Estimating Bond Credit P&L from CDS Curve Sensitivities
Summary
The document outlines a framework for measuring corporate bond credit risk through CDS spreads. It describes deriving default and survival probabilities from CDS quotes, then pricing bond cash flows with risk-free discounting and a recovery component. Since this model price may differ from the observed bond price, the method introduces a bond–CDS basis: a spread adjustment that makes the modeled bond price match the market price.
To estimate spread risk by maturity, hold that basis fixed, perturb one CDS tenor at a time, reprice the bond, and record the price change. Multiplying each sensitivity by its corresponding spread move gives an attribution of credit P&L. The response also recommends measuring basis sensitivity and accounting for interest-rate effects by recalculating survival probabilities when rates move. Second-order and cross sensitivities can help explain residual P&L. The answer cites a reference and Bloomberg’s VCDS function, but cautions that the function may not provide the needed analysis well; implementation details, recovery assumptions, and model errors remain important limitations.
Key ideas
- Derive default probabilities from CDS quotes to model bond cash flows and recovery.
- Use a bond–CDS basis adjustment to reconcile modeled bond value with its observed market price.
- Estimate tenor-specific CDS sensitivity by shifting one curve point at a time while holding the basis constant.
- Include basis and interest-rate sensitivities when attributing credit-related P&L.
- Second-order and cross effects can help account for residual P&L, while recovery and model assumptions remain sources of uncertainty.
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# CDS Spread sensitivity # CDS Spread sensitivity I am computing HVaR for corporate bonds using CDS spread to approach credit risk. I have data on cds spread for different maturities along the bond life and I need the sensitivity to spread change for each maturity to compute P&L's due to credit risk. I'd like to know if there is such data on bloomberg and if it's the case, how can I retrieve it. Thanks, PS: I am french and not very fluent in english thus I'm welcoming any observation regarding my grammar, etc. It would be very helpful. ## Answer by Dimitri Vulis (score 3, accepted) https://quant.stackexchange.com/a/43591 (Your English is fine!) A good reference is Darrell Duffie and Kenneth J. Singleton, Credit Risk: Pricing, Measurement, and Management, PUP 2003. The function on Bloomberg that sort of does what you want is VCDS. However it does not do it very well, so you will probably want to implement it yourself. I will outline my understanding of Duffie and Singleton methodology and VCDS (going back to their 1999 paper in the Review of Financial Studies https://web.stanford.edu/~duffie/ds.pdf ). Any errors are mine alone. Suppose you are given a bond price and a CDS. You calculate the model price of the bond using the CDS - that is, for each bond cash flow (coupon or notional), you calculate the probability of default derived from the CDS, and discount the cash flow using the risk-free discount factor and (1 - probability of default). You also add the value of the recovery of the notional in case of default. You don't need to assume that the bond will have the same recovery as the CDS if you don't have to (e.g. the bond is highly collateralized). This model price generally will not be the same as your observed market price. You solve for the bond-CDS basis - determine how much the CDS needs to be shifted in order to explain the market price. In order to calculate the sensitivity of the bond price to the CDS, you keep the bond-CDS basis constant, perturb the CDS curve (one tenor at a time), reprice the bond, and measure the impact. (Practically, you may prefer to perturb not the observable CDS, but the one shifted by the bond-CDS basis, that matches the observed bond price). Multiplying the CDS sensitivities by the change in CDS quotes at each tenor will tell you how much PL came from the change in each quote. You should also calculate the sensitivity to the change in the bond-CDS basis, and multiply this sensitivity by the change in the bond-CDS basis and include this product in your PL due to credit. Further if you follow this methodology and want to minimize the remaining unexplained PL: - when you calculate the sensitivity to interest rates (IR deltas), you should keep the CDS quotes constant and recalculate the survival probabilities using the perturbed IR curve - it helps to include all imaginable second-order sensitivities (various gammas and cross-gammas: CDS x basis, CDS x IR, CDS x recovery...) in your PL explanation
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