# Questions on CDS

I have a few questions on CDS and especially sovereign ones:

1. I've read that usually CDS are generally traded in millions of notional value, which means that not everybody can purchase sovereign CDS, but who will ? Banks, other countries, ... ?
2. Another thing that is a bit unclear, let's say a CDS is bought at day D with maturity T and at X bps. But at day N when the next premium is due the CDS is at Y bps. This premium is based on X bps or Y bps? (it would make more sense to me that it would be Y bps but I'm not 100% sure)
3. I've seen many different formulae for the CDS spread and pay-off, are the following formulae accurate?
• CDS Spread = n-Year Bond Yield – n-Year Risk-free Yield
• CDS Payoff = Notional Principal × (1 – Recover Rate)

1. In most cases min. value of CDS trade is 5M USD/EUR. Usually protection buyers are hedgers. A typical profile for protection buyer is a private equity fund, who hedge their credit risk on FI portfolio, sometimes not even for themselves. Protection sellers are financial institutes, but they use CDS to arbitrage credit derivatives market. For example there are some CDS Index instruments like iTraxx, CDX and some others which include protection of X different names. And single names (esp. corporates) priced with correlation to index. It's a simple example, but sometimes value of single names combined worth less, then index price or ..vice versa.

2. Yes, your logic about Y bps is right. But as I already mentioned above, it's an OTC instrument. So guess how many market participants will sell you CDS on 100% sure default tranches. Or buy protection on AAA-super-senior. (Well it's not pretty accurate, but I guess you already understood my logic) You could check your thesis at IHS Markit it's a data provider on CDS market and see how bid/offer bps prices changes.

3. The second formula about CDS payoff is correct, but it's a very simple way to evaluate payoff. You should visit http://www.creditfixings.com to make sure what happens with companies which face default procedure and how exactly Recovery is calculated.

• Hi @AlexZeDim thank you very much for your answer! Most of the things are quite clear to me expect your 2nd answer, is it a real yes ? :) Moreover, I have others questions may I ask them here or should I modify/edit my main question? – bixoez Oct 6 '18 at 14:15

2 in a standard CDS, the payment for the protection is fixed from the inception to the end. The protection buyer pays X. If later the same maturity protection is trading in the market at Y > X, it's good for the buyer and bad for the seller, but the cash flows don't change. Actually, in the standard CDS, the protection buyer pays (or sometimes receives) a substantial upfront fee, and then pays a standard running spread, typically 100 bps. There used to be a version of CDS called Constant Maturity CDS (CMCDS). It was pretty unusual before 2008 and I'm not aware of any printed after 2008. Suppose the protection is trading at X. For the first period, the protection buyer pays p * X, where p is fixed "participation" (say, 80%). Also, no material upfront fee. Suppose in the next period we observe (for example on IHS Markit) that the cost of 5-year protection has moved from X to Y. The buyer pays p * Y. However there is always a cap, like 700 bps. (Note that you need to consider the implied volatility of the credit in order to price this.)

3 are rough approximation. In particular, in PL in case of default includes not just notonal - recovery, but also the pv of the CDS contract (which can be substantual if the protection was bought when it was much cheaper). This CDS spread is an approximation of what the protection would cost without an upfront fee. In reality, there's an upfront fee and a stanard running spread of 100 or 500 bps.