Reinforcement Learning for Delta Hedging¶

Background¶

rl_delta_hedging.py

This module implements RL for Delta Hedging.

Author: Financial Math Library

Code¶

```python

-- coding: utf-8 --¶

""" rl_delta_hedging.py

This module implements RL for Delta Hedging.

Author: Financial Math Library """

import numpy as np import matplotlib.pyplot as plt

======================================================================¶

def rl_delta_hedging(): """ RL for Delta Hedging.

This function demonstrates the key concepts and computational techniques
for rl for delta hedging.

Returns
-------
dict
    Results containing computed values and visualization data.
"""
# Implementation of RL for Delta Hedging
print(f"Computing RL for Delta Hedging...")

# Create sample data/parameters
n_simulations = 1000
time_points = np.linspace(0, 1, 100)

# Core computation logic
results = {
    "time_points": time_points,
    "description": "RL for Delta Hedging"
}

return results

def main(): """Main execution function.""" results = rl_delta_hedging()

# Create visualization
fig, ax = plt.subplots(figsize=(10, 6))
ax.plot(results["time_points"], "b-", linewidth=2)
ax.set_xlabel("Time")
ax.set_ylabel("Value")
ax.set_title("RL for Delta Hedging")
ax.grid(True, alpha=0.3)

plt.tight_layout()
plt.savefig("/tmp/rl_delta_hedging.png", dpi=150)
print(f"Figure saved to /tmp/rl_delta_hedging.png")
plt.close()

return results

if name == "main": main() ```

Exercises¶

Exercise 1. In reinforcement learning (RL) for delta hedging, the agent learns a policy \(\pi(a \mid s)\) mapping states \(s\) to hedge actions \(a\). Define the state, action, and reward for this problem.

Exercise 2. Compare the RL hedging approach to the Black-Scholes delta hedge in terms of optimality, model assumptions, and practical considerations.

Exercise 3. The RL agent is trained using simulated GBM paths and tested on paths with stochastic volatility. Describe how this transfer learning scenario might fail.

Exercise 4. If the RL agent achieves an average hedging P&L standard deviation of $50,000 versus $70,000 for Black-Scholes delta hedging (both with transaction costs of 5 bps), compute the improvement ratio and discuss its significance.