Calculating the value of an interest rate swap

Question

Calculate the value of an interest rate swap with these features: Notional $100M

Pay: 3.5% semi-annually

Receive: BBSW semi-annually

Term: 3 years

Assume the BBSW curve is as presented here:

I literally have no idea how to do this question as I couldn't find it in my textbook or my lecture slides. So I tried to use the following method. I put the table of data into a graph (using excel) and found the approximate equation for it. From there I was able to find each year's rate.

Then i found each 'coupon payment' was 3.5m and used the discounted cash flow model to find the present value of the interest rate swap (97.66m).

What is the proper way to do this question.

Answer 1

The first step is to interpolate the curve into 6-month intervals. For simplicity, you can just linearly interpolate between the rates you're given so that you have rates for 0.5, 1, 1.5, ..., 3 year tenors.

Next, you prepare the cash flow schedule. The fixed leg (pay) is easy: every 6-month, you pay $100{,}000{,}000 \times 3.5 / 2$.

The floating leg requires 6-month forward rates. These can be easily computed from the zero rates you're given. For example, the 6m forward 6m rate is solved from $e^{2.5\% \times 0.5}e^{f \times 0.5} = e^{3\% \times 1}$. The corresponding floating leg payment is simply $100{,}000{,}000 \times f / 2$.

Finally, you need the present value of all the cash flows. AUD swaps are discounted using BBSW rates, which you're given. The 2-year discount factor, for example, is simply $e^{3.5\% \times 2}$. These can be used to calculate the present values of each cash flow, and you just sum these PVs up to obtain the overall swap's NPV.

Answer 2

It's really simpler than you think. I'm not sure where to find a good formula, but to do it manually:

1. Calculate the amount of money that you will receive in each period less the money that you will pay out in each period.
2. Calculate the interest that you will receive or pay depending on the cash balance in that period. In your example you will start negative since you are paying .035 and receiving .025. You have no know what rate structure you are using. Maybe OIS? Maybe LIBOR? If you are a commercial end-user you might end up paying a higher rate to borrow than you receive when you have a long cash balance.
3. Discount the payments. Receiving $x in the future gets discounted by some factor. To be safe use LIBOR.
4. Sum it up!