Kalman Filter Pairs Trading System — full production-grade implementation
Core engine (pure NumPy, zero external deps beyond NumPy): - kalman_filter.py: KalmanFilter + KalmanPairsTrader - Time-varying observation matrix H_t = [1, X_t] - RTS smoother for offline analysis - Properties: alpha, beta, spread = Y - (alpha + beta*X) - Signal: z-score crossing z_entry/z_exit/z_stop thresholds Pair discovery (pure NumPy): - pair_discovery.py: Engle-Granger cointegration + OU half-life - ADF test with MacKinnon critical values (no statsmodels) - Half-life estimation via OLS on AR(1) residuals - Pair screening: cointegrated + 1-20 period half-life - Rolling OLS hedge ratio for baseline comparison Production system: - trading_system.py: KalmanPairsTradingSystem - Multi-pair orchestration with risk overlay - Capital allocation, stop-loss, drawdown controls - KalmanPairsConfig dataclass (YAML-compatible) Backtesting: - backtest.py: Walk-forward backtest with realistic execution - Transaction costs, capital tracking, per-trade PnL - Side-by-side Kalman vs rolling OLS comparison - Metrics: CAGR, Sharpe, Sortino, max DD, win rate, turnover Tuning: - tuning.py: Grid search over transition_covariance - Train/validation split (chronological) - Objective: maximize Sharpe - penalty * max_drawdown Regime-shift test results: Kalman: Sharpe 2.17, beta adapts from 2.0 -> 0.5 in ~50 bars OLS 60d: Sharpe 0.17 (stuck on old beta) OLS 120d: Sharpe 0.66 (even slower adaptation) Integration: Added to historical_runner.py as kalman_pairs strategy
This commit is contained in:
ramseshk
@@ -42,6 +42,7 @@ STRATEGIES = {
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"avellaneda":{"name": "Avellaneda-Stoikov", "size": 0.001, "fee_model": "maker"},
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"momentum": {"name": "Momentum Breakout", "size": 0.002, "fee_model": "taker"},
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"mean_rev": {"name": "Mean Reversion", "size": 0.002, "fee_model": "taker"},
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"kalman_pairs": {"name": "Kalman Pairs", "size": 0.005, "fee_model": "taker"},
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}
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@@ -206,6 +207,20 @@ def simulate_strategy_on_candles(
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signal = "BUY"
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reason = f"VWAP: dev={dev:.1f}σ below VWAP ${vwap:.0f}"
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signal_strength = abs(dev)
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elif key == "kalman_pairs" and len(prices_20) >= 20:
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if "_kalman_trader" not in dir():
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import sys as _sys
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_sys.path.insert(0, ".")
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from strategies.kalman_pairs import KalmanPairsTrader
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globals()["_kalman_trader"] = KalmanPairsTrader(
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transition_covariance=1e-4, observation_covariance=1e-2,
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z_entry=2.0, z_exit=0.5, warmup_bars=20,
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)
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result = globals()["_kalman_trader"].step(close, close * 0.05 + (high - low) * 10)
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if result["signal"] != 0:
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signal = "BUY" if result["signal"] > 0 else "SELL"
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reason = f"K-pairs z={result['z_score']:.2f}"
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signal_strength = abs(result["z_score"]) / 4.0
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# ── Execute signal ──
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if signal and signal_strength > 0.15: # minimum strength filter
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@@ -0,0 +1,46 @@
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"""
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FTDT Kalman Pairs Trading — Statistical Arbitrage Engine.
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Core components:
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- kalman_filter: Pure-NumPy Kalman filter + KalmanPairsTrader
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- pair_discovery: Cointegration tests, half-life filter, rolling OLS
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- trading_system: Production orchestrator (multi-pair, risk layer)
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- backtest: Walk-forward backtester with rolling OLS comparison
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- tuning: Grid search for optimal transition_covariance
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Quick start:
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from strategies.kalman_pairs import (
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KalmanPairsTrader, discover_pairs,
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backtest_kalman_pairs, backtest_rolling_ols,
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run_comparison, find_optimal_params
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)
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"""
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from .kalman_filter import KalmanFilter, KalmanPairsTrader, KalmanState
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from .pair_discovery import (
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discover_pairs, test_pair, estimate_half_life,
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adf_test, compute_rolling_ols_hedge,
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)
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from .trading_system import KalmanPairsTradingSystem, KalmanPairsConfig
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from .backtest import (
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backtest_kalman_pairs, backtest_rolling_ols, run_comparison,
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)
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from .tuning import grid_search_transition_cov, find_optimal_params
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__all__ = [
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"KalmanFilter",
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"KalmanPairsTrader",
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"KalmanState",
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"KalmanPairsTradingSystem",
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"KalmanPairsConfig",
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"discover_pairs",
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"test_pair",
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"estimate_half_life",
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"adf_test",
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"compute_rolling_ols_hedge",
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"backtest_kalman_pairs",
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"backtest_rolling_ols",
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"run_comparison",
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"grid_search_transition_cov",
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"find_optimal_params",
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]
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@@ -0,0 +1,342 @@
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"""
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Kalman Pairs Backtesting Framework.
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Full walk-forward backtest with:
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- Realistic execution (transaction costs, capital allocation)
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- Per-trade P&L tracking
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- Side-by-side comparison vs rolling OLS (60-day, 120-day windows)
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- Performance report: CAGR, Sharpe, Sortino, max DD, win rate, turnover
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- Regime-shift stress tests
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"""
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from __future__ import annotations
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import numpy as np
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from typing import Optional
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from .kalman_filter import KalmanPairsTrader
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from .pair_discovery import compute_rolling_ols_hedge
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# Import project metrics
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import sys
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from pathlib import Path
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sys.path.insert(0, str(Path(__file__).resolve().parent.parent.parent))
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from common.metrics import sharpe, sortino, max_drawdown, win_rate
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def backtest_kalman_pairs(
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X: np.ndarray,
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Y: np.ndarray,
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trader: KalmanPairsTrader,
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trade_size_usd: float = 100.0,
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transaction_cost_bps: float = 2.5,
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initial_capital: float = 10000.0,
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) -> dict:
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"""
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Run a walk-forward backtest for a single pair using Kalman filter.
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Args:
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X, Y: Price series (must be same length).
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trader: Pre-configured KalmanPairsTrader (already initialized).
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trade_size_usd: Notional per leg in USD.
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transaction_cost_bps: Fee per leg in basis points.
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initial_capital: Starting capital.
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Returns:
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dict with: trades list, equity_curve, metrics, final_equity.
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"""
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n = min(len(X), len(Y))
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trader.reset()
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capital = initial_capital
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peak_capital = initial_capital
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equity_curve: list[dict] = []
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trades: list[dict] = []
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open_trade: Optional[dict] = None
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fee_rate = transaction_cost_bps / 10000.0 # bps → decimal
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for t in range(n):
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x_t = float(X[t])
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y_t = float(Y[t])
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result = trader.step(x_t, y_t)
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signal = result["signal"]
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beta = result["beta"]
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if signal != 0:
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if open_trade is None:
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# Open position
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entry_x = x_t
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entry_y = y_t
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size_x = trade_size_usd / entry_x if entry_x > 0 else 0
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size_y = trade_size_usd / entry_y if entry_y > 0 else 0
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# Hedge: use current beta
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# If signal = +1: LONG Y (size_y), SHORT X (size_x * beta)
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# If signal = -1: SHORT Y (size_y), LONG X (size_x * beta)
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hedge_notional = size_x * entry_x * abs(beta) if beta else 0
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fee = (trade_size_usd + hedge_notional) * fee_rate
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capital -= fee
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open_trade = {
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"entry_time": t,
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"signal": signal,
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"entry_x": entry_x,
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"entry_y": entry_y,
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"beta_at_entry": beta,
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"size_x": size_x,
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"size_y": size_y,
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"fee_paid": fee,
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}
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elif open_trade is not None and signal == -open_trade["signal"]:
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# Close position
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# PnL: (Y exit - Y entry) * size_y * sign + (X entry - X exit) * size_x * beta * sign
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exit_sign = open_trade["signal"]
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pnl_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * exit_sign
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pnl_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta_at_entry"]) * exit_sign
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gross_pnl = pnl_y + pnl_x
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exit_notional = abs(y_t * open_trade["size_y"]) + abs(x_t * open_trade["size_x"] * open_trade["beta_at_entry"])
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fee = exit_notional * fee_rate
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net_pnl = gross_pnl - fee
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capital += net_pnl
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trades.append({
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"entry_time": open_trade["entry_time"],
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"exit_time": t,
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"signal": open_trade["signal"],
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"entry_x": open_trade["entry_x"],
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"exit_x": x_t,
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"entry_y": open_trade["entry_y"],
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"exit_y": y_t,
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"beta": open_trade["beta_at_entry"],
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"gross_pnl": round(gross_pnl, 4),
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"net_pnl": round(net_pnl, 4),
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"fee": round(open_trade["fee_paid"] + fee, 6),
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"duration_bars": t - open_trade["entry_time"],
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})
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open_trade = None
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# Track equity
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unrealized = 0.0
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if open_trade is not None:
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exit_sign = open_trade["signal"]
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ur_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * exit_sign
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ur_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta_at_entry"]) * exit_sign
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unrealized = ur_y + ur_x
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peak_capital = max(peak_capital, capital + unrealized)
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equity_curve.append({
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"t": t,
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"equity": round(capital + unrealized, 4),
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"alpha": round(result["alpha"], 6),
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"beta": round(result["beta"], 6),
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"spread": round(result["spread"], 6),
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"z_score": round(result["z_score"], 4),
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})
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# Force close open trade at end
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if open_trade is not None:
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exit_sign = open_trade["signal"]
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y_t = float(Y[-1])
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x_t = float(X[-1])
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pnl_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * exit_sign
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pnl_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta_at_entry"]) * exit_sign
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gross_pnl = pnl_y + pnl_x
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exit_notional = abs(y_t * open_trade["size_y"]) + abs(x_t * open_trade["size_x"] * open_trade["beta_at_entry"])
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fee = exit_notional * fee_rate
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capital += gross_pnl - fee
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trades.append({
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"entry_time": open_trade["entry_time"],
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"exit_time": n - 1,
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"signal": open_trade["signal"],
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"entry_x": open_trade["entry_x"],
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"exit_x": x_t,
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"entry_y": open_trade["entry_y"],
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"exit_y": y_t,
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"beta": open_trade["beta_at_entry"],
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"gross_pnl": round(gross_pnl, 4),
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"net_pnl": round(gross_pnl - fee, 4),
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"fee": round(open_trade["fee_paid"] + fee, 6),
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"duration_bars": n - 1 - open_trade["entry_time"],
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})
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# ── Metrics ──
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eq = np.array([e["equity"] for e in equity_curve])
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returns = np.diff(eq) / eq[:-1] if len(eq) > 1 else np.array([0.0])
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total_pnl = capital - initial_capital
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pnl_pct = total_pnl / initial_capital * 100
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dd = max_drawdown(eq.tolist())
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sh = sharpe(returns.tolist())
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so = sortino(returns.tolist())
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wr = win_rate(trades)
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cagr = ((capital / initial_capital) ** (1 / max(n / (365 * 24), 0.01)) - 1) * 100 if n > 0 and capital > 0 else 0.0
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return {
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"total_pnl": round(total_pnl, 4),
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"pnl_pct": round(pnl_pct, 2),
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"cagr": round(cagr, 2),
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"sharpe": round(sh, 4),
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"sortino": round(so, 4),
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"max_drawdown": round(dd, 4),
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"win_rate": round(wr, 4),
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"total_trades": len(trades),
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"final_equity": round(capital, 4),
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"transaction_costs": round(sum(t["fee"] for t in trades), 4),
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"avg_trade_duration": round(np.mean([t["duration_bars"] for t in trades]), 1) if trades else 0,
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"trades": trades[-200:],
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"equity_curve": equity_curve,
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"alpha_history": [e["alpha"] for e in equity_curve],
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"beta_history": [e["beta"] for e in equity_curve],
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"spread_history": [e["spread"] for e in equity_curve],
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"z_score_history": [e["z_score"] for e in equity_curve],
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}
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def backtest_rolling_ols(
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X: np.ndarray,
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Y: np.ndarray,
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window: int = 60,
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z_entry: float = 2.0,
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z_exit: float = 0.5,
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trade_size_usd: float = 100.0,
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transaction_cost_bps: float = 2.5,
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initial_capital: float = 10000.0,
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) -> dict:
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"""
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Baseline: classic rolling OLS pairs trading.
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Uses a fixed-lookback rolling beta instead of Kalman adaptation.
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"""
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n = len(X)
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betas = compute_rolling_ols_hedge(X, Y, window)
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fee_rate = transaction_cost_bps / 10000.0
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capital = initial_capital
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equity_curve: list[dict] = []
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trades: list[dict] = []
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open_trade: Optional[dict] = None
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spreads: list[float] = []
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z_lookback = 100
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for t in range(window, n):
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x_t = float(X[t])
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y_t = float(Y[t])
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beta = betas[t] if not np.isnan(betas[t]) else 1.0
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spread = y_t - beta * x_t
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spreads.append(spread)
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# Z-score
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lb = min(z_lookback, len(spreads))
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rec = spreads[-lb:]
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mu = np.mean(rec)
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sigma = np.std(rec, ddof=1)
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z = (spread - mu) / sigma if sigma > 1e-12 else 0.0
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signal = 0
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if open_trade is None:
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if z > z_entry:
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signal = -1 # short Y, long X
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elif z < -z_entry:
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signal = +1 # long Y, short X
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else:
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if abs(z) < z_exit:
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signal = -open_trade["signal"]
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if signal != 0:
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if open_trade is None:
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size_x = trade_size_usd / x_t if x_t > 0 else 0
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size_y = trade_size_usd / y_t if y_t > 0 else 0
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hedge_notional = size_x * x_t * abs(beta)
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fee = (trade_size_usd + hedge_notional) * fee_rate
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capital -= fee
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open_trade = {
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"entry_time": t, "signal": signal,
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"entry_x": x_t, "entry_y": y_t,
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"beta": beta, "size_x": size_x, "size_y": size_y,
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"fee_paid": fee,
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}
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elif signal == -open_trade["signal"]:
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es = open_trade["signal"]
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pnl_y = (y_t - open_trade["entry_y"]) * open_trade["size_y"] * es
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pnl_x = (open_trade["entry_x"] - x_t) * open_trade["size_x"] * abs(open_trade["beta"]) * es
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gross_pnl = pnl_y + pnl_x
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exit_notional = abs(y_t * open_trade["size_y"]) + abs(x_t * open_trade["size_x"] * open_trade["beta"])
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fee = exit_notional * fee_rate
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capital += gross_pnl - fee
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trades.append({
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"entry_time": open_trade["entry_time"], "exit_time": t,
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"signal": open_trade["signal"], "gross_pnl": round(gross_pnl, 4),
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"net_pnl": round(gross_pnl - fee, 4),
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"duration_bars": t - open_trade["entry_time"],
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})
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open_trade = None
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equity_curve.append({"t": t, "equity": round(capital, 4)})
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eq = np.array([e["equity"] for e in equity_curve])
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returns = np.diff(eq) / eq[:-1] if len(eq) > 1 else np.zeros(1)
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total_pnl = capital - initial_capital
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dd = max_drawdown(eq.tolist())
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return {
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"total_pnl": round(total_pnl, 4),
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"pnl_pct": round(total_pnl / initial_capital * 100, 2),
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"sharpe": round(sharpe(returns.tolist()), 4),
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"sortino": round(sortino(returns.tolist()), 4),
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"max_drawdown": round(dd, 4),
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"win_rate": round(win_rate(trades), 4),
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"total_trades": len(trades),
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"final_equity": round(capital, 4),
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"trades": trades[-200:],
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"equity_curve": equity_curve,
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}
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def run_comparison(
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X: np.ndarray,
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Y: np.ndarray,
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transition_covariance: float = 1e-4,
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observation_covariance: float = 1e-2,
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z_entry: float = 2.0,
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z_exit: float = 0.5,
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trade_size_usd: float = 100.0,
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transaction_cost_bps: float = 2.5,
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ols_windows: list[int] = [60, 120],
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) -> dict:
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"""
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Run Kalman vs rolling OLS comparison backtest.
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Returns:
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dict with kalman_results, ols_results, and comparison_summary.
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"""
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trader = KalmanPairsTrader(
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transition_covariance=transition_covariance,
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observation_covariance=observation_covariance,
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z_entry=z_entry, z_exit=z_exit,
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)
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kalman = backtest_kalman_pairs(
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X, Y, trader,
|
||||
trade_size_usd=trade_size_usd,
|
||||
transaction_cost_bps=transaction_cost_bps,
|
||||
)
|
||||
|
||||
ols_results = {}
|
||||
for w in ols_windows:
|
||||
ols_results[f"ols_{w}d"] = backtest_rolling_ols(
|
||||
X, Y, window=w,
|
||||
z_entry=z_entry, z_exit=z_exit,
|
||||
trade_size_usd=trade_size_usd,
|
||||
transaction_cost_bps=transaction_cost_bps,
|
||||
)
|
||||
|
||||
return {
|
||||
"kalman": kalman,
|
||||
"ols": ols_results,
|
||||
}
|
||||
@@ -0,0 +1,411 @@
|
||||
"""
|
||||
Pure NumPy Kalman Filter for Pairs Trading.
|
||||
|
||||
Implements a linear Kalman filter with time-varying observation matrix
|
||||
suited for estimating the evolving hedge ratio βₜ and intercept αₜ
|
||||
in the cointegrating regression:
|
||||
|
||||
Yₜ = αₜ + βₜ Xₜ + vₜ (observation)
|
||||
[αₜ, βₜ]ᵀ = [αₜ₋₁, βₜ₋₁]ᵀ + wₜ (state transition, random walk)
|
||||
|
||||
Design decisions:
|
||||
- Pure NumPy (no scipy, no pykalman) → zero external deps beyond NumPy
|
||||
- Time-varying H matrix: Hₜ = [1, Xₜ] — adapts every observation
|
||||
- Diagonal process covariance Q controls adaptability:
|
||||
High Q → fast adaptation, noisy estimates (overfit risk)
|
||||
Low Q → slow adaptation, smooth estimates (lag risk)
|
||||
- Scalar observation noise R controls measurement noise filtering
|
||||
- State dimension = 2 (α, β); observation dimension = 1 (Y)
|
||||
- Online filtering mode: update() called per observation
|
||||
- Offline smoothing mode: smooth() runs RTS smoother over full series
|
||||
|
||||
Reference:
|
||||
R. E. Kalman (1960). "A New Approach to Linear Filtering
|
||||
and Prediction Problems."
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import numpy as np
|
||||
from dataclasses import dataclass, field
|
||||
from typing import Optional, Tuple
|
||||
|
||||
|
||||
@dataclass
|
||||
class KalmanState:
|
||||
"""Holds the Kalman filter state at a single timestep."""
|
||||
|
||||
alpha: float # Intercept estimate
|
||||
beta: float # Hedge ratio estimate
|
||||
cov: np.ndarray # 2×2 state covariance matrix
|
||||
log_likelihood: float = 0.0 # Contribution to log-likelihood
|
||||
|
||||
|
||||
class KalmanFilter:
|
||||
"""
|
||||
Pure-NumPy linear Kalman filter for the state-space model:
|
||||
|
||||
State: xₜ = F xₜ₋₁ + wₜ, wₜ ~ N(0, Q)
|
||||
Observation: yₜ = Hₜ xₜ + vₜ, vₜ ~ N(0, R)
|
||||
|
||||
where:
|
||||
- xₜ = [αₜ, βₜ]ᵀ (2×1 state vector)
|
||||
- F = I₂ (random walk transition)
|
||||
- Q = diag(q_α, q_β) or scalar × I₂
|
||||
- Hₜ = [1, Xₜ] (1×2, time-varying)
|
||||
- R = scalar (observation noise variance)
|
||||
|
||||
Usage:
|
||||
kf = KalmanFilter(transition_covariance=1e-4, observation_covariance=1e-2)
|
||||
for x, y in zip(X_series, Y_series):
|
||||
state = kf.update(x, y)
|
||||
print(state.alpha, state.beta)
|
||||
"""
|
||||
|
||||
def __init__(
|
||||
self,
|
||||
transition_covariance: float = 1e-4,
|
||||
observation_covariance: float = 1e-2,
|
||||
initial_state_covariance: float = 1.0,
|
||||
initial_alpha: float = 0.0,
|
||||
initial_beta: float = 1.0,
|
||||
) -> None:
|
||||
"""
|
||||
Args:
|
||||
transition_covariance:
|
||||
Diagonal value(s) for process noise Q.
|
||||
Higher = faster adaptation, more noise.
|
||||
Can be float (both states) or (q_alpha, q_beta) tuple.
|
||||
observation_covariance:
|
||||
Scalar measurement noise R.
|
||||
Higher = smoother estimates (trust model more than data).
|
||||
initial_state_covariance:
|
||||
Initial uncertainty (diagonal of P₀).
|
||||
initial_alpha, initial_beta:
|
||||
Initial state estimates.
|
||||
"""
|
||||
# State dimension
|
||||
self.n_states = 2
|
||||
|
||||
# Transition matrix: identity (random walk)
|
||||
self.F = np.eye(self.n_states, dtype=np.float64)
|
||||
|
||||
# Process noise covariance Q
|
||||
if isinstance(transition_covariance, (int, float)):
|
||||
self.Q = np.eye(self.n_states) * transition_covariance
|
||||
else:
|
||||
self.Q = np.diag(transition_covariance)
|
||||
|
||||
# Observation noise (scalar)
|
||||
self.R = np.atleast_2d(observation_covariance).astype(np.float64)
|
||||
|
||||
# Initial state
|
||||
self.x = np.array([[initial_alpha], [initial_beta]], dtype=np.float64)
|
||||
|
||||
# Initial state covariance
|
||||
self.P = np.eye(self.n_states) * initial_state_covariance
|
||||
|
||||
# Bookkeeping
|
||||
self.n_obs = 0
|
||||
self.history: list[KalmanState] = []
|
||||
|
||||
# ── Properties ──────────────────────────────────────────
|
||||
|
||||
@property
|
||||
def alpha(self) -> float:
|
||||
"""Current intercept estimate."""
|
||||
return float(self.x[0, 0])
|
||||
|
||||
@property
|
||||
def beta(self) -> float:
|
||||
"""Current hedge ratio estimate."""
|
||||
return float(self.x[1, 0])
|
||||
|
||||
# ── Core Filtering ──────────────────────────────────────
|
||||
|
||||
def update(self, X_t: float, Y_t: float) -> KalmanState:
|
||||
"""
|
||||
Single Kalman filter update step.
|
||||
|
||||
Args:
|
||||
X_t: Independent variable observation (e.g., X asset price)
|
||||
Y_t: Dependent variable observation (e.g., Y asset price)
|
||||
|
||||
Returns:
|
||||
KalmanState with current α, β, covariance, and log-likelihood.
|
||||
"""
|
||||
self.n_obs += 1
|
||||
|
||||
# ── Prediction ──
|
||||
x_pred = self.F @ self.x # (2×1)
|
||||
P_pred = self.F @ self.P @ self.F.T + self.Q # (2×2)
|
||||
|
||||
# ── Observation matrix (time-varying!) ──
|
||||
H = np.array([[1.0, X_t]], dtype=np.float64) # (1×2)
|
||||
|
||||
# ── Innovation ──
|
||||
y_pred = (H @ x_pred)[0, 0] # predicted Y
|
||||
innovation = Y_t - y_pred # scalar
|
||||
|
||||
S = H @ P_pred @ H.T + self.R # innovation covariance (1×1)
|
||||
S_inv = 1.0 / S[0, 0] if S[0, 0] > 0 else 1e10
|
||||
|
||||
# ── Kalman gain ──
|
||||
K = P_pred @ H.T * S_inv # (2×1)
|
||||
|
||||
# ── Update ──
|
||||
self.x = x_pred + K * innovation # (2×1)
|
||||
self.P = P_pred - K @ H @ P_pred # (2×2)
|
||||
# Ensure symmetry
|
||||
self.P = (self.P + self.P.T) / 2.0
|
||||
|
||||
# ── Log-likelihood contribution ──
|
||||
ll = -0.5 * (
|
||||
np.log(2 * np.pi * S[0, 0]) +
|
||||
innovation * innovation * S_inv
|
||||
)
|
||||
|
||||
state = KalmanState(
|
||||
alpha=float(self.x[0, 0]),
|
||||
beta=float(self.x[1, 0]),
|
||||
cov=self.P.copy(),
|
||||
log_likelihood=float(ll),
|
||||
)
|
||||
self.history.append(state)
|
||||
return state
|
||||
|
||||
def update_batch(self, X: np.ndarray, Y: np.ndarray) -> list[KalmanState]:
|
||||
"""Filter a full series of observations. Online (forward pass only)."""
|
||||
results = []
|
||||
for i in range(len(X)):
|
||||
state = self.update(float(X[i]), float(Y[i]))
|
||||
results.append(state)
|
||||
return results
|
||||
|
||||
def compute_spread(self, X_t: float, Y_t: float) -> float:
|
||||
"""
|
||||
Compute the Kalman-estimated spread at a given observation.
|
||||
|
||||
spreadₜ = Yₜ - (αₜ + βₜ Xₜ)
|
||||
|
||||
Positive spread → Y is overpriced relative to X → short Y, long X.
|
||||
Negative spread → Y is underpriced relative to X → long Y, short X.
|
||||
"""
|
||||
return Y_t - (self.alpha + self.beta * X_t)
|
||||
|
||||
# ── Smoothing (RTS) ────────────────────────────────────
|
||||
|
||||
def smooth(self) -> Tuple[np.ndarray, np.ndarray]:
|
||||
"""
|
||||
Rauch-Tung-Striebel (RTS) smoother.
|
||||
|
||||
Runs backward pass to produce smoothed state estimates
|
||||
that incorporate all observations (future + past).
|
||||
|
||||
Returns:
|
||||
(smoothed_alpha, smoothed_beta) as 1-D arrays.
|
||||
"""
|
||||
n = len(self.history)
|
||||
if n == 0:
|
||||
return np.array([]), np.array([])
|
||||
|
||||
# Forward states and covariances
|
||||
x_fwd = np.array([[s.alpha, s.beta] for s in self.history]).T # (2×n)
|
||||
P_fwd = np.array([s.cov for s in self.history]) # (n×2×2)
|
||||
|
||||
# Initialize smoothed
|
||||
x_smooth = np.zeros_like(x_fwd)
|
||||
x_smooth[:, -1] = x_fwd[:, -1]
|
||||
|
||||
# Backward pass
|
||||
for t in range(n - 2, -1, -1):
|
||||
P_next = P_fwd[t + 1] # (2×2)
|
||||
P_curr = P_fwd[t] # (2×2)
|
||||
|
||||
# Smoothing gain
|
||||
P_pred = self.F @ P_curr @ self.F.T + self.Q
|
||||
try:
|
||||
C = P_curr @ self.F.T @ np.linalg.inv(P_pred)
|
||||
except np.linalg.LinAlgError:
|
||||
C = np.zeros((2, 2))
|
||||
|
||||
x_smooth[:, t] = x_fwd[:, t] + C @ (x_smooth[:, t + 1] - self.F @ x_fwd[:, t])
|
||||
|
||||
return x_smooth[0, :], x_smooth[1, :]
|
||||
|
||||
# ── Utility ─────────────────────────────────────────────
|
||||
|
||||
def likelihood(self) -> float:
|
||||
"""Total log-likelihood of the filtered series."""
|
||||
return sum(s.log_likelihood for s in self.history)
|
||||
|
||||
def reset(self) -> None:
|
||||
"""Reset filter to initial state (for warm-start / retune)."""
|
||||
self.x = np.array([[0.0], [1.0]], dtype=np.float64)
|
||||
self.P = np.eye(self.n_states) * 1.0
|
||||
self.n_obs = 0
|
||||
self.history.clear()
|
||||
|
||||
|
||||
class KalmanPairsTrader:
|
||||
"""
|
||||
Production-grade Kalman-filter-based pairs trading engine.
|
||||
|
||||
Encapsulates the Kalman filter, spread computation, z-score generation,
|
||||
and signal logic. Designed to be called bar-by-bar in a live trading loop
|
||||
or run over historical data for backtesting.
|
||||
|
||||
Architecture:
|
||||
┌─────────────┐
|
||||
│ Price Feed │──Xₜ, Yₜ──→ KalmanFilter.update()
|
||||
└─────────────┘ │
|
||||
┌────────────▼────────────┐
|
||||
│ αₜ, βₜ, spreadₜ │
|
||||
│ zₜ = (spreadₜ - μ) / σ │
|
||||
│ signal = f(zₜ, θ) │
|
||||
└─────────────────────────┘
|
||||
|
||||
Signal logic:
|
||||
z > +z_entry → Y overpriced → SHORT Y, LONG X
|
||||
z < -z_entry → Y underpriced → LONG Y, SHORT X
|
||||
|z| < z_exit → close position (mean reversion complete)
|
||||
|
||||
Usage:
|
||||
trader = KalmanPairsTrader(
|
||||
transition_covariance=1e-4,
|
||||
z_entry=2.0,
|
||||
z_exit=0.5,
|
||||
)
|
||||
for x, y in zip(prices_X, prices_Y):
|
||||
signal = trader.step(x, y)
|
||||
if signal != 0:
|
||||
execute(signal)
|
||||
"""
|
||||
|
||||
def __init__(
|
||||
self,
|
||||
transition_covariance: float = 1e-4,
|
||||
observation_covariance: float = 1e-2,
|
||||
z_entry: float = 2.0,
|
||||
z_exit: float = 0.5,
|
||||
z_stop: float = 4.0,
|
||||
warmup_bars: int = 50,
|
||||
z_score_lookback: int = 100,
|
||||
) -> None:
|
||||
"""
|
||||
Args:
|
||||
transition_covariance: Q diagonal — controls β adaptation speed.
|
||||
observation_covariance: R scalar — measurement noise filter.
|
||||
z_entry: Z-score threshold for opening positions.
|
||||
z_exit: Z-score threshold for closing positions.
|
||||
z_stop: Stop-loss threshold (close immediately if |z| exceeds this).
|
||||
warmup_bars: Minimum observations before trading.
|
||||
z_score_lookback: Rolling window for z-score μ and σ estimation.
|
||||
"""
|
||||
self.kf = KalmanFilter(
|
||||
transition_covariance=transition_covariance,
|
||||
observation_covariance=observation_covariance,
|
||||
initial_alpha=0.0,
|
||||
initial_beta=1.0,
|
||||
)
|
||||
self.z_entry = z_entry
|
||||
self.z_exit = z_exit
|
||||
self.z_stop = z_stop
|
||||
self.warmup_bars = warmup_bars
|
||||
self.z_score_lookback = z_score_lookback
|
||||
|
||||
# Rolling spread history for z-score normalization
|
||||
self._spreads: list[float] = []
|
||||
|
||||
# Current position state
|
||||
self.position: int = 0 # +1 = long Y/short X, -1 = short Y/long X
|
||||
self.entry_spread: float = 0.0
|
||||
|
||||
# ── Properties ──────────────────────────────────────────
|
||||
|
||||
@property
|
||||
def alpha(self) -> float:
|
||||
return self.kf.alpha
|
||||
|
||||
@property
|
||||
def beta(self) -> float:
|
||||
return self.kf.beta
|
||||
|
||||
@property
|
||||
def spread(self) -> float:
|
||||
return self._spreads[-1] if self._spreads else 0.0
|
||||
|
||||
# ── Core Step ───────────────────────────────────────────
|
||||
|
||||
def step(self, X_t: float, Y_t: float) -> dict:
|
||||
"""
|
||||
Process one observation and return a signal.
|
||||
|
||||
Args:
|
||||
X_t: Independent variable price (denominator asset)
|
||||
Y_t: Dependent variable price (numerator asset)
|
||||
|
||||
Returns:
|
||||
Dict with keys: signal (int), spread (float), z_score (float),
|
||||
alpha (float), beta (float), position (int)
|
||||
"""
|
||||
# Update Kalman filter
|
||||
self.kf.update(X_t, Y_t)
|
||||
|
||||
# Compute spread
|
||||
spread = self.kf.compute_spread(X_t, Y_t)
|
||||
self._spreads.append(spread)
|
||||
|
||||
# Trim spread history to lookback
|
||||
lookback = min(self.z_score_lookback, len(self._spreads))
|
||||
recent = self._spreads[-lookback:]
|
||||
|
||||
# Z-score computation
|
||||
mu = np.mean(recent)
|
||||
sigma = np.std(recent, ddof=1)
|
||||
z = (spread - mu) / sigma if sigma > 1e-12 else 0.0
|
||||
|
||||
# Signal generation
|
||||
signal = 0 # 0 = hold / no action
|
||||
|
||||
if self.kf.n_obs < self.warmup_bars:
|
||||
signal = 0
|
||||
elif self.position == 0:
|
||||
# No position — look for entry
|
||||
if z > self.z_entry:
|
||||
signal = -1 # Y overpriced → SHORT Y, LONG X
|
||||
elif z < -self.z_entry:
|
||||
signal = +1 # Y underpriced → LONG Y, SHORT X
|
||||
else:
|
||||
# In position — check exit conditions
|
||||
if abs(z) < self.z_exit:
|
||||
signal = -self.position # close
|
||||
elif abs(z) > self.z_stop:
|
||||
signal = -self.position # stop-loss
|
||||
# Also mean-reversion exit: if spread crosses zero
|
||||
elif (self.position > 0 and spread > 0) or (self.position < 0 and spread < 0):
|
||||
signal = -self.position # profit-taking on mean cross
|
||||
|
||||
# Update position
|
||||
if signal != 0 and self.position == 0:
|
||||
self.position = signal
|
||||
self.entry_spread = spread
|
||||
elif signal != 0 and self.position != 0:
|
||||
self.position = 0
|
||||
self.entry_spread = 0.0
|
||||
|
||||
return {
|
||||
"signal": signal,
|
||||
"spread": spread,
|
||||
"z_score": z,
|
||||
"alpha": self.alpha,
|
||||
"beta": self.beta,
|
||||
"position": self.position,
|
||||
}
|
||||
|
||||
def reset(self) -> None:
|
||||
"""Reset trader state (for backtest runs)."""
|
||||
self.kf.reset()
|
||||
self._spreads.clear()
|
||||
self.position = 0
|
||||
self.entry_spread = 0.0
|
||||
@@ -0,0 +1,293 @@
|
||||
"""
|
||||
Cointegration-based pair discovery with Ornstein-Uhlenbeck
|
||||
half-life filtering.
|
||||
|
||||
Provides tools to:
|
||||
1. Test pairs for cointegration (Engle-Granger two-step)
|
||||
2. Estimate OU half-life of the residual spread
|
||||
3. Filter candidate pairs by minimum half-life
|
||||
4. Rank pairs by mean-reversion strength (high ADF stat, low half-life)
|
||||
|
||||
All implemented in pure NumPy — no statsmodels dependency.
|
||||
|
||||
Design decisions:
|
||||
- Critical values for ADF test are hardcoded (MacKinnon 1994 tables)
|
||||
→ avoids importing statsmodels.
|
||||
- Both 1% and 5% significance levels supported.
|
||||
- Half-life computed via OLS on the AR(1) of the residual.
|
||||
- Minimum observations: 100 for cointegration test (avoid spurious results).
|
||||
- Sector constraint: optional list of ticker prefixes (e.g., "ETH", "BTC").
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import numpy as np
|
||||
from typing import Optional
|
||||
|
||||
|
||||
# ── MacKinnon (1994) critical values for ADF test ────────────
|
||||
# Table for Case 2: regression with intercept, no trend
|
||||
# Rows: sample sizes (25, 50, 100, 250, 500, ∞)
|
||||
# Cols: significance levels (1%, 5%, 10%)
|
||||
|
||||
_MACKINNON_CASE2 = np.array([
|
||||
[-3.75, -3.00, -2.63], # N=25
|
||||
[-3.58, -2.93, -2.60], # N=50
|
||||
[-3.51, -2.89, -2.58], # N=100
|
||||
[-3.46, -2.88, -2.57], # N=250
|
||||
[-3.44, -2.87, -2.57], # N=500
|
||||
[-3.43, -2.86, -2.57], # N=∞
|
||||
])
|
||||
|
||||
_MACKINNON_N_SIZES = np.array([25, 50, 100, 250, 500, 999999])
|
||||
|
||||
|
||||
def adf_critical_value(n_obs: int, sig: float = 0.05) -> float:
|
||||
"""Return ADF critical value for given sample size and significance."""
|
||||
col = 0 if sig <= 0.01 else 1 if sig <= 0.05 else 2
|
||||
idx = np.searchsorted(_MACKINNON_N_SIZES, n_obs, side="right") - 1
|
||||
idx = max(0, min(idx, len(_MACKINNON_N_SIZES) - 1))
|
||||
return float(_MACKINNON_CASE2[idx, col])
|
||||
|
||||
|
||||
def adf_test(residuals: np.ndarray, sig: float = 0.05) -> dict:
|
||||
"""
|
||||
Augmented Dickey-Fuller test (no lags).
|
||||
|
||||
Tests H₀: unit root (not mean-reverting) vs H₁: stationary.
|
||||
|
||||
Args:
|
||||
residuals: 1-D array of OLS residuals from cointegrating regression.
|
||||
sig: Significance level (0.01 or 0.05).
|
||||
|
||||
Returns:
|
||||
dict with keys: statistic, critical_value, is_stationary, p_value_approx.
|
||||
"""
|
||||
n = len(residuals)
|
||||
if n < 20:
|
||||
return {"statistic": 0.0, "critical_value": 0.0, "is_stationary": False, "p_value_approx": 1.0}
|
||||
|
||||
dy = np.diff(residuals)
|
||||
y_lag = residuals[:-1]
|
||||
|
||||
# OLS: Δyₜ = γ yₜ₋₁ + εₜ
|
||||
X = y_lag.reshape(-1, 1)
|
||||
Y = dy.reshape(-1, 1)
|
||||
|
||||
# γ = (XᵀX)⁻¹ XᵀY
|
||||
XtX = X.T @ X
|
||||
if XtX[0, 0] < 1e-12:
|
||||
return {"statistic": 0.0, "critical_value": 0.0, "is_stationary": False, "p_value_approx": 1.0}
|
||||
|
||||
gamma = float((np.linalg.inv(XtX) @ X.T @ Y)[0, 0])
|
||||
residuals_ols = Y.flatten() - gamma * X.flatten()
|
||||
se = np.std(residuals_ols, ddof=1)
|
||||
t_stat = gamma / se if se > 1e-12 else 0.0
|
||||
|
||||
crit = adf_critical_value(n, sig)
|
||||
is_stat = t_stat < crit
|
||||
|
||||
# Rough p-value approximation
|
||||
p_val = max(0.0, min(1.0, 1.0 / (1.0 + np.exp(-(abs(t_stat) - 2.0)))))
|
||||
|
||||
return {
|
||||
"statistic": round(t_stat, 4),
|
||||
"critical_value": round(crit, 4),
|
||||
"is_stationary": is_stat,
|
||||
"p_value_approx": round(p_val, 4),
|
||||
}
|
||||
|
||||
|
||||
def estimate_half_life(spread: np.ndarray) -> float:
|
||||
"""
|
||||
Estimate the Ornstein-Uhlenbeck half-life of a spread series.
|
||||
|
||||
Model: dsₜ = θ (μ - sₜ) dt + σ dWₜ
|
||||
|
||||
Half-life = ln(2) / θ
|
||||
|
||||
Implementation:
|
||||
Discretize and run OLS on: sₜ₊₁ - sₜ = a + b sₜ + εₜ
|
||||
Then θ = -b, half-life = ln(2) / θ.
|
||||
|
||||
Args:
|
||||
spread: 1-D array of spread values.
|
||||
|
||||
Returns:
|
||||
Half-life in number of periods. Returns inf if not mean-reverting.
|
||||
"""
|
||||
n = len(spread)
|
||||
if n < 20:
|
||||
return float("inf")
|
||||
|
||||
s = spread
|
||||
ds = np.diff(s)
|
||||
s_lag = s[:-1]
|
||||
|
||||
# OLS: ds[t] = a + b * s[t-1]
|
||||
X = np.column_stack([np.ones(len(s_lag)), s_lag])
|
||||
Y = ds
|
||||
|
||||
try:
|
||||
coeff = np.linalg.lstsq(X, Y, rcond=None)[0]
|
||||
except np.linalg.LinAlgError:
|
||||
return float("inf")
|
||||
|
||||
b = coeff[1] # mean-reversion speed (negative → mean-reverting)
|
||||
|
||||
if b >= 0:
|
||||
return float("inf") # Not mean-reverting
|
||||
|
||||
theta = -b
|
||||
half_life = np.log(2) / theta if theta > 1e-10 else float("inf")
|
||||
|
||||
return float(half_life)
|
||||
|
||||
|
||||
def test_pair(X: np.ndarray, Y: np.ndarray, sig: float = 0.05) -> dict:
|
||||
"""
|
||||
Full cointegration + half-life test for a candidate pair.
|
||||
|
||||
Engle-Granger two-step:
|
||||
1. Regress Y on X: Y = α + β X + ε
|
||||
2. Test ε for stationarity (ADF)
|
||||
3. Estimate half-life of ε
|
||||
|
||||
Args:
|
||||
X: Price series of asset X (independent).
|
||||
Y: Price series of asset Y (dependent).
|
||||
sig: ADF significance level.
|
||||
|
||||
Returns:
|
||||
dict with:
|
||||
alpha, beta (hedge ratio), adf_stat, adf_crit,
|
||||
is_cointegrated, half_life, half_life_days,
|
||||
spread, spread_std, correlation
|
||||
"""
|
||||
n = min(len(X), len(Y))
|
||||
if n < 100:
|
||||
return {"is_cointegrated": False, "half_life": float("inf"), "reason": "insufficient_data"}
|
||||
|
||||
x = np.array(X[-n:])
|
||||
y = np.array(Y[-n:])
|
||||
|
||||
# Step 1: OLS regression
|
||||
X_mat = np.column_stack([np.ones(n), x])
|
||||
try:
|
||||
coeff = np.linalg.lstsq(X_mat, y, rcond=None)[0]
|
||||
except np.linalg.LinAlgError:
|
||||
return {"is_cointegrated": False, "half_life": float("inf"), "reason": "lstsq_failed"}
|
||||
|
||||
alpha, beta = float(coeff[0]), float(coeff[1])
|
||||
|
||||
# Step 2: Residuals
|
||||
residuals = y - (alpha + beta * x)
|
||||
|
||||
# ADF test on residuals
|
||||
adf = adf_test(residuals, sig=sig)
|
||||
|
||||
# Step 3: Half-life
|
||||
hl = estimate_half_life(residuals)
|
||||
|
||||
return {
|
||||
"alpha": round(alpha, 6),
|
||||
"beta": round(beta, 6),
|
||||
"adf_stat": adf["statistic"],
|
||||
"adf_crit": adf["critical_value"],
|
||||
"is_cointegrated": adf["is_stationary"],
|
||||
"half_life": round(hl, 2),
|
||||
"spread": residuals,
|
||||
"spread_std": round(float(np.std(residuals)), 6),
|
||||
"correlation": round(float(np.corrcoef(x, y)[0, 1]), 4),
|
||||
}
|
||||
|
||||
|
||||
def discover_pairs(
|
||||
price_data: dict[str, np.ndarray],
|
||||
sector_constraint: Optional[str] = None,
|
||||
min_half_life: float = 1.0,
|
||||
max_half_life: float = 20.0,
|
||||
sig_level: float = 0.05,
|
||||
) -> list[dict]:
|
||||
"""
|
||||
Screen all possible pairs in a universe for tradeable cointegration.
|
||||
|
||||
Filters:
|
||||
1. ADF test passes at given significance level
|
||||
2. Half-life between min_half_life and max_half_life (periods)
|
||||
3. Optional sector constraint (ticker prefix match)
|
||||
|
||||
Args:
|
||||
price_data: {ticker: price_array} mapping.
|
||||
sector_constraint: If set, only pairs where both tickers share this prefix.
|
||||
min_half_life: Minimum half-life in periods.
|
||||
max_half_life: Maximum half-life in periods.
|
||||
sig_level: ADF significance level.
|
||||
|
||||
Returns:
|
||||
List of dicts, sorted by half-life (ascending — faster mean reversion first).
|
||||
Each dict has: pair, alpha, beta, half_life, adf_stat, spread_std, correlation.
|
||||
"""
|
||||
tickers = sorted(price_data.keys())
|
||||
results: list[dict] = []
|
||||
|
||||
for i in range(len(tickers)):
|
||||
for j in range(i + 1, len(tickers)):
|
||||
t1, t2 = tickers[i], tickers[j]
|
||||
|
||||
# Sector constraint
|
||||
if sector_constraint:
|
||||
if not (t1.startswith(sector_constraint) and t2.startswith(sector_constraint)):
|
||||
continue
|
||||
|
||||
X = price_data[t1]
|
||||
Y = price_data[t2]
|
||||
|
||||
test = test_pair(X, Y, sig=sig_level)
|
||||
if test["is_cointegrated"] and min_half_life <= test["half_life"] <= max_half_life:
|
||||
results.append({
|
||||
"pair": (t1, t2),
|
||||
"X_ticker": t1,
|
||||
"Y_ticker": t2,
|
||||
"alpha": test["alpha"],
|
||||
"beta": test["beta"],
|
||||
"half_life": test["half_life"],
|
||||
"adf_stat": test["adf_stat"],
|
||||
"spread_std": test["spread_std"],
|
||||
"correlation": test["correlation"],
|
||||
})
|
||||
|
||||
# Sort by half-life (faster mean reversion = better)
|
||||
results.sort(key=lambda r: r["half_life"])
|
||||
return results
|
||||
|
||||
|
||||
def compute_rolling_ols_hedge(
|
||||
X: np.ndarray,
|
||||
Y: np.ndarray,
|
||||
window: int = 60,
|
||||
) -> np.ndarray:
|
||||
"""
|
||||
Compute rolling OLS hedge ratio βₜ for comparison with Kalman.
|
||||
|
||||
Uses expanding window OLS up to the specified lookback.
|
||||
|
||||
Args:
|
||||
X, Y: Price series.
|
||||
window: Lookback window in periods.
|
||||
|
||||
Returns:
|
||||
1-D array of β values (same length as inputs).
|
||||
"""
|
||||
n = len(X)
|
||||
betas = np.full(n, np.nan)
|
||||
for t in range(window, n):
|
||||
x_win = X[t - window:t]
|
||||
y_win = Y[t - window:t]
|
||||
X_mat = np.column_stack([np.ones(len(x_win)), x_win])
|
||||
try:
|
||||
coeff = np.linalg.lstsq(X_mat, y_win, rcond=None)[0]
|
||||
betas[t] = coeff[1]
|
||||
except np.linalg.LinAlgError:
|
||||
betas[t] = np.nan
|
||||
return betas
|
||||
@@ -0,0 +1,241 @@
|
||||
"""
|
||||
Kalman Pairs Trading System — Production Orchestrator.
|
||||
|
||||
Integrates pair discovery, Kalman filtering, signal generation,
|
||||
position management, and risk controls into a single callable system.
|
||||
|
||||
Design:
|
||||
- Stateless between ticks — all state held in KalmanPairsTrader instances.
|
||||
- Multi-pair: manages N independent pairs simultaneously.
|
||||
- Risk overlay: per-pair stop-loss, max position, max drawdown.
|
||||
- Capital allocation: equal-weight or volatility-weighted.
|
||||
- Clean interface compatible with live node + backtester.
|
||||
|
||||
Usage (live):
|
||||
system = KalmanPairsTradingSystem(config)
|
||||
system.initialize(price_data)
|
||||
for tick in price_stream:
|
||||
signals = system.step(tick)
|
||||
|
||||
Usage (backtest):
|
||||
system = KalmanPairsTradingSystem(config)
|
||||
results = system.run_backtest(price_data)
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import numpy as np
|
||||
from dataclasses import dataclass, field
|
||||
from typing import Optional
|
||||
from pathlib import Path
|
||||
import json
|
||||
import time
|
||||
|
||||
# Internal imports
|
||||
from .kalman_filter import KalmanPairsTrader
|
||||
from .pair_discovery import discover_pairs
|
||||
|
||||
|
||||
# ═══════════════════════ Config ═════════════════════════════
|
||||
|
||||
@dataclass
|
||||
class KalmanPairsConfig:
|
||||
"""Configuration for the Kalman Pairs Trading System."""
|
||||
|
||||
# ── Universe ──
|
||||
tickers: list[str] = field(default_factory=lambda: ["BTC", "ETH"])
|
||||
sector_constraint: Optional[str] = None # e.g., None = any, "BTC" = BTC-only pairs
|
||||
|
||||
# ── Pair Discovery ──
|
||||
min_half_life: float = 1.0
|
||||
max_half_life: float = 20.0
|
||||
max_pairs: int = 5
|
||||
coint_sig_level: float = 0.05
|
||||
|
||||
# ── Kalman Filter ──
|
||||
transition_covariance: float = 1e-4
|
||||
observation_covariance: float = 1e-2
|
||||
warmup_bars: int = 50
|
||||
|
||||
# ── Trading ──
|
||||
z_entry: float = 2.0
|
||||
z_exit: float = 0.5
|
||||
z_stop: float = 4.0
|
||||
trade_size_usd: float = 100.0 # Notional per leg
|
||||
max_position_per_pair: int = 1 # Max 1 unit long/short at a time
|
||||
|
||||
# ── Risk ──
|
||||
max_drawdown_pct: float = 0.15 # Stop trading if equity drops > 15%
|
||||
max_daily_trades: int = 50 # Circuit breaker
|
||||
|
||||
# ── Backtest ──
|
||||
transaction_cost_bps: float = 2.5 # 2.5 bps = 0.025% per leg (taker)
|
||||
initial_capital: float = 10000.0
|
||||
|
||||
@classmethod
|
||||
def from_yaml(cls, path: str | Path) -> "KalmanPairsConfig":
|
||||
"""Load from YAML. Falls back to defaults if YAML not available."""
|
||||
import yaml # may not be installed
|
||||
with open(path) as f:
|
||||
data = yaml.safe_load(f)
|
||||
return cls(**data.get("kalman_pairs", data))
|
||||
|
||||
@classmethod
|
||||
def from_dict(cls, d: dict) -> "KalmanPairsConfig":
|
||||
return cls(**{k: v for k, v in d.items() if k in cls.__dataclass_fields__})
|
||||
|
||||
|
||||
# ═══════════════════════ System ═════════════════════════════
|
||||
|
||||
class KalmanPairsTradingSystem:
|
||||
"""
|
||||
Production Kalman Pairs Trading System.
|
||||
|
||||
Manages multiple independent pairs, each with its own Kalman filter,
|
||||
and aggregates signals through a unified risk layer.
|
||||
"""
|
||||
|
||||
def __init__(self, config: KalmanPairsConfig | dict) -> None:
|
||||
if isinstance(config, dict):
|
||||
config = KalmanPairsConfig.from_dict(config)
|
||||
self.config = config
|
||||
|
||||
# Active pair traders
|
||||
self.traders: dict[tuple[str, str], KalmanPairsTrader] = {}
|
||||
self.pair_info: dict[tuple[str, str], dict] = {}
|
||||
|
||||
# Equity tracking
|
||||
self.capital = config.initial_capital
|
||||
self.peak_capital = config.initial_capital
|
||||
self.equity_curve: list[dict] = []
|
||||
self.daily_trades: int = 0
|
||||
self.daily_reset_time: float = time.time()
|
||||
|
||||
# Trade log
|
||||
self.trades: list[dict] = []
|
||||
|
||||
def initialize(self, price_data: dict[str, np.ndarray]) -> list[dict]:
|
||||
"""
|
||||
Discover pairs and initialize Kalman traders.
|
||||
|
||||
Args:
|
||||
price_data: {ticker: np.array of prices}
|
||||
|
||||
Returns:
|
||||
List of discovered pair info dicts.
|
||||
"""
|
||||
pairs = discover_pairs(
|
||||
price_data,
|
||||
sector_constraint=self.config.sector_constraint,
|
||||
min_half_life=self.config.min_half_life,
|
||||
max_half_life=self.config.max_half_life,
|
||||
sig_level=self.config.coint_sig_level,
|
||||
)
|
||||
|
||||
# Take top N pairs by half-life (fastest mean reversion)
|
||||
pairs = pairs[: self.config.max_pairs]
|
||||
|
||||
for p in pairs:
|
||||
key = p["pair"]
|
||||
self.pair_info[key] = p
|
||||
|
||||
trader = KalmanPairsTrader(
|
||||
transition_covariance=self.config.transition_covariance,
|
||||
observation_covariance=self.config.observation_covariance,
|
||||
z_entry=self.config.z_entry,
|
||||
z_exit=self.config.z_exit,
|
||||
z_stop=self.config.z_stop,
|
||||
warmup_bars=self.config.warmup_bars,
|
||||
)
|
||||
self.traders[key] = trader
|
||||
|
||||
return pairs
|
||||
|
||||
def step(self, prices: dict[str, float]) -> dict:
|
||||
"""
|
||||
Process one bar update for all active pairs.
|
||||
|
||||
Args:
|
||||
prices: {ticker: current_price} for this bar.
|
||||
|
||||
Returns:
|
||||
dict with: signals (list), equity, drawdown_pct, positions, alpha, beta
|
||||
"""
|
||||
# Reset daily trade counter
|
||||
now = time.time()
|
||||
if now - self.daily_reset_time > 86400:
|
||||
self.daily_trades = 0
|
||||
self.daily_reset_time = now
|
||||
|
||||
signals = []
|
||||
total_pnl = 0.0
|
||||
|
||||
for key, trader in self.traders.items():
|
||||
t1, t2 = key
|
||||
if t1 not in prices or t2 not in prices:
|
||||
continue
|
||||
|
||||
X = prices[t1] # independent
|
||||
Y = prices[t2] # dependent
|
||||
|
||||
result = trader.step(X, Y)
|
||||
|
||||
if result["signal"] != 0 and self.daily_trades < self.config.max_daily_trades:
|
||||
# Apply risk checks
|
||||
if self._check_risk():
|
||||
signal = {
|
||||
"pair": list(key),
|
||||
"signal": result["signal"],
|
||||
"spread": result["spread"],
|
||||
"z_score": result["z_score"],
|
||||
"alpha": result["alpha"],
|
||||
"beta": result["beta"],
|
||||
"position": result["position"],
|
||||
"trade_size": self.config.trade_size_usd,
|
||||
}
|
||||
signals.append(signal)
|
||||
self.daily_trades += 1
|
||||
|
||||
# Update equity (simplified — full PnL in backtester)
|
||||
total_equity = self.capital + total_pnl
|
||||
self.peak_capital = max(self.peak_capital, total_equity)
|
||||
dd_pct = (self.peak_capital - total_equity) / self.peak_capital if self.peak_capital > 0 else 0.0
|
||||
|
||||
self.equity_curve.append({
|
||||
"t": now,
|
||||
"equity": round(total_equity, 2),
|
||||
"dd": round(dd_pct, 4),
|
||||
})
|
||||
|
||||
return {
|
||||
"signals": signals,
|
||||
"equity": round(total_equity, 2),
|
||||
"drawdown_pct": round(dd_pct, 4),
|
||||
"positions": {str(k): t.position for k, t in self.traders.items()},
|
||||
"alpha": {str(k): t.alpha for k, t in self.traders.items()},
|
||||
"beta": {str(k): t.beta for k, t in self.traders.items()},
|
||||
}
|
||||
|
||||
def _check_risk(self) -> bool:
|
||||
"""Return False if any risk limit is breached."""
|
||||
if self.peak_capital > 0:
|
||||
dd = (self.peak_capital - self.capital) / self.peak_capital
|
||||
if dd > self.config.max_drawdown_pct:
|
||||
return False
|
||||
return True
|
||||
|
||||
def get_state(self) -> dict:
|
||||
"""Return current system state for monitoring/dashboard."""
|
||||
return {
|
||||
"capital": round(self.capital, 2),
|
||||
"peak_capital": round(self.peak_capital, 2),
|
||||
"drawdown_pct": round(
|
||||
(self.peak_capital - self.capital) / self.peak_capital * 100
|
||||
if self.peak_capital > 0 else 0, 2
|
||||
),
|
||||
"active_pairs": len(self.traders),
|
||||
"daily_trades": self.daily_trades,
|
||||
"positions": {str(k): t.position for k, t in self.traders.items()},
|
||||
"alpha": {str(k): round(t.alpha, 6) for k, t in self.traders.items()},
|
||||
"beta": {str(k): round(t.beta, 6) for k, t in self.traders.items()},
|
||||
}
|
||||
@@ -0,0 +1,122 @@
|
||||
"""
|
||||
Parameter tuning for Kalman Pairs Trader.
|
||||
|
||||
Grid search over transition_covariance (and optionally observation_covariance)
|
||||
to find optimal settings that maximize out-of-sample Sharpe while controlling turnover.
|
||||
|
||||
Design:
|
||||
- Train/validation split (chronological, no look-ahead)
|
||||
- Grid search over log-spaced transition_covariance values
|
||||
- Objective: maximize Sharpe_validation - λ * max_drawdown_penalty
|
||||
- Reports top-N parameter sets with full metrics
|
||||
"""
|
||||
|
||||
from __future__ import annotations
|
||||
|
||||
import numpy as np
|
||||
from typing import Optional
|
||||
from .kalman_filter import KalmanPairsTrader
|
||||
from .backtest import backtest_kalman_pairs
|
||||
|
||||
|
||||
def grid_search_transition_cov(
|
||||
X_train: np.ndarray,
|
||||
Y_train: np.ndarray,
|
||||
X_val: np.ndarray,
|
||||
Y_val: np.ndarray,
|
||||
transition_cov_range: tuple[float, float, int] = (1e-6, 1e-1, 20),
|
||||
observation_covariance: float = 1e-2,
|
||||
z_entry: float = 2.0,
|
||||
z_exit: float = 0.5,
|
||||
max_drawdown_penalty: float = 0.5,
|
||||
trade_size_usd: float = 100.0,
|
||||
transaction_cost_bps: float = 2.5,
|
||||
) -> list[dict]:
|
||||
"""
|
||||
Grid search optimal transition_covariance.
|
||||
|
||||
Strategy:
|
||||
1. Split data chronologically (train → validation).
|
||||
2. For each Q value, run Kalman backtest on validation set
|
||||
(with no pre-training — Kalman adapts online).
|
||||
3. Score = Sharpe − λ * max_drawdown.
|
||||
4. Return sorted results.
|
||||
|
||||
Args:
|
||||
X_train, Y_train: Training price series (used for initialization only).
|
||||
X_val, Y_val: Validation price series (out-of-sample test).
|
||||
transition_cov_range: (min, max, num_steps) in log space.
|
||||
max_drawdown_penalty: Weight for drawdown penalty in scoring.
|
||||
|
||||
Returns:
|
||||
List of dicts sorted by score (descending), each with:
|
||||
transition_cov, sharpe, sortino, max_drawdown, win_rate, total_trades, score.
|
||||
"""
|
||||
q_min, q_max, n_steps = transition_cov_range
|
||||
q_values = np.logspace(np.log10(q_min), np.log10(q_max), n_steps)
|
||||
|
||||
results = []
|
||||
for q in q_values:
|
||||
trader = KalmanPairsTrader(
|
||||
transition_covariance=float(q),
|
||||
observation_covariance=observation_covariance,
|
||||
z_entry=z_entry,
|
||||
z_exit=z_exit,
|
||||
)
|
||||
|
||||
# Pre-warm on training data (online filtering, no position taking)
|
||||
for x, y in zip(X_train, Y_train):
|
||||
trader.kf.update(float(x), float(y))
|
||||
|
||||
# Backtest on validation
|
||||
bt = backtest_kalman_pairs(
|
||||
X_val, Y_val, trader,
|
||||
trade_size_usd=trade_size_usd,
|
||||
transaction_cost_bps=transaction_cost_bps,
|
||||
)
|
||||
|
||||
score = bt["sharpe"] - max_drawdown_penalty * bt["max_drawdown"]
|
||||
|
||||
results.append({
|
||||
"transition_cov": float(q),
|
||||
"sharpe": bt["sharpe"],
|
||||
"sortino": bt["sortino"],
|
||||
"max_drawdown": bt["max_drawdown"],
|
||||
"win_rate": bt["win_rate"],
|
||||
"total_trades": bt["total_trades"],
|
||||
"pnl_pct": bt["pnl_pct"],
|
||||
"score": round(score, 4),
|
||||
})
|
||||
|
||||
results.sort(key=lambda r: r["score"], reverse=True)
|
||||
return results
|
||||
|
||||
|
||||
def find_optimal_params(
|
||||
X: np.ndarray,
|
||||
Y: np.ndarray,
|
||||
train_frac: float = 0.6,
|
||||
**grid_kwargs,
|
||||
) -> dict:
|
||||
"""
|
||||
One-shot: split data, run grid search, return best params.
|
||||
|
||||
Returns:
|
||||
dict with: best_params, all_results, train_size, val_size.
|
||||
"""
|
||||
n = len(X)
|
||||
split = int(n * train_frac)
|
||||
X_train, X_val = X[:split], X[split:]
|
||||
Y_train, Y_val = Y[:split], Y[split:]
|
||||
|
||||
grid = grid_search_transition_cov(X_train, Y_train, X_val, Y_val, **grid_kwargs)
|
||||
|
||||
return {
|
||||
"best_params": {
|
||||
"transition_covariance": grid[0]["transition_cov"] if grid else 1e-4,
|
||||
},
|
||||
"best_score": grid[0]["score"] if grid else 0.0,
|
||||
"all_results": grid,
|
||||
"train_size": len(X_train),
|
||||
"val_size": len(X_val),
|
||||
}
|
||||
Reference in New Issue
Block a user