CDS Curve Stripping – Simple vs Exact Model

This repository implements CDS curve stripping using two different approaches and compares their implied hazard rates and default probabilities.

Overview

We analyze CDS spreads for maturities 1Y, 3Y, 5Y, 7Y and 10Y under:

1. Simple Model

   • Continuous premium assumption
   • Hazard rate approximation: λ = R / LGD
   • No explicit discounting structure

2. Exact Model

   • Quarterly premium payments
   • Accrued premium at default
   • Piecewise constant forward hazard rates
   • Iterative root-finding to ensure: Premium Leg = Protection Leg

The project highlights how proper cashflow timing and discounting affect implied hazard rates, especially in high interest rate environments.

Key Insights

• At low interest rates (3%), both models produce similar hazard term structures.
• At higher rates (10%), differences widen because the exact model correctly incorporates discounting.
• The simple model is useful for intuition, but the exact model is required for pricing consistency.

Technical Details

• Implemented from scratch (no pricing libraries).
• Numerical root-finding used to strip forward hazard rates.
• Explicit validation of Premium and Protection leg equality.