# CDS - Page 139

" The payments made by the protection buyer to the seller are the premium leg. On the other side of the contract, the protection seller must make a payment to the protection buyer in case of a default; these contingent payments make up the protection leg.

The difference between the present value of the premium leg and the present value of the protection leg determines the upfront payment.

Question: Doesn’t the protection leg only kick in when there is a default? I always thought that the CDS buyer pays the premium annually and only when there is a default, the protection leg kicks in.

up front payment (paid by protection buyer) = PV(protection leg) - PV(premium leg).

I think the protection leg will also kick in in case the CDS spread is higher than the CDS coupon and in that case seller will pay the pv of the difference to the buyer.

The PV(protection leg) is the PV of the contingent obligation of the credit protection seller to the credit protection buyer. This is essentially an expected loss number (i.e. probability adjusted), not a binary one as you are more or less thinking about.

So, take it to it’s extreme simplest example:

I want to buy 1 year protection from you on \$100 worth of bonds. This means in 1 year, if the bond defaults, you pay me \$100 less the recovery on the bond (i.e. the “loss” or “protection leg”). In return for this 1 year of protection i will pay you 200bps premium (“premium leg”).

Now, lets say that you and i both believe that the bond will default in 1 year, and will recover 60% of it’s value (40% loss). So, what would be the “fair value” for me to pay you to want to enter into this contract? If you think you will have to pay me 40% in one year, you will demand the PV of 40% upfront.

In this case, however, i am also paying you 200bps in premium. So, the amount you would require upfront, is:

~38% = PV(40%) - PV(2%)

Then, your return over the year is: ~38% (upfront amount ) + 2% (premium paid) = 40%

this is vs. a loss expectation of 40%, so you are NPV zero, which is the no-arbitrage price

this is an incredible oversimplification, but conceptually the point; the numbers just move around based on investors expectations of riskiness (loss).

A CDS is really nothing more than an insurance policy; it’s easiest to understand it by viewing it as you would any other insurance policy.

You (the insured) pay an insurance premium (monthly, quarterly, annually, whatever). If you incur a loss that is covered by your policy, the insurance company makes a payment on your claim. The amount and timing of such a payment is uncertain, hence, risky.

Insurance companies set the premium to cover, statistically, the claim payments they will have to make, plus a profit.

ok, thanks…

So in reference to this statement: up front payment (paid by protection buyer) = PV(protection leg) - PV(premium leg)

It is saying that there is an upfront payment that equals what it expectes to lose and the premiums you are expected to pay them. So there would be an upfront payment of the formula above, plus premiums every quarter (as an example).

Does that make sense?

I wouldn’t be surprised.

You could adjust the premium payment to eliminate the upfront payment, or to make the upfront payment the same amount as the other (quarterly, say) payments, or to require a large upfront payment, like the down payment on a car or on a house.

Is the Upfront Payment the same as the Upfront Premium?

Upfront Payment ( paid by protection buyer)= PV (Protection Leg) - PV (Premium Leg)