I need to model the market value of CDS in a portfolio. My current approach is to calculate the present value of the future spread payments - does anybody have a better idea to solve the problem?
Edit: I calculated the spread in the following way (as in Hull-White):
$PV_{surv} = \sum_{i=1}^T {(1−p_d )^i \cdot e^{-y\cdot i }}; $
$PV_{def}=\sum_{i=1}^{t}{p_d \cdot (1-p_d)^{i-1} \cdot (1-R)}$
$s=PV_{def}/PV_{surv}$
2nd edit: I found the following statement: http://www.yieldcurve.com/Mktresearch/files/Abukar_Dissertation_Sep05.pdf "the market value of a cds is the difference between the two legs", leading to:
$MV_{CDS} = s\cdot PV_{surv} - PV_{def}$
Answer
There is a much better pricing formula which is an accurate approximation. Anecdotally I believe that the difference between this and the "offical" CDSW calculator on Bloomberg will be within about 0.5% or less of the notional, especially if the CDS curve is flat.
For a \$1 notional of short-protection contract with coupon $C$, market spread $S$ and $T$ years to maturity, where $R$ is the expected recovery rate, and $r$ is the continuously compounded $T$-year swap rate, we have
$$ V= (C-S) \cdot\frac{1- e^{ -gT } }{g} \cdot\frac{365}{360} $$
where
$$ g=r+\frac{S}{1-R} $$
This approximation is exact in the limit of a continuously paying premium leg with a flat credit and interest rate curve. As CDS pay quarterly and as credit curves are often quoted using a flat spread, this formula is a good approximation. Note that the factor of 365/360 corrects for the Actual 360 basis used to calculate CDS premium payments, while $T$ is calculated in calendar years.
To get a more accurate pricing would require you to calculate all of the premium flows correctly. You would also need to have the ability to value the protection leg which requires a time-integral to contract expiry. Finally you would need to fit your model to the term structure of CDS spreads. There is a more detailed description at this link.
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