Value-at-Risk Computation (Historical, Parametric, Monte Carlo)¶

Background¶

var_computation_methods.py

This module implements VaR Computation Methods.

Author: Financial Math Library

Code¶

```python

-- coding: utf-8 --¶

""" var_computation_methods.py

This module implements VaR Computation Methods.

Author: Financial Math Library """

import numpy as np import matplotlib.pyplot as plt

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

def var_computation_methods(): """ VaR Computation Methods.

This function demonstrates the key concepts and computational techniques
for var computation methods.

Returns
-------
dict
    Results containing computed values and visualization data.
"""
# Implementation of VaR Computation Methods
print(f"Computing VaR Computation Methods...")

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

# Core computation logic
results = {
    "time_points": time_points,
    "description": "VaR Computation Methods"
}

return results

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

# 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("VaR Computation Methods")
ax.grid(True, alpha=0.3)

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

return results

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

Exercises¶

Exercise 1. Compare the three main VaR computation methods: historical simulation, parametric (variance-covariance), and Monte Carlo simulation. Summarize the key assumption and computational cost of each.

Exercise 2. For a portfolio of two assets with weights \(w_1 = 0.6\), \(w_2 = 0.4\), individual VaRs of $1M and $1.5M, and correlation \(\rho = 0.5\), compute the parametric portfolio VaR at \(99\%\) confidence.

Exercise 3. Explain why the parametric method underestimates VaR for portfolios with options or other nonlinear instruments.

Exercise 4. A risk manager computes VaR using all three methods and obtains: historical $3.2M, parametric $2.5M, Monte Carlo $3.0M. Discuss possible reasons for the discrepancies and which estimate to trust.