I am trying to work out a formula to derive the expected loss from the credit risk of a bond.

My idea is to tie the credit risk to credit valuation adjustment and derive the expected loss from there, but then how would I relate credit risk and credit valuation adjustment?

Help would be greatly appreciated.

Thanks in advance!


1 Answer 1


One way to estimate the credit risk of a bond is to look at the price of insuring the bond using a Credit Default Swap, which will cost roughly the spread between the bond's yield and the yield of a risk free bond with the same maturity (typically we use a government bond here).

Using simple assumptions, this leads us to the Credit Triangle, $$K = (1-R)\lambda$$ where $K$ is the credit spread, $R$ is the recovery-given-default (ie. what you expect to get back out of 100 if there's a credit event), and $\lambda$ is the probability of default per unit time. Given any two of these by the market, we can calculate the third.

Note that if we can only see $K$, we need to make some assumptions about either $R$ or $\lambda$ - the market will charge the same for a bond with high probability of default but low loss-given-default as it will for a bond with low probability of default but high loss-given-default.

If you want to calculate CVA of a contract expiring at time $T_f$, that is typically done using either the credit spreads from either CDS contracts or calculated spreads between the company's bonds and the risk free bonds to calculate values for $R$ and $\lambda$, and then solving $$CVA = (1-R) \int_0^{T_f} EPE(t) \cdot P(0,t) \cdot S'(t) dt$$ where $S'(t)$ is the derivative of the probability of survival until $t$ (depends on modelling assumptions, but this often assumed to be $-\lambda e^{-\lambda t}$), $P(0,t)$ is the discount factor to time $t$, and $EPE(t)$ is the expected positive exposute at time $t$. This complicates things a bit (especially of $S$ and $EPE$ are correlated...) and turns CVA calculations even for simple instruments into a derivtives pricing problem - the procedure is discussed in more depth in this article


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.