Volatility Misspecification Impact¶

Background¶

volatility_misspecification_impact.py

This module implements Volatility Misspecification Impact.

Author: Financial Math Library

Code¶

```python

-- coding: utf-8 --¶

""" volatility_misspecification_impact.py

This module implements Volatility Misspecification Impact.

Author: Financial Math Library """

import numpy as np import matplotlib.pyplot as plt

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

def volatility_misspecification_impact(): """ Volatility Misspecification Impact.

This function demonstrates the key concepts and computational techniques
for volatility misspecification impact.

Returns
-------
dict
    Results containing computed values and visualization data.
"""
# Implementation of Volatility Misspecification Impact
print(f"Computing Volatility Misspecification Impact...")

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

# Core computation logic
results = {
    "time_points": time_points,
    "description": "Volatility Misspecification Impact"
}

return results

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

# 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("Volatility Misspecification Impact")
ax.grid(True, alpha=0.3)

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

return results

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

Exercises¶

Exercise 1. If the true volatility is \(\sigma_{\text{true}} = 0.25\) but you hedge using \(\sigma_{\text{hedge}} = 0.20\), is the hedging P&L biased? In which direction?

Exercise 2. Derive the instantaneous hedging P&L when the hedge volatility differs from the realized volatility.

Exercise 3. If \(\sigma_{\text{true}} = 0.3\) and \(\sigma_{\text{hedge}} = 0.2\), compute the expected annual P&L per unit gamma for \(S = 100\).

Exercise 4. Explain why selling options at high implied volatility and hedging at realized volatility is a common strategy, and what risks remain.