Valuing a Three-Year BBSW Interest Rate Swap
Summary
The document outlines a basic valuation workflow for a three-year swap with a fixed leg paying 3.5% semi-annually and a floating leg receiving BBSW, on a stated notional of $100 million. It begins by interpolating the supplied curve to six-month tenors, then builds the payment schedule. Fixed coupons follow directly from the notional, fixed rate, and payment interval. Floating coupons require six-month forward rates inferred from successive zero rates.
The scheduled net cash flows are then discounted and summed to obtain the swap’s present value. The response illustrates how to derive a forward rate from continuously compounded zero rates and notes that the discount curve matters. However, the curve data needed to reproduce a valuation are absent from the document, so no independent value can be calculated from the text. The stated discount-factor example uses a positive exponential, which conflicts with the usual present-value discounting convention; the curve and discounting setup should therefore be checked before applying the procedure.
Key ideas
- Interpolate the supplied curve to the swap’s six-month payment dates before constructing cash flows.
- Calculate each fixed payment from notional, fixed rate, and accrual period.
- Derive floating payments from forward rates implied by the zero curve.
- Discount scheduled cash flows and sum their present values to value the swap.
- The stated discount-factor example should be checked because its exponential sign conflicts with standard discounting.
Tags
Full text
# Calculating the value of an interest rate swap
# Calculating the value of an interest rate swap
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 by Helin (score 1)
https://quant.stackexchange.com/a/29561
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 by JoshK (score 0)
https://quant.stackexchange.com/a/29556
It's really simpler than you think. I'm not sure where to find a good formula, but to do it manually:
- Calculate the amount of money that you will receive in each period less the money that you will pay out in each period.
- 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.
- Discount the payments. Receiving $x in the future gets discounted by some factor. To be safe use LIBOR.
- Sum it up!Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.