Valuation of CDS

[ravishankar80]

Hi David,

This is regarding the valuation of CDS. I have some very basic questions. I did not understand the whole thing clearly

1.What is the % of per Annum (what does it mean) and how is this equal to survival probability
2.What is the difference between expected payment and expected accrual? I understand payment is the premium paid by CDS buyer in order to buy protection what is the accrual over and above the payment.
3.From the seller point of view what is the % of notional? What is relation between this and default prob.

Thanks for the clarifications

 

[David Harper CFA FRM]

Hi ravi,

I will be including this in a cluster of focused screencasts after i conclude the regular sessions. It among the tougher exercises in the FRM and needs special attention

1. It means % of per annum CDS spread; e.g., where Hull has .9800(s) as the first expected payment, I have the corresponding 98% of the per annum credit spread premium (s)

2. I personally think this is the hardest part! In one sense, you are right, the accrual seems additional. But the key to both sides is that all the flows are probability-adjusted. The payments are not 100%, they are 98%, 96%, etc. And note it is merely an *assumption* of this model that defaults occur at mid-year. Given defaults occur mid-year, if you only count the probability adjusted (<100%) payments and exclude the accrual, then you will be falling short under any mid-year default. Another way to look at this, perhaps: the payment side (98%, 96%), I am pretty sure, could be adjusted to incorporate the accruals (bumped up). Hull could have had one payment side with times 0.5, 1.5, etc but he broke them out

3. If the notional is $100 million with PD of 2% and recovery of 40% (Hull assumptions), then with 2% probability there will be a default in 1st year: 40% recovered, 60% is the payoff. So the expected payoff in first year is:
2% * 60% = 1.2% of the notional; e.g., if notional is $100 million, then
1.2% of $100 million

David

 

[danielkan2000]

I totally understand your CDS valuation spreadsheet. But I have one question regarding the structure of the CDS.

To simplify, I assume
buyer = some fund who purchases the CDS from the CDS sellser
seller = insurance companies who offer CDS protection

In order to calculate the premium from the buyer, we discount the survival probabilities*spread. This is because the buyer has to pay for their survival in order to receive the seller's protection.

"Therefore, if their survival probability increases, they have to pay more premium"

From this statement, I get confused:
If a company has higher survival prob, why are they willing to pay more premium in order to get protection?
The only reason why people would like to buy insurance because they are uncertain about the future. If the company already knows that they are not gonna default, why are they willing to pay for others to protect himself, instead of keeping more cash inside their balance sheet?

The only reason I can think of is because the company they are gambling (whether that company is default or not) is not the buyer itself. That's why the buyer is willing to gamble. Otherwise, I cannot think of any reason why the buyer is willing to pay money to buy the protection.

Please correct me if I am wrong.

Thanks

 

[rahul.goyl]

Hi Daniel,

I am just trying to make a point here.

"In order to calculate the premium from the buyer, we discount the survival probabilities*spread. This is because the buyer has to pay for their survival in order to receive the seller’s protection".

In your above statement, the buyer is not paying fot their own survival, but for the counterparty they are buying protection on. The buyer has to pay for the survial probability of counterparty say (GM , FORD) not for themselves. Becoz in CDS both the parties are exposed to each other credit risk (Default by either Counterparty) but it shud be greater for the protection buyer compare to protection seller.

Hope it will help..
Regrads,
Rahul