How did I compute the survival probabilities?

I took the same formula. It's going to be the survival probability

1 times step before times 1 minus the hazard rate.

The only difference is before I was using survival probabilities in absolute

numbers, here I'm looking at them at percentages.

What about the fixed payments, which are the fixed coupon payments that.

The buyer has to make. This is simply going to be the quantity

of the spread divided by 4, and I've left off the notional amount, and I'm going to

look at the notional amount in a moment. So that's the fixed payment that's going

to happen. Now in this column, row F, what we have

done is we have taken the fixed payments and found an expected value, the expected

value which takes into account the probability of default.

So that's e7 times d7, divided by 100. And this 100 just comes because the

probability of survival is written as percentages.

So, the values in this column simply reflect the fact that fixed coupon

payment has to be paid only if the reference entity survives up to that

time. This is the present value.

We have taken the expected value, multiplied it by the notional amount, and

because, these spreads are in basis points, I multiplied it by 0.0001 to

covert into absolute numbers. And multiplied it by b7, which is the

discount value to get the present value. Of the coupon payments.

Done this for all time periods. That tells me what the total fixed coupon

payments are. But we still have to figure out what the

accrued interest is. And, in order to compute the accrued

interest, we need the default probabilities.

So here's the default probability. This default probability is just a

survival probability. Times the hazard rate, and I put that

along this column all the way through. What is the accrued interest?

If you click on that, it's we've assumed it to be half of what the coupon payment

is going to be, because we have assumed that this is going to be half way

between. Times the default probability again

divided by 100 to convert the default probability, which is in percentages,

into absolute numbers. What is the present value?

You take the notional amount, N, which is of $1,000,000 times the accrued interest,

times the discount times again 0.0001 to convert the basis points into.

absolute numbers. So this is going to be the present value

of the accrued interest, in different periods.

Finally, what about the protection. What is the expected value of the

protection, it's the default probability times 1 minus R divided by 100.

The 100 again to take the default probabilities and convert them into

absolute numbers. What is the present value of the

protection? You multiply by the notional amount,

multiply by the discount rate, that tells me what is the present value of the

protection for the different time periods.

So the premium leg now is going to be the sum of the present value of all the

premiums and sum of all the present value of the accrued interest.

And that tells you what the buyer has to pay.

What the buyer will receive is just the sum of all the expected present values of

the protection payments. This is the net value of the swap at time

zero. The difference between the premium leg

and the protection leg. So, since the value of the CDS is

positive. It, it suggests that this spread is set

too low. it's a good deal for the buyer.

The buyer is getting protection at too lower rate.

If you increase that spread, to say from 218 to 220 basis points, then you end up

getting that that spread is too high, you end up getting that the difference

between the premium leg and the protection leg is negative.

Which means that it's not been, it's not a good deal for the buyer.

This spread has been set too high. You can compute out what the correct

spread is going to be. So we're going to set the objective which

is the value and try to solve for the value equal to zero by changing the

variable cells S, it's just a reference cell.

And I'm assuming that it's going to be positives.

If you solve that and you wait for Solver you end up getting that the spread is

going to 218.89 which is slightly smaller then then spread that we had started

with. And this brings us to the end of this

module.