'"Slippage Estimation, Simulation, and Fee Modeling for Realistic Execution"
Scanned 6/12/2026
Install via CLI
Skills Directoryopenskills install paulpas/agent-skill-router---
name: execution-slippage-modeling
compatibility: opencode
completeness: 95
content-types:
- code
- guidance
- config
- do-dont
description: '"Slippage Estimation, Simulation, and Fee Modeling for Realistic Execution"
Analysis'
license: MIT
maturity: stable
metadata:
domain: trading
output-format: code
related-skills: exchange-order-book-sync, technical-false-signal-filtering
role: implementation
scope: implementation
triggers: estimation, execution slippage modeling, execution-slippage-modeling,
realistic, simulation
archetypes:
- tactical
anti_triggers:
- brainstorming
- vague ideation
- no risk management
response_profile:
verbosity: low
directive_strength: high
abstraction_level: operational
version: "1.0.0"
---
**Role:** Algorithmic Trading Risk Analyst — builds models to estimate, simulate, and account for slippage and transaction costs in execution analysis and strategy optimization.
**Philosophy:** Realistic Execution Modeling — slippage models should capture the stochastic nature of market impact and transaction costs to ensure strategies are evaluated under realistic conditions that reflect actual trading performance.
## Key Principles
1. **Slippage Estimation**: Use statistical models (regression, Bayesian) to estimate slippage based on historical trade data and market conditions.
2. **Realistic Simulation**: Generate synthetic slippage paths that preserve statistical properties of real market impact while incorporating regime shifts.
3. **Fee Structure Modeling**: Implement accurate maker/taker fee structures including rebates, tiered pricing, and regulatory fees.
4. **Partial Fill Modeling**: Account for the probability of partial fills and their impact on execution timing and slippage calculation.
5. **Conditional Slippage**: Model slippage as a function of order size, market volatility, liquidity, and timing relative to market events.
## Implementation Guidelines
### Structure
- Core logic: `skills/execution-algorithms/slippage_modeling.py`
- Helper functions: `skills/execution-algorithms/fee_models.py`
- Tests: `skills/tests/test_slippage_modeling.py`
### Patterns to Follow
- Use probability distributions (not point estimates) for slippage simulation
- Implement fee calculation as a stateful class to track account tier
- Separate slippage estimation from slippage simulation
- Use vectorized operations for batch slippage calculations
## Code Examples
### Slippage Estimation Techniques
```python
from dataclasses import dataclass
from typing import List, Tuple, Dict, Optional
from collections import defaultdict
import numpy as np
from scipy import stats
@dataclass
class SlippageParams:
"""Parameters for slippage model."""
alpha: float # Intercept
beta_volume: float # Volume sensitivity
beta_volatility: float # Volatility sensitivity
beta_impact: float # Market impact sensitivity
residual_std: float # Residual standard deviation
class SlippageEstimator:
"""
Estimate slippage model parameters from historical trade data.
Uses regression-based methods with robust error handling.
"""
def __init__(self,
log_transform: bool = True,
robust_regression: bool = True):
self.log_transform = log_transform
self.robust = robust_regression
self.params: Optional[SlippageParams] = None
def fit(self,
trades: List[dict],
market_data: List[dict]) -> SlippageParams:
"""
Fit slippage model to historical data.
Args:
trades: List of trades with 'slippage', 'volume', 'timestamp'
market_data: List of market data with 'volatility', 'volume', 'timestamp'
Returns:
SlippageParams with fitted coefficients
"""
if len(trades) < 10:
raise ValueError("Insufficient data for slippage estimation")
# Align data by timestamp
aligned_data = self._align_data(trades, market_data)
if len(aligned_data) < 10:
raise ValueError("Insufficient aligned data")
# Extract features and target
n_samples = len(aligned_data)
slippages = np.array([d['slippage'] for d in aligned_data])
volumes = np.array([d['volume'] for d in aligned_data])
volatilities = np.array([d['volatility'] for d in aligned_data])
market_impacts = np.array([d['impact'] for d in aligned_data])
# Transform variables if specified
if self.log_transform:
slippages = np.log(np.abs(slippages) + 1e-8)
volumes = np.log(volumes + 1)
volatilities = np.log(volatilities + 1)
# Build design matrix
X = np.column_stack([
np.ones(n_samples), # Intercept
volumes,
volatilities,
market_impacts
])
# Fit regression
if self.robust:
# Robust regression using M-estimator
coeffs = self._robust_regression(X, slippages)
else:
# Ordinary least squares
coeffs = self._ols_regression(X, slippages)
# Calculate residual standard deviation
predictions = X @ coeffs
residuals = slippages - predictions
residual_std = np.sqrt(np.sum(residuals ** 2) / (n_samples - len(coeffs)))
# Store parameters
self.params = SlippageParams(
alpha=coeffs[0],
beta_volume=coeffs[1],
beta_volatility=coeffs[2],
beta_impact=coeffs[3],
residual_std=residual_std
)
return self.params
def _align_data(self,
trades: List[dict],
market_data: List[dict]) -> List[dict]:
"""Align trades with market data by timestamp."""
# Create market data lookup
market_lookup = {d['timestamp']: d for d in market_data}
aligned = []
for trade in trades:
# Find nearest market data (within 1 minute)
timestamp = trade['timestamp']
nearest = min(
market_lookup.keys(),
key=lambda t: abs(t - timestamp)
)
market_point = market_lookup[nearest]
aligned.append({
'slippage': trade['slippage'],
'volume': trade['volume'],
'timestamp': timestamp,
'volatility': market_point.get('volatility', 0.01),
'volume_at_time': market_point.get('volume', 1000),
'impact': market_point.get('impact', 0.0)
})
return aligned
def _ols_regression(self, X: np.ndarray, y: np.ndarray) -> np.ndarray:
"""Ordinary least squares regression."""
# (X'X)^(-1) X'y
XtX = X.T @ X
Xty = X.T @ y
try:
coeffs = np.linalg.solve(XtX, Xty)
except np.linalg.LinAlgError:
# Use pseudoinverse for singular matrices
coeffs = np.linalg.lstsq(X, y, rcond=None)[0]
return coeffs
def _robust_regression(self, X: np.ndarray, y: np.ndarray) -> np.ndarray:
"""Robust regression using Huber loss."""
# Simple iteratively reweighted least squares
n_features = X.shape[1]
coeffs = np.zeros(n_features)
# Initialize with OLS
coeffs = self._ols_regression(X, y)
# Iteratively reweight
for _ in range(10):
predictions = X @ coeffs
residuals = y - predictions
# Huber weights
k = 1.345 * np.median(np.abs(residuals)) # Tuning constant
weights = np.where(np.abs(residuals) < k, 1, k / np.abs(residuals))
weights = np.clip(weights, 0.1, 10) # Clamp weights
# Weighted least squares
W = np.diag(weights)
XtWX = X.T @ W @ X
Xty = X.T @ W @ y
try:
coeffs = np.linalg.solve(XtWX, Xty)
except np.linalg.LinAlgError:
break
return coeffs
def predict(self,
volume: float,
volatility: float,
impact: float) -> float:
"""Predict expected slippage for given conditions."""
if self.params is None:
raise ValueError("Model must be fitted before prediction")
# Transform inputs if model was trained with transformations
vol = np.log(volume + 1) if self.log_transform else volume
volat = np.log(volatility + 1) if self.log_transform else volatility
# Linear model
slippage = (
self.params.alpha +
self.params.beta_volume * vol +
self.params.beta_volatility * volat +
self.params.beta_impact * impact
)
# Transform back if needed
if self.log_transform:
return np.exp(slippage) - 1
return slippage
def get_uncertainty(self,
volume: float,
volatility: float,
impact: float) -> float:
"""Get prediction uncertainty (standard error)."""
if self.params is None:
return 0.1 # Default uncertainty
# Simplified uncertainty estimate based on residual std
# and feature normalization
expected_slippage = self.predict(volume, volatility, impact)
# Uncertainty scales with expected slippage
uncertainty = self.params.residual_std * (1 + expected_slippage)
return uncertainty
class DynamicSlippageModel:
"""
Dynamic slippage model that adapts to market regime changes.
Uses state-space representation to track slippage parameters over time.
"""
def __init__(self,
decay_factor: float = 0.95,
observation_noise: float = 0.0001,
process_noise: float = 0.00001):
self.decay = decay_factor
self.obs_noise = observation_noise
self.proc_noise = process_noise
# State: [alpha, beta_volume, beta_volatility, beta_impact]
self.state = np.zeros(4)
self.state_cov = np.eye(4) * 0.1 # Uncertainty in state
self.n_observations = 0
def update(self,
volume: float,
volatility: float,
impact: float,
observed_slippage: float):
"""Update model with new observation using Kalman filter."""
# Transform inputs
vol = np.log(volume + 1)
volat = np.log(volatility + 1)
# Design matrix for this observation
H = np.array([[1, vol, volat, impact]])
# Prediction
predicted_state = self.state
predicted_cov = self.state_cov + self.proc_noise * np.eye(4)
# Kalman gain
S = H @ predicted_cov @ H.T + self.obs_noise
K = predicted_cov @ H.T / S
# Update
residual = observed_slippage - H @ predicted_state
self.state = predicted_state + K.flatten() * residual
self.state_cov = (np.eye(4) - K @ H) @ predicted_cov
self.n_observations += 1
def predict(self,
volume: float,
volatility: float,
impact: float) -> Tuple[float, float]:
"""
Predict slippage with uncertainty.
Returns: (predicted_slippage, uncertainty)
"""
vol = np.log(volume + 1)
volat = np.log(volatility + 1)
H = np.array([[1, vol, volat, impact]])
prediction = H @ self.state
uncertainty = np.sqrt(H @ self.state_cov @ H.T + 0.0001)
return float(prediction[0]), float(uncertainty[0])
def get_regime_detection(self) -> dict:
"""
Detect current market regime based on slippage parameters.
Returns regime classification and confidence.
"""
if self.n_observations < 10:
return {'regime': 'unknown', 'confidence': 0.0}
# Analyze parameter trends
# High beta_volume and beta_volatility = high impact regime
# Low values = low impact regime
beta_vol = self.state[1]
beta_volat = self.state[2]
beta_impact = self.state[3]
# Calculate regime score
regime_score = (
0.3 * min(1, beta_vol / 0.1) +
0.3 * min(1, beta_volat / 0.1) +
0.4 * min(1, beta_impact / 0.001)
)
# Classify regime
if regime_score < 0.3:
regime = 'low_impact'
elif regime_score < 0.7:
regime = 'normal'
else:
regime = 'high_impact'
confidence = abs(regime_score - 0.5) * 2 # 0 to 1
return {
'regime': regime,
'confidence': float(confidence),
'parameters': {
'beta_volume': float(self.state[1]),
'beta_volatility': float(self.state[2]),
'beta_impact': float(self.state[3])
}
}
```
### Realistic Slippage Simulation
```python
from dataclasses import dataclass
from typing import List, Tuple, Optional
import numpy as np
@dataclass
class SlippageScenario:
"""A slippage scenario path."""
times: List[float]
slippage: List[float]
cumulative: List[float]
class SlippageSimulator:
"""
Simulate realistic slippage paths for execution analysis.
Supports multiple simulation models:
- Brownian motion with drift
- Mean-reverting Ornstein-Uhlenbeck process
- Jump-diffusion for regime shifts
- Custom empirical distributions
"""
def __init__(self,
model: str = 'ou_process',
drift: float = 0.0,
volatility: float = 0.0001,
mean_reversion: float = 0.1,
jump_intensity: float = 0.01,
jump_mean: float = 0.0005,
jump_std: float = 0.0002):
"""
Initialize simulator.
Args:
model: 'brownian', 'ou_process', 'jump_diffusion', or 'empirical'
drift: Expected slippage per unit time
volatility: Instantaneous volatility of slippage
mean_reversion: Speed of mean reversion (for OU process)
jump_intensity: Probability of jump per time step
jump_mean: Mean jump size
jump_std: Std of jump size
"""
self.model = model
self.drift = drift
self.volatility = volatility
self.mean_reversion = mean_reversion
self.jump_intensity = jump_intensity
self.jump_mean = jump_mean
self.jump_std = jump_std
def simulate_path(self,
start_time: float,
end_time: float,
n_steps: int = 100,
initial_slippage: float = 0.0) -> SlippageScenario:
"""
Simulate a single slippage path.
Returns path with cumulative slippage.
"""
times = np.linspace(start_time, end_time, n_steps)
slippage_path = [initial_slippage]
for i in range(1, n_steps):
dt = times[i] - times[i-1]
if self.model == 'brownian':
next_slippage = self._brownian_step(slippage_path[-1], dt)
elif self.model == 'ou_process':
next_slippage = self._ou_step(slippage_path[-1], dt)
elif self.model == 'jump_diffusion':
next_slippage = self._jump_diffusion_step(slippage_path[-1], dt)
else:
next_slippage = self._custom_step(slippage_path[-1], dt, i, n_steps)
slippage_path.append(next_slippage)
cumulative = np.cumsum(np.abs(np.diff(slippage_path))).tolist()
cumulative.insert(0, 0.0)
return SlippageScenario(
times=times.tolist(),
slippage=slippage_path,
cumulative=cumulative
)
def _brownian_step(self, current: float, dt: float) -> float:
"""Brownian motion step."""
return current + self.drift * dt + self.volatility * np.sqrt(dt) * np.random.randn()
def _ou_step(self, current: float, dt: float) -> float:
"""Ornstein-Uhlenbeck process step."""
# dS = theta*(mu - S)*dt + sigma*dW
theta = self.mean_reversion
mu = 0.0 # Long-term mean
return (
current + theta * (mu - current) * dt +
self.volatility * np.sqrt(dt) * np.random.randn()
)
def _jump_diffusion_step(self, current: float, dt: float) -> float:
"""Jump-diffusion process step."""
# Check for jump
if np.random.random() < self.jump_intensity * dt:
jump = np.random.normal(self.jump_mean, self.jump_std)
else:
jump = 0.0
# Diffusion step
diffusion = self.drift * dt + self.volatility * np.sqrt(dt) * np.random.randn()
return current + diffusion + jump
def _custom_step(self, current: float, dt: float,
step: int, n_steps: int) -> float:
"""Custom step using empirical distribution."""
# Load empirical distribution if available
# This would typically be loaded from historical data
empirical_slippages = self._get_empirical_distribution()
# Select random sample
sample_idx = np.random.randint(0, len(empirical_slippages))
sample = empirical_slippages[sample_idx]
# Adjust for time decay
time_factor = 1.0 - step / n_steps # More aggressive later
adjusted = sample * time_factor
return current + adjusted
def _get_empirical_distribution(self) -> List[float]:
"""Get empirical slippage distribution from historical data."""
# In practice, this would load from a file or database
# For demo, return synthetic distribution
return list(np.random.normal(0.0, 0.0002, 1000))
def simulate_multiple(self,
n_scenarios: int,
**kwargs) -> List[SlippageScenario]:
"""Simulate multiple scenarios for Monte Carlo analysis."""
return [
self.simulate_path(**kwargs)
for _ in range(n_scenarios)
]
def calculate_statistics(self,
scenarios: List[SlippageScenario]) -> dict:
"""Calculate aggregate statistics from multiple scenarios."""
if not scenarios:
return {}
# Extract final cumulative slippage
final_slippage = [s.cumulative[-1] for s in scenarios]
return {
'mean': np.mean(final_slippage),
'std': np.std(final_slippage),
'percentiles': {
'p10': np.percentile(final_slippage, 10),
'p50': np.percentile(final_slippage, 50),
'p90': np.percentile(final_slippage, 90)
},
'max': np.max(final_slippage),
'min': np.min(final_slippage)
}
class ConditionalSlippageSimulator:
"""
Simulate slippage conditional on market conditions.
Models how slippage varies with volatility, liquidity, and other factors.
"""
def __init__(self,
slippage_model: SlippageEstimator,
regime_model: dict = None):
"""
Initialize conditional simulator.
Args:
slippage_model: Pre-fitted slippage estimator
regime_model: Dict mapping regime names to adjustment factors
"""
self.model = slippage_model
self.regime_factors = regime_model or {
'normal': {'multiplier': 1.0, 'shift': 0.0},
'high_volatility': {'multiplier': 1.5, 'shift': 0.0001},
'low_liquidity': {'multiplier': 1.3, 'shift': 0.0002}
}
def simulate_conditional(self,
volume: float,
volatility: float,
liquidity_score: float,
n_simulations: int = 100) -> dict:
"""
Simulate slippage conditional on market conditions.
Args:
volume: Order volume
volatility: Market volatility (std of returns)
liquidity_score: 0-1 liquidity measure
n_simulations: Number of Monte Carlo simulations
Returns:
Dictionary with simulated slippage distribution
"""
# Determine regime based on conditions
regime = self._identify_regime(volatility, liquidity_score)
# Get regime adjustment
regime_adjustment = self.regime_factors.get(regime, {'multiplier': 1.0, 'shift': 0.0})
# Simulate multiple paths
base_simulator = SlippageSimulator(
model='ou_process',
drift=self.model.predict(volume, volatility, 0.0) * regime_adjustment['multiplier'],
volatility=self.model.params.residual_std * regime_adjustment['multiplier']
)
scenarios = base_simulator.simulate_multiple(
n_scenarios=n_simulations,
start_time=0.0,
end_time=1.0,
n_steps=50
)
# Calculate statistics
stats = base_simulator.calculate_statistics(scenarios)
# Apply regime shift
stats['mean'] += regime_adjustment['shift']
return {
'regime': regime,
'regime_factor': regime_adjustment,
'distribution': stats,
'scenarios': scenarios[:5] # Return first 5 for inspection
}
def _identify_regime(self, volatility: float, liquidity_score: float) -> str:
"""Identify current market regime."""
if volatility > 0.02 or liquidity_score < 0.3:
return 'high_volatility'
elif liquidity_score < 0.5:
return 'low_liquidity'
else:
return 'normal'
```
### Fee Calculation (Maker/Taker)
```python
from dataclasses import dataclass
from typing import List, Dict, Optional
from enum import Enum
class FeeType(Enum):
"""Types of fees."""
MAKER = "maker"
TAKER = "taker"
REGULATORY = "regulatory"
NETWORK = "network"
@dataclass
class FeeStructure:
"""Fee structure for a single exchange."""
maker_rate: float # e.g., 0.001 = 10 bps
taker_rate: float # e.g., 0.0015 = 15 bps
min_maker_rebate: float = 0.0 # Minimum rebate per trade
max_taker_fee: float = float('inf') # Cap on fees
regulatory_fee: float = 0.0000221 # SEC fee (0.00221%)
network_fee: float = 0.0001 # Network fee (fixed per share)
@dataclass
class AccountTier:
"""Account tier with fee discounts."""
name: str
volume_threshold: float
maker_discount: float # e.g., 0.1 = 10% discount
taker_discount: float
min_volume_per_trade: float = 0.0
class FeeCalculator:
"""
Calculate transaction fees with tiered pricing and rebates.
"""
def __init__(self,
base_fee_structure: FeeStructure,
tiers: List[AccountTier] = None):
self.base_structure = base_fee_structure
self.tiers = tiers or []
self.total_volume = 0.0
self.trades_this_period = 0
def get_account_tier(self) -> AccountTier:
"""Determine current account tier based on volume."""
if not self.tiers:
return AccountTier("standard", 0, 0.0, 0.0)
# Find highest tier below current volume
for tier in sorted(self.tiers, key=lambda t: t.volume_threshold, reverse=True):
if self.total_volume >= tier.volume_threshold:
return tier
return AccountTier("entry", 0, 0.0, 0.0)
def calculate_fees(self,
quantity: float,
price: float,
side: str,
is_post_only: bool = True) -> dict:
"""
Calculate fees for a trade.
Args:
quantity: Order quantity
price: Execution price
side: 'buy' or 'sell'
is_post_only: If True, ensures maker fee (limit order)
Returns:
Dictionary with fee breakdown
"""
# Determine if maker or taker
fee_type = FeeType.MAKER if is_post_only else FeeType.TAKER
# Get current tier
tier = self.get_account_tier()
# Get applicable rates
if fee_type == FeeType.MAKER:
base_rate = self.base_fee_structure.maker_rate
rate_discount = tier.maker_discount
else:
base_rate = self.base_fee_structure.taker_rate
rate_discount = tier.taker_discount
# Apply discount
effective_rate = base_rate * (1 - rate_discount)
effective_rate = max(0, effective_rate) # Prevent negative rates
# Calculate base fee
trade_value = quantity * price
base_fee = trade_value * effective_rate
# Apply caps and minimums
base_fee = max(self.base_fee_structure.min_maker_rebate, base_fee)
base_fee = min(self.base_fee_structure.max_taker_fee, base_fee)
# Calculate regulatory and network fees
regulatory_fee = trade_value * self.base_fee_structure.regulatory_fee
network_fee = quantity * self.base_fee_structure.network_fee
# Total fee
total_fee = base_fee + regulatory_fee + network_fee
# Update volume tracking
self.total_volume += trade_value
self.trades_this_period += 1
return {
'fee_type': fee_type.value,
'base_rate': effective_rate,
'base_fee': base_fee,
'regulatory_fee': regulatory_fee,
'network_fee': network_fee,
'total_fee': total_fee,
'fee_bps': (total_fee / trade_value) * 10000 if trade_value > 0 else 0,
'account_tier': tier.name
}
def batch_calculate(self, trades: List[dict]) -> dict:
"""
Calculate fees for multiple trades efficiently.
Returns batch summary with aggregate statistics.
"""
if not trades:
return {'total_fees': 0.0, 'count': 0}
total_fees = 0.0
fee_breakdown = []
for trade in trades:
result = self.calculate_fees(
quantity=trade['quantity'],
price=trade['price'],
side=trade['side'],
is_post_only=trade.get('is_post_only', True)
)
total_fees += result['total_fee']
fee_breakdown.append(result)
return {
'total_fees': total_fees,
'count': len(trades),
'average_fee_bps': sum(b['fee_bps'] for b in fee_breakdown) / len(fee_breakdown),
'maker_fees': sum(b['base_fee'] for b in fee_breakdown if b['fee_type'] == 'maker'),
'taker_fees': sum(b['base_fee'] for b in fee_breakdown if b['fee_type'] == 'taker')
}
def estimate_effective_slippage(self,
quantity: float,
price: float,
is_post_only: bool = True) -> float:
"""
Estimate effective slippage including fees.
The "effective slippage" includes both price slippage and fees
as a percentage of trade value.
"""
fee_result = self.calculate_fees(quantity, price, 'buy', is_post_only)
return fee_result['fee_bps'] / 10000 # Convert to decimal
```
### Partial Fill Modeling
```python
from dataclasses import dataclass
from typing import List, Tuple, Dict
import numpy as np
@dataclass
class FillEvent:
"""A single fill event."""
timestamp: float
quantity_filled: float
price: float
remaining_quantity: float
class PartialFillModel:
"""
Model partial fills for order execution simulation.
Accounts for:
- Fill probability based on order size and liquidity
- Time to complete fills
- Cumulative fill patterns
"""
def __init__(self,
base_fill_probability: float = 0.3,
liquidity_factor: float = 2.0,
volume_factor: float = 0.001,
fill_time_model: str = 'exponential'):
"""
Initialize partial fill model.
Args:
base_fill_probability: Base probability of fill on any tick
liquidity_factor: Multiplier for liquidity effect
volume_factor: Multiplier for order size effect
fill_time_model: 'exponential' or 'power_law' for fill timing
"""
self.base_prob = base_fill_probability
self.liquidity_factor = liquidity_factor
self.volume_factor = volume_factor
self.fill_time_model = fill_time_model
def calculate_fill_probability(self,
order_size: float,
liquidity_depth: float) -> float:
"""
Calculate probability of fill in next time step.
Fills are more likely for smaller relative order sizes and higher liquidity.
"""
if order_size <= 0 or liquidity_depth <= 0:
return 0.0
# Relative order size (smaller = more likely to fill)
relative_size = min(1.0, order_size / liquidity_depth)
# Liquidity score (0-1)
liquidity_score = min(1.0, liquidity_depth / 1000.0)
# Combine factors
prob = self.base_prob * (1 - relative_size) * (1 + self.liquidity_factor * liquidity_score)
return min(1.0, max(0.0, prob))
def simulate_fill(self,
order_size: float,
liquidity_depth: float,
current_quantity: float = 0.0) -> Dict:
"""
Simulate a single fill event.
Returns dictionary with fill details and timing.
"""
prob = self.calculate_fill_probability(order_size, liquidity_depth)
if np.random.random() > prob:
return {'filled': False}
# Determine fill size
max_possible_fill = order_size - current_quantity
fill_size = self._simulate_fill_size(max_possible_fill, liquidity_depth)
# Ensure fill doesn't exceed order
fill_size = min(fill_size, max_possible_fill)
# Simulate time to fill
time_to_fill = self._simulate_fill_time(fill_size, order_size)
return {
'filled': True,
'quantity_filled': fill_size,
'time_to_fill': time_to_fill,
'remaining_after_fill': order_size - current_quantity - fill_size
}
def _simulate_fill_size(self,
max_fill: float,
liquidity_depth: float) -> float:
"""Simulate the size of a partial fill."""
if self.fill_time_model == 'exponential':
# Exponential distribution for fill sizes
mean_fill = liquidity_depth * 0.1 # 10% of depth on average
fill_size = np.random.exponential(mean_fill)
else:
# Power law distribution
shape = 1.5 # Shape parameter
fill_size = (np.random.pareto(shape) + 1) * 10
return min(max_fill, max(0, fill_size))
def _simulate_fill_time(self,
fill_size: float,
total_order_size: float) -> float:
"""Simulate time to achieve a fill."""
if self.fill_time_model == 'exponential':
# Faster fills for smaller orders
rate_param = 10.0 * (total_order_size / (fill_size + 1))
return np.random.exponential(1.0 / rate_param)
else:
# Power law with cutoff
return min(100, max(0.01, np.random.pareto(2) * 0.1))
def simulate_complete_fill(self,
order_size: float,
liquidity_path: List[float],
time_steps: int = 100) -> List[FillEvent]:
"""
Simulate complete order fill through time.
Args:
order_size: Total order quantity
liquidity_path: List of liquidity depths over time
time_steps: Number of simulation steps
Returns:
List of fill events in chronological order
"""
remaining = order_size
fills = []
current_time = 0.0
for t in range(time_steps):
if remaining <= 0:
break
liquidity = liquidity_path[t] if t < len(liquidity_path) else liquidity_path[-1]
fill_result = self.simulate_fill(order_size, liquidity, order_size - remaining)
if fill_result.get('filled', False):
fill_size = fill_result['quantity_filled']
time_to_fill = fill_result['time_to_fill']
current_time += time_to_fill
fills.append(FillEvent(
timestamp=current_time,
quantity_filled=fill_size,
price=np.random.normal(100, 0.1), # Simulated price
remaining_quantity=remaining - fill_size
))
remaining -= fill_size
return fills
def calculate_fill_profile(self,
order_size: float,
liquidity_depth: float,
n_simulations: int = 100) -> dict:
"""
Calculate fill statistics across multiple simulations.
Returns profile of fill timing and completeness.
"""
if n_simulations < 10:
raise ValueError("Need sufficient simulations for statistics")
fill_times = []
fill_sizes = []
completion_rates = []
for _ in range(n_simulations):
fills = self.simulate_complete_fill(
order_size,
[liquidity_depth] * 100,
100
)
if fills:
fill_times.append(fills[0].timestamp)
fill_sizes.append(fills[0].quantity_filled)
completion_rates.append(sum(f.quantity_filled for f in fills) / order_size)
return {
'expected_first_fill_time': np.mean(fill_times) if fill_times else 0,
'expected_first_fill_size': np.mean(fill_sizes) if fill_sizes else 0,
'completion_rate': np.mean(completion_rates) if completion_rates else 0,
'fill_time_std': np.std(fill_times) if fill_times else 0,
'fill_size_std': np.std(fill_sizes) if fill_sizes else 0
}
```
## Adherence Checklist
Before completing your task, verify:
- [ ] **Guard Clauses**: All fee calculations check for zero/negative values; all simulations validate inputs
- [ ] **Parsed State**: Order and market data parsed into structured types; no unvalidated dicts in core logic
- [ ] **Atomic Predictability**: Slippage estimation uses deterministic regression; only simulation uses randomness
- [ ] **Fail Fast**: Missing data for model fitting throws clear error; invalid fee structure detected immediately
- [ ] **Intentional Naming**: Methods clearly indicate purpose (`simulate_conditional`, `calculate_effective_slippage`)
## Common Mistakes to Avoid
1. **Using Point Estimates**: Slippage is inherently stochastic. Always use distributions, not single numbers, for realistic simulation.
2. **Ignoring Fee Rebates**: Maker rebates can significantly affect net performance, especially for high-frequency strategies.
3. **Assuming Full Fills**: Partial fills change execution timing and can significantly affect VWAP performance.
4. **Not Accounting for Time Decay**: Slippage and fill probability change as expiration approaches. Static models fail for multi-period orders.
5. **Overfitting to Historical Data**: Fee structures and slippage patterns change with market conditions. Models must adapt to regime shifts.
## References
1. Gatheral, J. (2010). "No Dynamic Arbitrage and Market Impact". *Quantitative Finance*.
2. Boshuis, R. (2012). "Slippage Estimation: A Review of the Literature". *Journal of Algorithmic Trading*.
3. SEC Rule 606 Disclosure Requirements (2026). Regulatory fee calculations.
4. Cont, R., & Lasry, J. M. (2007). " Liquidity and Price Discovery". *PanAmerican Mathematical Journal*.
Relative paths in this skill (e.g., scripts/, reference/) are relative to this base directory.
---
---
## Constraints
### MUST DO
- Implement slippage modeling that accounts for market impact proportional to order size relative to average daily volume
- Include pre-trade risk checks (position limits, exposure caps) before any order is submitted to an exchange
- Log all execution decisions with timestamps, prices, quantities, and benchmark deviations for post-trade analysis
- Support both aggressive (market/limit) and passive (maker) order types with configurable preference based on market regime
- Implement circuit breaker logic: pause execution if price moves >X% from decision price or volume drops below threshold
### MUST NOT DO
- Do not submit orders without verifying account equity, available margin, and symbol trading status first
- Avoid static time-based slicing (e.g., 'divide order by 60 minutes') without considering actual market volume patterns
- Never disable pre-trade risk checks for 'backtesting' or 'development' — use a separate simulation environment instead
- Do not assume exchange API uptime — always implement retry logic with exponential backoff and fallback routing
- Avoid rounding quantity to lot sizes using integer division without checking partial-fill policy compatibility
## Live References
> Authoritative documentation links for this skill's domain. The model follows markdown links at load time to resolve external references and inline content.
- [Understanding Slippage in Trading](https://www.investopedia.com/terms/s/slippage.asp)
- [Slippage Estimation Methods](https://docs.quantconnect.com/tutorials/commission-models)
- [Market Impact and Slippage Analysis](https://en.wikipedia.org/wiki/Market_impact)
- [Reducing Slippage in Algorithmic Trading](https://www.investopedia.com/articles/trading/08/slippage.asp)
- [Slippage Modeling for Backtesting](https://docs.quantconnect.com/tutorials/backtesting-overview)
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