancelVolume) (newVolume) • The logarithm of ticker per VS TickerPerVSLOG = ln (numTicker) (numVS) 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 22
- 22. Data outline • Aug. 2015: All 21 business days • Before VS merging: 4616 VSs • After VS merging: 2664 VSs • Only HFT: 253 VSs <= based on ActionsPerTicker ≥ 100 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 23 2455 2455 2161 209 253
- 23. Hierarchical Clustering [Uno et al. 18] • Normalizations for each indices & clustering • Euclidean distance • Ward’s method • 10 clusters 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 24 HFT-MM cluster based on indices
- 24. Ordering Price Distribution • HFT-MM ordering price distribution = How many ticks far from the last transaction price 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 25 − 5 0 5 10 15 0.0e+0 5.0e+8 1.0e+9 1.5e+9 2.0e+9 2.5e+9 Order Executed Order Ticks Freq.
- 25. Study Outline 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 26 Data Simulation HFT-MM Order Data HFT-MM Order Data in Simulation Comparison Processing, VS merging, Clustering
- 26. Ordering Price Distribution − 5 0 5 10 15 0.00 0.20 0.40 0.60 0.80 1.00 Order (Actual) Order (Simulation) Ticks Relative Freq. (vs tick 0) 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 27
- 27. Statistical test: Entropy • T-test for • Entropy for −5~15 tick • Entropy for −2~5 tick • This suggests: • −2~5 tick: simulation & real data has small difference • −5~2, 5~15 tick: simulation & real data has significant diff. 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 28 𝐸 = −𝑝 𝑥 log2 𝑝 𝑥
- 28. Ordering Price Distribution − 5 0 5 10 15 0.00 0.20 0.40 0.60 0.80 1.00 Order (Actual) Order (Simulation) Ticks Relative Freq. (vs tick 0) 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 29 Long tail: know as “layering”
- 29. Discussion & Conclusion • Near the best price, simulation and data are similar • => our clustering method work • => our simulation also work • But, our simulation lost some features in real data • Ex. Long tail 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 30 Future work • Build more realistic simulation • Also use data-driven approach for simulation • Build simulation (trader) model automatically • There are limitation for human to build perfect model • Human-made model can drop some features
- 30. Thank you for your attention! • The paper for social track will be published JASSS. • You can access our preprint on ResearchGate https://s.mhirano.jp/prima2019-preprint • Or contact me: hirano@g.ecc.u-tokyo.ac.jp https://mhirano.jp/ 10/31/19 PRIMA 2019 ©︎M.HIRANO & Izumi Lab. 31