Spot rate Vs Swap rate..

[rajeshtr]

Hi David,
In Malz material Example 7.7 - the material reads "We assume a flat swap curve for all maturities : with a continuously compounded spot rate of 4.5%" so the swap rate is assumed to be close to spot rate and hence it is 4.5%

in the below equation : how do you easily spot whether this is spot rate or Swap rate.. (Is it because it is positive i.e. swap rate (equating to bond price) ) I am confused because in the very next page Malz uses negative value in the same equation (I am assuming this case is spot rate. )

eg. when substituting 576 1yr spread and calculating Lambda(1).

 

[David Harper CFA FRM]

Hi @rajeshtr I don't have current time to deconstruct Malz CDS formula, apologies (it's easier to follow Hull's discrete example which I have modeled in our CDS learning workbook). Looking at it currently, to your point, i think it's possible he has a typo such that after the summation, it should be exp(-0.045*u/4) rather than exp(0.045*u/4). Because that (yellow) term is supposed to be discounting at the risk-free spot rate. The two terms inside the square brackets are, respectively, the cumulative survival probability and the unconditional default probability; e.g., the negatives here make sense, as for example, the 3-year cumulative survival probability given a hazard rate (conditional PD) of λ is equal to exp(-λ*3). So the negatives exponents inside the square brackets should be understood as appropriate to survival probabilities feeding into the value of the premium payer (protection buyer leg). The yellow should be doing the discounting, hence I don't know why it isn't exp(-0.045*u/4), and I assume Malz is assuming that is the spot rate. I recently recorded a youtube video on the (subtle) difference between a swap and spot rate here, which i hope is helpful: