Rock around the Clock: An Agent-Based Model of Low- and High-Frequency Trading

I. INTRODUCTION

• The literature debate remains unsettled: HFT is associated both with liquidity provision and efficiency benefits and with illiquidity, flash crashes, and volatility concerns.The paper situates its investigation within this debate.Source: §I · p. 1
• The paper examines whether HFT helps explain flash crashes and higher volatility, and which HF features relate to crashes and post-crash price recovery.It develops a limit-order-book model in which heterogeneous HF and LF traders interact.Source: §I · pp. 1–2
• The model combines LF traders who switch between fundamentalist and chartist strategies with directional HF traders exploiting price and volume information from LF traders.LF strategies follow chronological time, while HF participation is event-driven by price fluctuations.Source: §I · p. 2
• Earlier HFT agent-based models mainly used zero-intelligence traders with exogenous trading frequency, while few modeled HF–LF interaction.The paper adds event-based HF activation, volume-informed orders, many interacting traders, and analysis of crash formation and recovery.Source: §I · p. 2
• The study compares an LF-only market with a baseline containing both LF and HF traders, and varies HF order-cancellation rates in Monte Carlo experiments.The two-scenario comparison assesses HFT's contribution to volatility and flash crashes.Source: §I · p. 2
• Flash crashes and high price volatility occur only when HF traders are present, while the model reproduces financial-market stylized facts in both scenarios.The proposed crash mechanisms are high bid-ask spreads and HF traders synchronizing on the sell side of the book.Source: §I · p. 2
• HF order cancellations have mixed effects: higher cancellation rates increase volatility and flash-crash frequency but speed recovery and reduce crash duration.Fast post-crash recoveries also coincide with more balanced HF presence on both sides of the book and lower persistence of HF orders.Source: §I · p. 2

II. THE MODEL

• Heterogeneous, boundedly rational agents trade one asset for T periods through a limit-order book that stores order type, size, and price.The market contains NL low-frequency agents and NH high-frequency agents, with N = NL + NH.Source: §II · p. 2
• Agents differ in trading frequency, strategies, and activation rules, and the paper details LF and HF behavior separately.A representative trading session's timeline is presented first.Source: §II · p. 2
• Although the numbers of LF and HF agents remain fixed during simulations, their active proportions vary because agents may be inactive in a trading session.Source: §II · p. 2

A. The Timeline of Events

• At the session's start, active LF and HF agents know the past closing price and past and current fundamental values.Source: A. The Timeline of Events · p. 2
• Active LF traders submit buy or sell orders with sizes and limit prices before active HF traders submit their orders.HF agents trade sequentially after observing LF orders.Source: A. The Timeline of Events · pp. 2–3
• Orders are matched by price and then arrival time; unexecuted orders remain in the limit-order book for the next session.Source: A. The Timeline of Events · p. 3
• The session's closing price is the maximum price among transactions executed during that session.Source: A. The Timeline of Events · p. 3
• After the closing price is determined, agents compute profits and LF agents update their strategy for the next session.Source: A. The Timeline of Events · p. 3

B. Low-Frequency Traders

• LF trading frequency is exogenous and constant over time, with trading speeds drawn from a truncated exponential distribution bounded by θmin and θmax and having mean θ.Source: B. Low-Frequency Traders · p. 3
• Chartist orders follow a trend-based rule, while fundamentalist orders respond to the difference between fundamental value and the last closing price.Each strategy's order rule includes a stochastic term: Gaussian with standard deviation σc for chartists and σf for fundamentalists.Source: B. Low-Frequency Traders · p. 3
• The asset's fundamental value evolves according to a geometric random walk with a positive constant term δ and i.i.d. normal shocks.Source: B. Low-Frequency Traders · p. 3
• LF orders expire after γL periods, and their limit-order prices are set relative to the last closing price using a Gaussian-distributed tick distance.The tick distance has mean zero and standard deviation σz.Source: B. Low-Frequency Traders · p. 3
• At each session's end, LF agents calculate profits under chartist and fundamentalist strategies and can switch strategies according to profitability.The probability of following a chartist rule in the next period is specified as Φc_i,t.Source: B. Low-Frequency Traders · p. 3

C. High-Frequency Traders

• HF traders activate according to price fluctuations, making their trading speed endogenous rather than chronological.Each trader has a fixed price threshold drawn from a uniform distribution bounded by ηmin and ηmax.Source: C. High-Frequency Traders · p. 3
• HF traders use price and order information released by LF agents to anticipate price movements.Active HF agents choose buy or sell orders with equal probability.Source: C. High-Frequency Traders · p. 3
• HF order sizes depend on available volume on the opposite side of the limit order book, helping traders absorb LF orders.Order size is drawn from a truncated Poisson distribution.Source: C. High-Frequency Traders · pp. 3–4
• HF traders place limit orders near the best ask or bid, with prices adjusted by κj drawn uniformly between κmin and κmax.Buy and sell prices are formed relative to the best ask and bid, respectively.Source: C. High-Frequency Traders · p. 4
• Unexecuted HF orders are automatically removed after γH, a shorter period than the γL period for LF orders.The model uses this shorter cancellation period to represent the high order-cancellation rate associated with HFT.Source: C. High-Frequency Traders · p. 4

III. SIMULATION RESULTS

• The study runs 50 Monte-Carlo iterations of 1,200 trading sessions each using the baseline parameterization.The parameterization is described in Table IV.Source: §III · p. 4
• The first analysis checks whether the model reproduces the main stylized facts of financial markets.This is followed by tests of flash-crash properties and their determinants.Source: §III · p. 4
• The final analysis examines post-flash-crash recovery under different degrees of HF order cancellation.The study investigates how cancellation affects model dynamics.Source: §III · p. 4

A. Stylized Facts of Financial Markets

• Price-return autocorrelations are not significantly different from zero, while absolute and squared returns show slowly decaying autocorrelation.The decay is more pronounced for absolute returns, indicating volatility clustering; Figure 1 shows return autocorrelations across lags and runs, and Figure 2 shows the absolute- and squared-return functions.Source: A. Stylized Facts of Financial Markets · p. 4, Figure 1 · p. 4, Figure 2 · p. 4
• The pooled price-return distribution significantly departs from the Gaussian benchmark, especially in the tails.Figure 3 compares the pooled-return density with a normal fit; Figure 4 shows negative-return tails well approximated by a power law.Source: A. Stylized Facts of Financial Markets · pp. 4–5, Figure 3 · p. 5, Figure 4 · p. 5

B. Stylized Facts of Flash Crashes

• Flash crashes are defined as price drops of at least 5% followed by recovery within 30 minutes, and the model generates them endogenously.The definition follows evidence about the May 6, 2010 flash crash.Source: B. Stylized Facts of Flash Crashes · p. 5
• During flash crashes, price returns correlate negatively with total and HFT volumes, while LFT volume remains positively correlated with returns.Normal times show a weak positive returns-volume correlation; the table reports averages across 50 Monte-Carlo runs.Source: B. Stylized Facts of Flash Crashes · p. 5, Table II · p. 6
• Flash crashes do not emerge without HF traders, and removing them significantly lowers price-return volatility.The main stylized facts are reproduced in the only-LFT scenario as well as the baseline.Source: B. Stylized Facts of Flash Crashes · pp. 5–6

C. The Anatomy of Flash Crashes

• Bid-ask spread distributions are significantly shifted to the right during crash phases of sharp asset-price drops relative to normal times, based on pooled observations across 50 independent Monte-Carlo runs.Source: C. The Anatomy of Flash Crashes · p. 6, Figure 6 · p. 6
• HF traders’ directional orders widen spreads, but large spreads alone do not produce large closing-price drops when orders remain balanced across book sides.The model’s LF orders tend to fill the bid-ask gap, whereas HF orders are placed a few ticks beyond the best ask or bid.Source: C. The Anatomy of Flash Crashes · pp. 6–7
• Crash-phase HF orders concentrate on the sell side while LF orders concentrate on the buy side; these extreme concentrations are absent in normal times.The reported distributions overlap in normal times but not during crashes.Source: C. The Anatomy of Flash Crashes · p. 7, Figure 8 · p. 7, Figure 9 · p. 7
• Flash crashes combine wide bid-ask spreads with HF sell-side and LF buy-side order concentration.The three conditions are identified as jointly generating crashes in the model.Source: C. The Anatomy of Flash Crashes · p. 8
• Price-dependent activation and heterogeneous thresholds can shrink the active HF sample, raising the chance of sell-side concentration despite each trader’s 0.5 sell probability.The smaller active sample makes concentrated sell orders more probable and can contribute to a flash crash.Source: C. The Anatomy of Flash Crashes · p. 8

D. Accounting for Post-Crash Recoveries

• During recovery, spread and HF sell-concentration distributions return to levels not statistically different from normal times.The return of liquidity and the disappearance of concentrated HF selling accompany the rapid price recovery.Source: D. Accounting for Post-Crash Recoveries · p. 8
• After a crash, increased HF order volume is more evenly split between buys and sells, helping prices recover; canceled unexecuted orders also keep quotes aligned with current conditions.High baseline cancellation reduces the persistence of wide spreads and supports recovery of liquidity and price.Source: D. Accounting for Post-Crash Recoveries · p. 8
• Lower HF order-cancellation rates decrease market volatility and flash-crash counts but increase flash-crash duration.The experiment varies how long unexecuted HF orders remain in the book; Table III reports cancellation rates and crash statistics.Source: D. Accounting for Post-Crash Recoveries · p. 9, Table III · p. 9

• LF traders switch between fundamentalist and chartist strategies, while HF traders use directional strategies activated by price fluctuations.Source: §IV · p. 9
• The model reproduces financial-market stylized facts; flash crashes arise with wide spreads, synchronized HF selling, and LF concentration on the buy side.Source: §IV · p. 9
• Higher HF order-cancellation rates increase volatility and crash occurrence, but speed post-crash price recovery.Source: §IV · p. 9
• Proposed extensions include richer HF strategy sets, multiple markets for systemic crashes and latency arbitrage, and policy tests such as halts or transaction taxes.Source: §IV · p. 9