Here on screen is a five year CDS.

You will see the default and survival probabilities in the central columns of the table.

These have now been extended to five years using the same process as before.

You will also notice down at the bottom is a calculation of the cumulative default probability.

This is just one minus the probability of surviving all five years, so we can see that if we assume a default intensity of 5%, which remains constant throughout, there is a 22.6% chance the reference entity defaults at some point in the next five years.

The swap on screen makes a simplification in order to keep the logic the same as the examples we used before that simplification is that the premium leg pays based on the probability of surviving to the start of year end rather than surviving to the end of your in.

In practice, moving in annual steps is too crude for an accurate price, and to be more precise, we should use a continuous probability distribution.

This would mean that the probability of default at any point in time is measured and the correct timing of the default leg and accrual of the premium leg can be calculated.

However, using annual steps will give us a good approximation and will certainly suffice for illustrative purposes.

Once we have our probabilities, the swap is priced just like an interest rate swap.

Each expected premium and default cash flow is projected and discounted back to today.

We then solve for a coupon in the top left, which solves the whole swap to an NPV of zero.

In this case, the coupon is 300 basis points per year.

There are a couple of other things to note about this approach.

Firstly, we have kept the default intensity constant, which we have already seen, means that the premium leg is the same for any maturity of swap.

In fact, you can see this for yourself.

If you look at the PV premium and PV default columns, not only is the sum of each column equal, but the value in each year is also constant.

So a five year swap has the same price as a four year swap and so on.

This is the flat CDS curve assumption we mentioned when we talked about calculating valuations for margining in the clearing system.

In practice, CDF curves are not flat.

Each maturity will have a different CDS spread.

So what we see here is a simplification of reality as well as default intensity.

There is another variable which affects the CDS price, and that is the recovery rate.

In the top left of the table, you'll see that this has been fixed at 40%.

If you are trying to match a market CDS spread, it is unfortunately not possible to solve for both default intensity and recovery rate.

So we have to fix one and solve for the other.

It is common to fix the recovery rate, and here you can see we have used the common 40% assumption for senior debt.

Again, this was one of the assumptions we mentioned is used for margining cleared swaps.

In summary, we can price credit default swaps by modeling the default probability and projecting expected cash flows.

This will then give us a cumulative and year default probability that we can compare to other sources of data and possibly use to form our opinion whether the CDS is fairly priced in the market.

It is important to bear in mind that we have ignored the concept of a risk premium in our risk neutral pricing.

So let's discuss that briefly. Now.

When someone asks for compensation to take on an economic commitment of uncertain size, they will normally ask for more than the risk neutral expected value.

Risk neutral pricing assumes people don't care about taking on uncertainty and in practice they do put another way.

Our pricing approach assumes the seller is happy to break even on average in return for providing insurance and accepting the uncertain payouts.

That requires who would do this trade at a break even price.

Why accept uncertainty for no return? The reality is that CDS spreads are going to be higher than that required to break even to include a risk premium to tempt the protection seller to take on the risk.

The magnitude of the risk premium is unknowable and can only be guessed at.

This means that what we have is an overestimate of the default probabilities, and in reality, they will be lower.

However, it is good at least to have established an upper bound.

Once we have our simple approach to pricing credit default swaps, we can easily see how the upfront PV calculation for clearing would work.

As we move from the market agreed spread to one of the standardized coupons.

Here we change our calculated 300 basis points coupon to either the 100 or 500 standard coupons and observe the PV change.

The PV here is calculated from the point of view of the buyer, so you can see when we drop the coupon to 100, the NPV is positive and we see the opposite When we raise it to 500 in practice, either the 100 or 500 coupon would work for this trade because the market level is right in the middle.

The clearinghouse will usually have a mapping function that will automatically assign a standard coupon to a cleared trade and calculate the upfront PV effect.