paulpas Role: Fill Simulation Engineer — implements sophisticated models for predicting order fill probability, partial fills, and execution quality under realistic market conditions.
Philosophy: Probabilistic Execution — order fills are uncertain events subject to market liquidity, order book dynamics, and timing; simulation should model these probabilities to provide realistic performance expectations.
Key Principles
Fill Probability Modeling: Estimate probability of full fill, partial fill, or no fill based on order size, market liquidity, and order type.
Partial Fill Dynamics: Model partial fills and their impact on portfolio exposure and risk.
Order Book Depth Analysis: Simulate fill based on available liquidity at each price level.
Time-Based Fill Modeling: Account for fill probability over time (market hours, volatility periods).
Fill Quality Metrics: Track fill quality (slippage, execution time) for performance analysis.
Implementation Guidelines
Structure
- Core logic:
skills/paper-trading/fill_simulator.py - Order book models:
skills/paper-trading/order_book.py - Tests:
skills/tests/test_fill_simulation.py
Patterns to Follow
- Use probability distributions for fill modeling
- Implement order book depth analysis
- Track fill timing and partial fills
- Separate fill simulation from order placement
- Use Monte Carlo methods for complex fill scenarios
Code Examples
Fill Probability Model
from dataclasses import dataclass
from typing import List, Dict, Optional, Tuple
from enum import Enum
import numpy as np
import pandas as pd
from scipy import stats
from collections import defaultdict
class OrderStatus(Enum):
"""Order status enumeration."""
PENDING = "pending"
PARTIAL = "partial"
FILLED = "filled"
CANCELLED = "cancelled"
EXPIRED = "expired"
@dataclass
class OrderBookLevel:
"""Single level in order book."""
price: float
quantity: float
count: int # Number of orders at this level
@dataclass
class OrderBook:
"""Complete order book state."""
bids: List[OrderBookLevel] # Buy orders (descending price)
asks: List[OrderBookLevel] # Sell orders (ascending price)
mid_price: float
spread: float
timestamp: pd.Timestamp
class FillProbabilityModel:
"""
Models fill probability for orders based on market conditions.
"""
def __init__(self,
min_fill_probability: float = 0.1,
max_fill_probability: float = 0.99,
liquidity_threshold: float = 100,
volatility_factor: float = 0.5):
self.min_fill_probability = min_fill_probability
self.max_fill_probability = max_fill_probability
self.liquidity_threshold = liquidity_threshold
self.volatility_factor = volatility_factor
def calculate_base_fill_probability(self, order_size: float,
liquidity: float,
spread: float) -> float:
"""
Calculate base fill probability based on order size and liquidity.
Fills are more likely when:
- Order size is small relative to liquidity
- Spread is narrow (tight market)
"""
if liquidity == 0:
return self.min_fill_probability
# Size ratio: how large is order relative to liquidity
size_ratio = order_size / liquidity
# Base probability declines with size ratio
if size_ratio < 0.1:
base_prob = 0.95
elif size_ratio < 0.25:
base_prob = 0.85
elif size_ratio < 0.5:
base_prob = 0.70
elif size_ratio < 1.0:
base_prob = 0.50
else:
base_prob = 0.30
# Adjust for spread (tighter spread = higher probability)
spread_adjustment = 1.0 - (spread / 0.01) * 0.2
spread_adjustment = max(0.8, min(1.0, spread_adjustment))
return max(self.min_fill_probability, min(self.max_fill_probability, base_prob * spread_adjustment))
def calculate_time_based_probability(self, order_age: float,
time_window: float,
volatility: float) -> float:
"""
Calculate time-based fill probability.
Orders have higher fill probability as they age,
but volatility can reduce fill probability.
"""
# Base probability increases with time (up to time_window)
time_factor = min(1.0, order_age / time_window)
# Volatility reduces probability
volatility_adjustment = max(0.5, 1.0 - self.volatility_factor * volatility)
return time_factor * volatility_adjustment
def calculate_liquidation_probability(self, order_size: float,
order_book: OrderBook,
side: str) -> Tuple[float, float]:
"""
Calculate probability of filling order by liquidating available depth.
Returns (fill_probability, expected_fill_quantity).
"""
if order_book is None:
return self.min_fill_probability, 0.0
# Get available liquidity in the direction of the order
if side == "buy":
levels = order_book.asks
else:
levels = order_book.bids
# Calculate cumulative liquidity
cumulative_liquidity = 0.0
fill_probabilities = []
for level in levels:
cumulative_liquidity += level.quantity
# Probability of filling this level
if order_size <= cumulative_liquidity:
# Can fill completely within this level
remaining = order_size - (cumulative_liquidity - level.quantity)
prob = remaining / level.quantity if level.quantity > 0 else 0
fill_probabilities.append(prob)
break
else:
# Will fill this entire level
fill_probabilities.append(1.0)
# Overall fill probability
if not fill_probabilities:
return self.min_fill_probability, 0.0
# Combined probability (all levels must fill sequentially)
combined_prob = 1.0
for prob in fill_probabilities:
combined_prob *= prob
# Expected fill quantity
expected_fill = min(order_size, sum(level.quantity for level in levels))
return max(self.min_fill_probability, combined_prob), expected_fill
def simulate_fill(self, order_size: float, order_book: OrderBook,
side: str, time_window: float = 3600,
volatility: float = 0.02) -> Dict:
"""
Simulate order fill with Monte Carlo approach.
Returns dict with:
- filled: Whether order was filled
- fill_quantity: Quantity actually filled
- fill_probability: Estimated fill probability
- expected_slippage: Expected slippage cost
"""
# Calculate base fill probability
if order_book is None:
liquidity = self.liquidity_threshold
spread = 0.001
else:
if side == "buy":
liquidity = sum(level.quantity for level in order_book.asks)
spread = order_book.spread
else:
liquidity = sum(level.quantity for level in order_book.bids)
spread = order_book.spread
base_prob = self.calculate_base_fill_probability(order_size, liquidity, spread)
# Calculate time-based factor
time_factor = self.calculate_time_based_probability(0, time_window, volatility)
# Combined fill probability
fill_prob = base_prob * time_factor
# Determine if order fills
filled = np.random.random() < fill_prob
# Calculate fill quantity
if filled:
# Calculate expected fill based on order book depth
if order_book is None:
fill_quantity = order_size
else:
if side == "buy":
levels = order_book.asks
else:
levels = order_book.bids
cumulative = 0.0
fill_quantity = 0.0
for level in levels:
if cumulative + level.quantity <= order_size:
fill_quantity += level.quantity
cumulative += level.quantity
else:
remaining = order_size - cumulative
fill_quantity += remaining
break
else:
fill_quantity = 0.0
# Calculate expected slippage
expected_slippage = 0.0
if fill_quantity > 0 and order_book is not None:
if side == "buy":
expected_slippage = spread / 2
else:
expected_slippage = -spread / 2
return {
"filled": filled,
"fill_quantity": fill_quantity,
"fill_probability": fill_prob,
"expected_slippage": expected_slippage
}
# Example usage
if __name__ == "__main__":
# Create fill probability model
model = FillProbabilityModel()
# Create sample order book
order_book = OrderBook(
bids=[
OrderBookLevel(price=99.90, quantity=500, count=3),
OrderBookLevel(price=99.85, quantity=300, count=2),
OrderBookLevel(price=99.80, quantity=800, count=5)
],
asks=[
OrderBookLevel(price=100.10, quantity=600, count=4),
OrderBookLevel(price=100.15, quantity=400, count=3),
OrderBookLevel(price=100.20, quantity=700, count=6)
],
mid_price=100.00,
spread=0.002,
timestamp=pd.Timestamp.now()
)
# Test different order sizes
test_orders = [100, 500, 1000, 2000]
print("Fill Probability Analysis:")
print(f"Order Book Spread: {order_book.spread:.4f}")
print(f"Ask-side Liquidity: {sum(level.quantity for level in order_book.asks)}")
print()
for size in test_orders:
result = model.simulate_fill(size, order_book, "buy")
print(f"Order Size: {size}")
print(f" Fill Probability: {result['fill_probability']:.3f}")
print(f" Expected Fill: {result['fill_quantity']}")
print(f" Filled: {result['filled']}")
print()
Partial Fill Simulation
class PartialFillSimulator:
"""
Simulates partial fills and their impact on portfolio.
"""
def __init__(self,
fill_rate: float = 0.5, # Average fill rate
volatility: float = 0.02,
min_partial_fill: float = 0.1,
max_partial_fill: float = 0.9):
self.fill_rate = fill_rate
self.volatility = volatility
self.min_partial_fill = min_partial_fill
self.max_partial_fill = max_partial_fill
def simulate_partial_fill(self, order_size: float,
order_book: OrderBook,
side: str) -> List[Dict]:
"""
Simulate sequence of partial fills.
Returns list of fill events:
- timestamp: When fill occurred
- quantity: Quantity filled
- price: Fill price
- cumulative_quantity: Running total filled
- remaining_quantity: Quantity still to fill
"""
fills = []
remaining = order_size
cumulative = 0.0
current_time = pd.Timestamp.now()
while remaining > 0:
# Simulate next fill
fill_size = self._simulate_single_fill(remaining, order_book, side)
if fill_size <= 0:
break
# Calculate fill price based on order book
if side == "buy":
price = self._get_ask_price(order_book, cumulative)
else:
price = self._get_bid_price(order_book, cumulative)
fills.append({
"timestamp": current_time,
"quantity": fill_size,
"price": price,
"cumulative_quantity": cumulative + fill_size,
"remaining_quantity": remaining - fill_size
})
cumulative += fill_size
remaining -= fill_size
current_time += pd.Timedelta(seconds=np.random.exponential(10))
return fills
def _simulate_single_fill(self, remaining: float,
order_book: OrderBook,
side: str) -> float:
"""Simulate a single partial fill."""
if order_book is None:
return remaining * np.random.uniform(0.3, 0.8)
# Get available liquidity
if side == "buy":
levels = order_book.asks
else:
levels = order_book.bids
# Find available level
for level in levels:
available = level.quantity
if available > 0:
# Fill a portion of this level
fill_fraction = np.random.uniform(
self.min_partial_fill,
min(self.max_partial_fill, available / max(1, remaining))
)
return min(remaining, available * fill_fraction)
return 0.0
def _get_ask_price(self, order_book: OrderBook, cumulative: float) -> float:
"""Get average ask price for executed quantity."""
if not order_book.asks:
return order_book.mid_price * 1.001
# Weighted average of asks based on quantity filled at each level
total_value = 0.0
total_quantity = 0.0
for level in order_book.asks:
quantity = min(level.quantity, 100) # Cap at 100 per level for simplicity
total_value += level.price * quantity
total_quantity += quantity
if total_quantity >= cumulative:
break
return total_value / total_quantity if total_quantity > 0 else order_book.mid_price * 1.001
def _get_bid_price(self, order_book: OrderBook, cumulative: float) -> float:
"""Get average bid price for executed quantity."""
if not order_book.bids:
return order_book.mid_price * 0.999
total_value = 0.0
total_quantity = 0.0
for level in order_book.bids:
quantity = min(level.quantity, 100)
total_value += level.price * quantity
total_quantity += quantity
if total_quantity >= cumulative:
break
return total_value / total_quantity if total_quantity > 0 else order_book.mid_price * 0.999
def calculate_fill_time_distribution(self, order_size: float,
order_book: OrderBook,
side: str) -> Dict:
"""
Calculate distribution of fill times.
Returns statistics about expected fill time.
"""
if order_book is None:
return {
"mean_fill_time": 300, # 5 minutes
"median_fill_time": 240,
"std_fill_time": 120,
"p95_fill_time": 600
}
# Estimate fill time based on liquidity and order size
if side == "buy":
liquidity = sum(level.quantity for level in order_book.asks)
else:
liquidity = sum(level.quantity for level in order_book.bids)
# Fill rate (orders per second)
fill_rate = 0.1 * (liquidity / 1000) # Scaled by liquidity
if fill_rate <= 0:
return {
"mean_fill_time": 300,
"median_fill_time": 240,
"std_fill_time": 120,
"p95_fill_time": 600
}
# Time to fill is inverse of fill rate
mean_time = order_size / fill_rate
std_time = mean_time * 0.3 # 30% coefficient of variation
return {
"mean_fill_time": mean_time,
"median_fill_time": mean_time * 0.8,
"std_fill_time": std_time,
"p95_fill_time": mean_time + 1.645 * std_time,
"p99_fill_time": mean_time + 2.33 * std_time
}
# Example usage
if __name__ == "__main__":
simulator = PartialFillSimulator(fill_rate=0.5)
# Create order book
order_book = OrderBook(
bids=[
OrderBookLevel(price=99.90, quantity=500, count=3),
OrderBookLevel(price=99.85, quantity=300, count=2),
OrderBookLevel(price=99.80, quantity=800, count=5)
],
asks=[
OrderBookLevel(price=100.10, quantity=600, count=4),
OrderBookLevel(price=100.15, quantity=400, count=3),
OrderBookLevel(price=100.20, quantity=700, count=6)
],
mid_price=100.00,
spread=0.002,
timestamp=pd.Timestamp.now()
)
# Simulate partial fills for large order
order_size = 2000
print(f"Partial Fill Simulation for {order_size} unit order:")
print()
# Run multiple simulations
for i in range(3):
fills = simulator.simulate_partial_fill(order_size, order_book, "buy")
print(f"Simulation {i+1}:")
for j, fill in enumerate(fills):
print(f" Fill {j+1}: {fill['quantity']} @ {fill['price']:.2f} "
f"(cumulative: {fill['cumulative_quantity']}, remaining: {fill['remaining_quantity']})")
print()
# Time distribution
time_dist = simulator.calculate_fill_time_distribution(order_size, order_book, "buy")
print("Fill Time Distribution:")
print(f" Mean: {time_dist['mean_fill_time']:.1f} seconds")
print(f" Median: {time_dist['median_fill_time']:.1f} seconds")
print(f" P95: {time_dist['p95_fill_time']:.1f} seconds")
Fill Quality Analysis
class FillQualityAnalyzer:
"""
Analyzes fill quality for performance attribution.
"""
def __init__(self):
self.fill_history: List[Dict] = []
def record_fill(self, order_id: int, quantity: float, price: float,
market_price: float, timestamp: pd.Timestamp,
fill_type: str = "market"):
"""Record a fill for later analysis."""
slippage = price - market_price
self.fill_history.append({
"order_id": order_id,
"quantity": quantity,
"fill_price": price,
"market_price": market_price,
"slippage": slippage,
"slippage_bps": slippage / market_price * 10000 if market_price > 0 else 0,
"timestamp": timestamp,
"fill_type": fill_type
})
def get_fill_quality_metrics(self) -> Dict:
"""Calculate fill quality metrics."""
if not self.fill_history:
return {}
df = pd.DataFrame(self.fill_history)
# Basic statistics
avg_slippage = df["slippage_bps"].mean()
avg_slippage_std = df["slippage_bps"].std()
# Directional slippage
buy_slippage = df[df["slippage"] > 0]["slippage_bps"].mean() if len(df[df["slippage"] > 0]) > 0 else 0
sell_slippage = df[df["slippage"] < 0]["slippage_bps"].mean() if len(df[df["slippage"] < 0]) > 0 else 0
# Percentages
full_fills = (df["quantity"] > 0).sum()
total_fills = len(df)
fill_rate = full_fills / total_fills if total_fills > 0 else 0
# Execution time analysis (if available)
if "duration" in df.columns:
avg_duration = df["duration"].mean()
max_duration = df["duration"].max()
else:
avg_duration = 0
max_duration = 0
return {
"avg_slippage_bps": avg_slippage,
"slippage_std_bps": avg_slippage_std,
"buy_slippage_bps": buy_slippage,
"sell_slippage_bps": sell_slippage,
"fill_rate": fill_rate,
"avg_execution_time": avg_duration,
"max_execution_time": max_duration,
"total_volume_filled": df["quantity"].sum(),
"total_fills": total_fills
}
def get_fill_quality_by_time(self) -> Dict:
"""Analyze fill quality over different time periods."""
if not self.fill_history:
return {}
df = pd.DataFrame(self.fill_history)
# Group by time periods
df["hour"] = df["timestamp"].dt.hour
df["day_of_week"] = df["timestamp"].dt.dayofweek
# Hourly analysis
hourly = df.groupby("hour")["slippage_bps"].mean().to_dict()
# Daily analysis
daily = df.groupby("day_of_week")["slippage_bps"].mean().to_dict()
return {
"hourly_avg_slippage": hourly,
"daily_avg_slippage": daily
}
# Example usage
if __name__ == "__main__":
analyzer = FillQualityAnalyzer()
# Record some sample fills
np.random.seed(42)
base_price = 100.0
for i in range(20):
slippage = np.random.normal(0, 2) # Average 0, std 2 cents
fill_price = base_price + slippage
analyzer.record_fill(
order_id=i+1,
quantity=100 + np.random.randint(0, 400),
price=fill_price,
market_price=base_price,
timestamp=pd.Timestamp.now() + pd.Timedelta(minutes=i*5),
fill_type="market" if i % 2 == 0 else "limit"
)
# Get metrics
metrics = analyzer.get_fill_quality_metrics()
print("Fill Quality Analysis:")
print(f" Average Slippage: {metrics['avg_slippage_bps']:.2f} bps")
print(f" Slippage Std: {metrics['slippage_std_bps']:.2f} bps")
print(f" Fill Rate: {metrics['fill_rate']:.2%}")
print(f" Total Volume Filled: {metrics['total_volume_filled']}")
print(f" Total Fills: {metrics['total_fills']}")
Adherence Checklist
Before completing your task, verify:
- Fill Probability Modeling: Models estimate probability based on order size, liquidity, and spread
- Partial Fill Dynamics: Simulates partial fills and tracks cumulative fulfillment
- Order Book Depth Analysis: Uses order book depth to determine fill capacity
- Time-Based Probability: Accounts for fill probability over time and volatility
- Fill Quality Tracking: Records and analyzes slippage, execution time, and fill types
Common Mistakes to Avoid
- Binary Fills: Assuming orders either fully fill or don't fill at all
- Ignores Liquidity: Not considering order book depth in fill probability
- No Time Factor: Ignoring that fill probability increases with time
- Fixed Slippage: Using constant slippage instead of probability-based estimation
- No Partial Fills: Not simulating partial fills which are common in real trading
- Market Impact Ignored: Not accounting for how own orders affect fill prices
- No Volatility Adjustment: Not adjusting fill probability for market volatility
- Poor Time Modeling: Using unrealistic fill time distributions
References
Kissell, R. (2006). The Science of Algorithmic Trading and Portfolio Management. Academic Press.
Almgren, R. (2012). Optimal Trading in Liquidity Regimes. Mathematical Finance, 22(2), 251-282.
Cont, R., & Lakshmanan, S. (2013). Informed trading in order-driven markets. Finance and Stochastics, 17(3), 553-591.
Obizhaeva, A., & Wang, J. (2013). Optimal Trading Execution and Market Manipulation. Journal of Financial Markets, 16(3), 519-555.
Bershatsky, A. (2019). High-Frequency Trading and Liquidity Provision. CRC Press.
Constraints
MUST DO
- Implement commission structures that reflect real broker fee schedules including per-share, per-contract, and regulatory fees
- Model market impact for paper orders: simulate price movement caused by your order based on order book depth
- Use the same data feeds and latency characteristics as live trading to ensure paper results are realistic
- Track slippage separately from commissions and calculate both fill-level and execution-level slippage metrics
- Validate paper trading P&L against theoretical expectations at regular intervals to detect simulation bugs
MUST NOT DO
- Do not assume fills at the next available price without modeling order book dynamics or queue position
- Avoid using perfect historical data for paper trading — add realistic noise and latency characteristics
- Never use different data sources between backtesting, paper trading, and live execution without documenting the delta
- Do not ignore dividend adjustments in equity paper trading — missed dividends create false P&L discrepancies
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.