High-Frequency Trading and Latency Arbitrage › Key Parameters
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The key parameters for latency arbitrage simulation are:
- n_events: Number of signal events observed (e.g., 1000), with more events providing better statistical sampling of strategy performance.
- signal_volatility: Typical magnitude of signal price changes (basis points), representing market volatility that creates arbitrage opportunities.
- beta: Statistical sensitivity between signal and target instruments (dimensionless), quantifying how much the target moves when the signal moves and forming the core of the prediction model.
- latency_advantage_ms: Speed advantage over competitors (milliseconds), determining the time window for capturing moves before prices converge.
- market_response_time_ms: Time for market to fully adjust to signals (milliseconds), defining how long arbitrage opportunities persist before information is fully incorporated.
- execution_prob: Probability of successfully executing each trade (0 to 1), accounting for infrastructure reliability and competition for available liquidity.
- transaction_cost_bps: Round-trip transaction cost (basis points), determining minimum profitable signal threshold and representing the hurdle that must be cleared for profitable trading.
The Speed Arms Race
The profitability of latency arbitrage depends critically on relative speed. Being the fastest trader captures most of the available profit; being second-fastest may capture nothing. This creates intense competition to reduce latency.
def analyze_speed_competition(
latencies_ms: list,
total_opportunity_bps: float = 1.0,
market_adjustment_ms: float = 5.0,
):
"""
Analyze how profits are distributed among competitors with different speeds.
Parameters:
-----------
latencies_ms : List of latencies for each competitor
total_opportunity_bps : Total arbitrage opportunity per event
market_adjustment_ms : Time for market to fully adjust
"""
latencies = np.array(latencies_ms)
n_competitors = len(latencies)
# Sort by speed (lowest latency first)
speed_rank = np.argsort(latencies)
sorted_latencies = latencies[speed_rank]
# Calculate profit share for each competitor
# Fastest trader captures opportunity until second-fastest arrives
profit_shares = np.zeros(n_competitors)
for i, rank in enumerate(speed_rank):
if i == 0:
# Fastest trader: captures from their arrival until second-fastest
if n_competitors > 1:
time_window = sorted_latencies[1] - sorted_latencies[0]
else:
time_window = market_adjustment_ms - sorted_latencies[0]
profit_shares[rank] = min(time_window / market_adjustment_ms, 1.0)
else:
# Other traders: may capture nothing if market already adjusted
remaining_opportunity = 1.0 - sum(profit_shares)
if (
remaining_opportunity > 0
and sorted_latencies[i] < market_adjustment_ms
):
if i < n_competitors - 1:
time_window = sorted_latencies[i + 1] - sorted_latencies[i]
else:
time_window = market_adjustment_ms - sorted_latencies[i]
profit_shares[rank] = min(
time_window / market_adjustment_ms, remaining_opportunity
)
# Convert to basis points
profits_bps = profit_shares * total_opportunity_bps
return {
"latencies": latencies,
"profit_shares": profit_shares,
"profits_bps": profits_bps,
}
# Analyze competition among 5 HFT firms
latencies = [1.0, 1.2, 1.5, 2.0, 3.0] # milliseconds
competition = analyze_speed_competition(latencies)Speed Competition Analysis ======================================================= Firm Latency (ms) Profit Share Profit (bps) ------------------------------------------------------- Firm 1 1.0 4.0% 0.0400 Firm 2 1.2 6.0% 0.0600 Firm 3 1.5 10.0% 0.1000 Firm 4 2.0 20.0% 0.2000 Firm 5 3.0 40.0% 0.4000 ------------------------------------------------------- Total: 80.0% of opportunity captured
This simplified model partitions the five-millisecond adjustment window into intervals between successive arrivals. Under that assumption, a firm receives the interval after it arrives and before the next firm arrives; the last arriving firm receives the remaining interval before full adjustment. The resulting allocation therefore depends on the spacing between latencies, not only their rank. In this example, the widest residual interval belongs to the slowest firm, so the calculation does not by itself demonstrate a winner-take-most outcome.