Yield Curve Bootstrapping¶

Background¶

yield_curve_bootstrapping.py

This module implements Yield Curve Bootstrapping.

Author: Financial Math Library

Code¶

```python

-- coding: utf-8 --¶

""" yield_curve_bootstrapping.py

This module implements Yield Curve Bootstrapping.

Author: Financial Math Library """

import numpy as np import matplotlib.pyplot as plt

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

def yield_curve_bootstrapping(): """ Yield Curve Bootstrapping.

This function demonstrates the key concepts and computational techniques
for yield curve bootstrapping.

Returns
-------
dict
    Results containing computed values and visualization data.
"""
# Implementation of Yield Curve Bootstrapping
print(f"Computing Yield Curve Bootstrapping...")

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

# Core computation logic
results = {
    "time_points": time_points,
    "description": "Yield Curve Bootstrapping"
}

return results

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

# 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("Yield Curve Bootstrapping")
ax.grid(True, alpha=0.3)

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

return results

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

Exercises¶

Exercise 1. Yield curve bootstrapping sequentially extracts discount factors from market instruments. Given a 1-year zero rate of \(3\%\) and a 2-year par swap rate of \(3.5\%\), compute the 2-year discount factor.

Exercise 2. Explain why bootstrapping proceeds sequentially from shorter to longer maturities and why the order matters.

Exercise 3. After bootstrapping, the zero rates at maturities 1, 2, 3, 5 are \(\{3.0\%, 3.5\%, 3.8\%, 4.2\%\}\). Compute the 1-year forward rate from year 2 to year 3.

Exercise 4. Describe two common issues that arise in yield curve bootstrapping and how they are typically addressed.