# Market Value of a CDS

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:

$MV_{CDS} = s\cdot PV_{surv} - PV_{def}$

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## 2 Answers

I'm not expert. However, it seems clear that you're generating an upper bound on the seller value. You have to model the risk of default, as well as any convenantal terms for structured default, to generate an expected payout rate, and deduct that from the DCFs, to get a more realistic value. If the terms include a swap put model that separately. To set a bid, you need to model counter-party and (ideally) liquidity risk as well. You might want to read the standard: http://www.cdsmodel.com/

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Thanks for the reply. I thought I allready dealt with the default risk in the calculation of the spread (see edit above). –  Owe Jessen Jul 13 '11 at 8:26

A simpler solution I found is to discount the differences between current spread and original spread:

$MV_{CDS}=T \cdot (s_0 - s_t )\cdot \sum_{i=1}^{T}{e^{-r\cdot i }}$

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