Hedging Error vs Rebalancing Frequency¶

Background¶

hedging_error_rebalancing.py

This module implements Hedging Error vs Rebalancing Frequency.

Author: Financial Math Library

Code¶

```python

-- coding: utf-8 --¶

""" hedging_error_rebalancing.py

This module implements Hedging Error vs Rebalancing Frequency.

Author: Financial Math Library """

import numpy as np import matplotlib.pyplot as plt

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

def hedging_error_rebalancing(): """ Hedging Error vs Rebalancing Frequency.

This function demonstrates the key concepts and computational techniques
for hedging error vs rebalancing frequency.

Returns
-------
dict
    Results containing computed values and visualization data.
"""
# Implementation of Hedging Error vs Rebalancing Frequency
print(f"Computing Hedging Error vs Rebalancing Frequency...")

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

# Core computation logic
results = {
    "time_points": time_points,
    "description": "Hedging Error vs Rebalancing Frequency"
}

return results

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

# 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("Hedging Error vs Rebalancing Frequency")
ax.grid(True, alpha=0.3)

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

return results

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

Exercises¶

Exercise 1. Plot (conceptually) the hedging error standard deviation versus \(1/\sqrt{N}\) where \(N\) is the number of rebalancing steps. What slope do you expect?

Exercise 2. For \(N = 10, 50, 250, 1000\) rebalancing steps, the hedging error std ratios should be approximately \(1 : 1/\sqrt{5} : 1/5 : 1/10\). Verify this scaling.

Exercise 3. Explain the economic tradeoff between rebalancing frequency and transaction costs. What is the optimal rebalancing frequency?

Exercise 4. If transaction costs are \(c = 0.1\%\) per trade and the option has \(\Gamma = 0.02\), \(S = 100\), \(\sigma = 0.2\), \(T = 1\), estimate the optimal number of rebalancing steps.