pricing-credit-derivatives

name	pricing-credit-derivatives
description	Structures credit derivative pricing with hazard rate calibration and default probability estimation. Use when pricing CDS, calculating credit spreads, or modeling default risk.
tags	["valuation","quantitative-finance","risk","credit"]
metadata	{"author":"casemark","practice_areas":["Derivatives","Quantitative Analysis","Structured Products"],"document_types":["Valuation Report"],"skill_modes":["Valuation","Calculation"]}

Pricing Credit Derivatives

When To Use

• Pricing single-name or index CDS contracts (standard or bespoke tenors)
• Bootstrapping hazard rates from quoted CDS spreads to build a term structure of default probabilities
• Calculating fair-value credit spreads for bonds, loans, or structured tranches relative to CDS-implied levels
• Marking credit derivative books to market or to model for P&L and risk reporting
• Modeling default and recovery scenarios for CVA/DVA adjustments on counterparty exposures
• Pricing credit-linked notes (CLNs), total return swaps (TRS), or nth-to-default baskets

Inputs To Gather

• Reference entity and obligation: Legal name, RED code, reference obligation ISIN, seniority (senior unsecured, subordinated, secured), restructuring clause type (CR, MR, MM, XR) [VERIFY jurisdiction-specific ISDA definitions apply]
• Market CDS spreads: Par spreads or upfront quotes across standard tenors (6M, 1Y, 2Y, 3Y, 5Y, 7Y, 10Y); source (Markit, Bloomberg CDSW, dealer runs) and snapshot date
• Recovery rate assumption: Market-standard (typically 40% for senior unsecured corporates, 25% for subordinated, 20–25% for sovereigns) or entity-specific recovery from auction history [VERIFY against current ISDA credit event auction results]
• Risk-free discount curve: OIS or SOFR swap curve (post-LIBOR transition); specify curve date, source, and interpolation method [VERIFY which benchmark is contractually specified]
• Contract terms: Notional, trade date, effective date, maturity, coupon (running spread for legacy or standard 100/500 bps), payment frequency (quarterly), day count (ACT/360), business day convention
• Correlation parameters (for basket/tranche products): Base correlation surface or compound correlation by tranche attachment/detachment points

Workflow

1. Build the discount curve

   • Strip OIS/SOFR swap rates to derive zero-coupon discount factors
   • Interpolate using log-linear on discount factors or monotone convex on zero rates
   • Confirm curve date aligns with CDS quote date (T+1 settlement convention for standard CDS)

2. Bootstrap the hazard rate curve

   • Start from the shortest tenor CDS spread; assume piecewise-constant hazard rates between standard tenors
   • For each tenor, solve for the hazard rate λ that equates the present value of the premium leg to the protection leg:
     • Premium leg PV = Σ (spread × Δt × DF(tᵢ) × Survival(tᵢ)) including accrued-on-default
     • Protection leg PV = Σ ((1 − R) × DF(tᵢ) × [Survival(tᵢ₋₁) − Survival(tᵢ)])
   • Survival probability: S(t) = exp(−∫₀ᵗ λ(s) ds)
   • Include accrual-on-default adjustment (integral of accrued premium over the payment period weighted by default probability)

3. Price the target instrument

   • Single-name CDS: Compute mark-to-market as the difference between protection leg PV and premium leg PV at the contract's running coupon; convert to upfront amount using ISDA Standard Model conventions
   • CDS index: Price as portfolio of single-name CDS with intrinsic/index basis adjustment; account for defaulted names (fixed recovery payment at settlement)
   • Credit-linked note: Bond-equivalent pricing = risk-free bond PV minus protection leg PV funded by note proceeds
   • Nth-to-default basket: Require correlation modeling; use Gaussian copula or Student-t copula to simulate joint defaults; compute expected loss on nth default
   • Synthetic CDO tranche: Apply base correlation framework—interpolate base correlations for attachment and detachment points; tranche expected loss = base EL(detachment) − base EL(attachment)

4. Compute risk sensitivities

   • CS01 (Credit Spread 01): Bump each CDS spread by 1 bp, re-bootstrap, and re-price; report per-tenor and parallel CS01
   • CR01 (Recovery 01): Shift recovery assumption by 1% and re-price
   • IR01: Bump discount curve by 1 bp to isolate interest rate sensitivity
   • Jump-to-default (JTD): Compute loss on instantaneous default at assumed recovery vs. current MTM
   • Theta/carry: Estimate daily P&L from premium accrual and curve roll-down

Output

• Pricing summary table: Fair value (upfront amount or PV), par spread, running spread + upfront, accrued premium, clean vs. dirty price
• Hazard rate term structure: Bootstrapped piecewise-constant hazard rates by tenor, with corresponding cumulative default probabilities and survival probabilities
• Risk report: CS01 (per-tenor and parallel), CR01, IR01, JTD exposure, theta/carry
• Methodology statement: Model used (ISDA Standard Model, reduced-form intensity, copula), recovery assumption, discount curve specification, interpolation method, and any deviations from standard conventions
• Sensitivity analysis: Price impact across a range of spread levels (±50, ±100 bps) and recovery assumptions (20%, 30%, 40%, 50%)

Quality Checks

• Hazard rates must be non-negative; flag any negative implied hazard rates as indicative of curve fitting issues or stale quotes
• Premium leg PV + upfront payment should equal protection leg PV at fair value (no-arbitrage check)
• Par spread computed from bootstrapped curve should reproduce input market spreads within ±0.1 bps (round-trip consistency)
• For standard ISDA CDS contracts, upfront amount must reflect the correct standard coupon (100 or 500 bps) and settlement conventions [VERIFY Big Bang/Small Bang protocol applicability by region]
• Confirm day count (ACT/360), payment frequency (quarterly on IMM dates), and business day conventions match contract terms
• Recovery rate should be consistent between bootstrapping and pricing—mixing assumptions introduces arbitrage
• For tranche pricing, verify that base correlations are monotonically increasing with detachment point; non-monotonicity signals interpolation or data issues