Question

A semi-annual interest rate swap on a notional principal of A$200 million has a remaining life of nine months. Under the terms of the swap, BATCO pays a fixed rate of 4% p.a. (compounded semi-annually) and receives six-month BBSW. What is the current value of the swap to BATCO if sixmonth BBSW rate was 2.6% p.a. (compounded semi-annually) three months ago and the current BBSW/swap curve in Australia is as follows:

Term (months)	% p.a (c.c)
3	2.2
6	2.5
9	2.9
12	3.0

Answer 1

To calculate the value of the swap, we’ll need to find the floating rate cash flows by calculating the expected forward rates via the BBSW based Swap Curve.

The first floating rate cash flow is calculated by using BBSW rate (last payment date): 2.6%

Floating rate cash flow in 3 months: A$200 × 0.026 / 2 = A$ 2.6.

The second floating rate cash flow is calculated by finding the forward rate that corresponds to the period between 3 months and 9 months.

To calculate forward rate for the period between 3 and 9 months, use this forward rate formula:

= 2.9 + (2.9 – 2.2) * 0.25 / (0.75 – 0.25)

= 3.25%

This rate is a continuously compounded rate, so we need to find the equivalent forward rate with semi-annual compounding:

Rforward (SC) = 2 × [e (0.0325/2) − 1] = 0.032765 = 3.2765%

Floating rate cash flow in 9 months: A$200 × 3.2765% / 2 = A$ 3.2765

Time	Fixed	Floating	Present Value	PV of Fixed	PV of Floating
	Cash Flow	Cash Flow	Factor	Cash Flow	Cash Flow
3 Months	=200*4%/2	=200*0.026/2	=1/(1+0.022/4)	=B9*D9	=C9*D9
9 Months	=200*4%/2	=200*3.2765%/2	=1/(1+0.029*9/12)	=B10*D10	=C10*D10
				=SUM(E9:E10)	=SUM(F9:F10)

Time	Fixed	Floating	Present Value	PV of Fixed	PV of Floating
	Cash Flow	Cash Flow	Factor	Cash Flow	Cash Flow
3 Months	4	2.60	0.99	3.98	2.59
9 Months	4	3.28	0.98	3.91	3.21
				7.89	5.79

The value of the swap based on Excel Calculation = 5.79 – 7.89 = -A$2.10

Feel free to ask any Query in Comment Section

Please provide feedback.

Cheers