📈 Valuation and hedging of a BNP Paribas capped/floored Floating Rate Note (FRN) using QuantLib.
End-to-end pipeline combining curve construction, option pricing, credit risk adjustment, and risk management.
- Objective: Price a 5-year capped/floored FRN (BNP Paribas, ISIN: XS2392609181) as of Nov 2024 and design an effective hedging strategy.
- Motivation: Structured fixed-income products embed optionality (caps/floors) that complicates valuation and risk management. Accurate modelling of rates and credit risk is essential for banks and hedge funds managing such exposures.
- Data: EURIBOR deposit rates, IRS quotes, cap volatilities, and 5Y BNP Paribas CDS spreads (early 2024).
- Curve construction: Built linear, flat, cubic, and log-cubic discount curves; log-cubic chosen for smooth forward rates.
- Bond decomposition: FRN + long floor + short cap. Coupons replicated using cap/floor strips in QuantLib.
- Option pricing: Calibrated shifted Black model to interpolated caplet volatility surface.
- Credit risk adjustment: Applied simplified Credit Valuation Adjustment (CVA) using survival probabilities bootstrapped from CDS spreads.
- Hedging strategy: Constructed hedges with EURIBOR swaps (interest-rate risk) and CDS contracts (credit risk).
- Risk metrics: Monte Carlo simulation of factor shocks (parallel/slope/curvature/CDS) to compute 99% VaR and Expected Shortfall; decomposed into marginal risk contributions.
- Valuation: Bond priced at 1.52% undervalued relative to market clean price (98.43 vs 96.91).
- Hedging: Optimised swap hedge reduced DV01 exposure by 92%, mitigating interest-rate sensitivity.
- Risk analysis:
- Monte Carlo simulations of yield curve and CDS shocks produced 99% VaR and Expected Shortfall estimates.
- Simulations highlighted heavier-tailed risk than analytical approximations, underlining the limits of normality assumptions.
- Market-implied CDS: Derived using Brent’s root-finding on CVA-adjusted price, consistent with observed credit spreads.
- Ignoring CVA leads to significant mispricing of structured bonds.
- Curve construction choice (log-cubic interpolation) materially affects forward rates and valuations.
- Effective swap + CDS hedging can neutralise most IR and credit risk, leaving mainly basis risk.
- Monte Carlo risk simulations provide valuable insight into extreme-event behaviour beyond simple parametric VaR.
Python + QuantLib; dependencies listed in requirements.txt
- Brigo, D. & Mercurio, F. (2006). Interest Rate Models: Theory and Practice.
- Veronesi, P. (2010). Fixed Income Securities.
- Market data: Suomen Pankki, Investing.com BNP Paribas CDS, EuroTLX.