lev-os 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
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)
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)
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)
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
Cross-validate results
- Compare model price to Bloomberg CDSW, Markit CDS Calculator, or QuantLib output
- Check that bootstrapped survival probabilities are monotonically decreasing and bounded in [0, 1]
- Verify upfront vs. running spread conversion matches ISDA Standard Model (using standard 3% flat hazard rate for IMM date accruals) [VERIFY ISDA Standard Model version in use]
- For indices, confirm model-implied index spread vs. quoted spread falls within expected basis range
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