Bootstrap Yield Curve

Category: Quantitative Finance
Status: ✅ Complete
Language: Python, Jupyter Notebook

Overview

Implementation of three classical methods for bootstrapping the yield curve from bond prices: linear interpolation, cubic spline interpolation, and Nelson-Siegel parameterization.

Problem Statement

Extracting zero-coupon bond prices from observed coupon-bearing bond prices is a fundamental task in fixed income:

• Market data contains only coupon bond prices
• Pricing derivatives requires a smooth zero-coupon curve
• Different interpolation methods yield different curves

Methodology

Methods Implemented

1. Linear Bootstrapping

   • Simplest approach: straight-line interpolation between points
   • Fast but not smooth

2. Cubic Spline Interpolation

   • Smooth piecewise cubic polynomials
   • Industry standard for curve building
   • Matches observed bond prices exactly

3. Nelson-Siegel Model

   • Parametric approach with economic interpretation
   • 4 parameters control curve shape
   • Smoother extrapolation

Data

• Historical Treasury bond prices
• Multiple maturities (3m to 30y)
• Real market data

Results

Method	Interpolation Error	Smoothness	Use Case
Linear	High	Low	Quick estimates
Cubic Spline	<1 bp	High	Production systems
Nelson-Siegel	<2 bp	High	Risk management

Technical Implementation

# Bootstrap yield curve
curve = YieldCurve(bonds_df, method='spline')
zero_prices = curve.bootstrap()
spot_rates = curve.spot_rates(maturities)

Files

• bootstrap_yield_curve.ipynb - Full analysis with plots
• yield_curve.py - Production implementation
• data/ - Sample bond data

Applications

• Bond Valuation: Price non-standard bonds using derived curve
• Derivative Pricing: Input for pricing swaps, swaptions, etc.
• Risk Management: Basis for DV01 and duration calculations
• Trading: Identify rich/cheap bonds relative to smooth curve

References

• Bloomberg Curve Building Framework
• QuantLib Yield Curve Methodology

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See full analysis in bootstrap_yield_curve.ipynb