NO.PZ2025040202000068
问题如下：
A 1-year plain vanilla interest rate swap has semiannual resets. The fixed swap rate is 5.2% and the subsequent floating MRRs through the life of the contract are given as follows:
If the 30/360 day count method is used, the pay-fixed, receive-floating net cash flow at t = 6 months is closest to:
选项：
A.A.–0.002 per unit notional. B.B.–0.001 per unit notional. C.C.0.001 per unit notional.解释：
A Incorrect because this neglects the fact
that the floating interest rate is set in advance and settled in arrears, i.e.,
it uses the MRR at t = 6 months rather than the MRR at t =
0; 0.5 × (0.048 – 0.052) = –0.002.
This is also the value if the cash flow is
stated on an annual basis.
B Correct because
the convention in the swap market is that the floating interest rate is assumed
to be advanced set and settled in arrears; thus, rFLT,i (the
floating-leg rate) is set at the beginning of the period and paid at the end.
Therefore, the appropriate floating rate to use for the 6-month cash flow is
the MRR at t = 0, i.e., 5.0%.
Moreover, the pay-fixed,
receive-floating net cash flow can be expressed as AP × (rFLT,i –
rFIX), where rFIX is the swap's fixed rate and AP
denotes the accrual period, which accounts for the payment frequency and day
count methods. Since the 30/360 day count method is assumed and the payment
frequency is semi-annual, AP = 180/360 = 0.5. Therefore, the net cash flow
at t = 6 months, for every unit of the notional amount, is 0.5
× (0.050 – 0.052) = –0.001.
C Incorrect because this is the net cash
flow at t = 6 months for a receive-fixed, pay-floating swap,
not a pay-fixed, received-floating swap (i.e., it is the negative of the
correct cash flow).
It is also the answer if the MRR at t =
12 months is used rather than the MRR at t = 0; 0.5 × (0.054 –
0.052) = 0.001 per unit notional.
