Hedging¶

qufin provides classical and quantum hedging strategies for derivatives risk management.

Delta Hedging¶

The simplest hedging strategy: maintain a position in the underlying that offsets the option's delta.

from qufin.hedging.delta import DeltaHedger
from qufin.options.classical.black_scholes import bs_greeks

# Hedge a short call position
hedger = DeltaHedger(rebalance_freq="daily")
greeks = bs_greeks(s=100, k=105, sigma=0.2, r=0.05, T=1.0)
hedge_ratio = greeks["delta"]  # Buy this many shares per option sold

Discrete Delta Hedging Backtest¶

import numpy as np
from qufin.hedging.delta import delta_hedge_backtest
from qufin.data.synthetic import gbm_paths

# Simulate underlying price paths
paths = gbm_paths(s0=100, mu=0.08, sigma=0.2, T=1.0, n_steps=252, n_paths=1000)

# Backtest delta hedging with transaction costs
results = delta_hedge_backtest(
    paths=paths,
    strike=105,
    sigma=0.2,
    r=0.05,
    T=1.0,
    rebalance_freq=1,  # daily
    tx_cost=0.001,     # 10 bps per trade
)
print(f"Mean P&L: {results['mean_pnl']:.4f}")
print(f"P&L Std:  {results['std_pnl']:.4f}")

Deep Hedging¶

Neural network-based hedging that learns optimal strategies directly from data, accounting for transaction costs and market frictions.

Requires PyTorch

Install with pip install "qufin[ml]" to enable deep hedging.

from qufin.hedging.deep_hedging import DeepHedger

hedger = DeepHedger(
    n_layers=3,
    hidden_dim=64,
    n_steps=30,        # hedging steps
    tx_cost=0.001,
    risk_measure="cvar",  # optimize for CVaR of P&L
    alpha=0.95,
)

# Train on simulated paths
hedger.fit(paths_train, strikes=[100, 105, 110], epochs=200)

# Evaluate
pnl = hedger.evaluate(paths_test, strike=105)
print(f"CVaR(95%): {np.percentile(pnl, 5):.4f}")

Quantum Deep Hedging¶

Replaces the classical neural network with a variational quantum circuit (VQC) as the policy network. Research has shown VQC-based hedging can match classical performance with fewer trainable parameters.

from qufin.hedging.quantum_deep_hedging import QuantumDeepHedger
from qufin.backends.qiskit_backend import QiskitAerBackend

backend = QiskitAerBackend(shots=1024)
hedger = QuantumDeepHedger(
    n_qubits=4,
    n_layers=3,
    backend=backend,
    tx_cost=0.001,
)

hedger.fit(paths_train, strike=105, epochs=100)

RL-Quantum Hedging¶

Reinforcement learning agent with a quantum policy network for dynamic hedging decisions.

from qufin.hedging.rl_quantum import QuantumRLHedger

agent = QuantumRLHedger(
    n_qubits=4,
    n_layers=2,
    learning_rate=0.001,
    gamma=0.99,         # discount factor
    risk_aversion=0.5,
)

# Train with PPO
agent.train(env="heston", n_episodes=5000, n_steps=252)

Comparison¶

Strategy	Strengths	Limitations
Delta hedging	Simple, model-based, no training	Assumes BS dynamics, ignores tx costs
Deep hedging	Learns from data, handles frictions	Requires training data, black box
Quantum deep hedging	Fewer parameters, potential speedup	NISQ noise, limited qubits
RL-quantum hedging	Adaptive, handles complex dynamics	Training instability, sample inefficient