[BLANK_AUDIO] . In this short module, we're going to

discuss the mechanics of a synthetic CDO tranche.

While we haven't actually described for you what a synthetic CDO tranche is yet,

we will actually do that in a later module.

In particular, we will distinguish between a cash CDO and a synthetic CDO.

But for now, we're just going to go into the details of the mechanics, of how a

synthetic CDO tranche actually works. So now let's discuss the mechanics of the

synthetic CDO tranche. I'm going to describe or explain for you,

the distinction between a synthetic and a cash CDO in a later module.

For now we're just going to discuss the details of a synthetic tranche.

As I said, I will distinguished between the synthetic and a cache CDO, in the

later model. So recall there are N credits in the

reference portfolio. Each credit has the same notional amount,

A. If the ith credit defaults, then the

portolio incurs a loss of A times 1 minus r.

Where R is the recovery rate which is assumed fixed, known, and constant across

all credits. A tranche is defined by the lower and

upper attachment points, L and U respectively.

So, we've already seen examples of L and U, L and U, 0 to 3 and so on.

3 to 6, 6 to 9. Usually L and U are given as percentages

of the total portfolio notional amount. In our simple example on the previous two

modules, L and U were given as the number of losses.

0, 1, 2, or 3, 4, 5, or 6, 7, 8 or 9, or so on.

But, typically in practice, they're given as percentages.

The tranche loss function, TL for tranche loss, superscript l and u, to denote the

lower and upper attachment points are parameters of this function.

So its a function of the number of losses in the portfolio L, is a function given

as follows. First of all we take the minimum of LA1

minus R and U. So this, here, is actually the total

portfolio loss. So if the total portfolio loss exceeds U,

then the tranche loss is given by U. After all, the tranche cannot lose more

than U. U is the upper attachment point, it

cannot lose more than U. So if the total portfolio loss exceeds U,

then this minimum is given to us by U. Otherwise the minimum is given by the

total portfolio loss. Now the lower attachment point is L, so

we then have to subtract L from this minimum here.