NO.PZ2023041003000016
问题如下:
Troubadour identifies an arbitrage opportunity
relating to a fixed-income futures contract and its underlying bond. Current
data on the futures contract and underlying bond are presented in Exhibit 1.
The current annual compounded risk-free rate is 0.30%.
Based on Exhibit 1 and assuming annual compounding, the arbitrage
profit on the bond futures contract is closest to:
选项:
A.0.4158
0.5356
0.6195
解释:
The no-arbitrage futures price is equal to the
following:
F0(T) =FV0,T(T)[B0(T + Y) +Al0– PVCI0,T]
F0(T)= (1 + 0.003)0.25(112.00 + 0.08 - 0)
F0(T) = (1
+ 0.003)0.25 (112.08) = 112.1640
The adjusted price of the futures contract is
equal to the conversion factor multiplied by the quoted futures price:
F0(T)=CF(T)QF0(T)
F0(T) = (0.90)(125) = 112.50
Adding the accrued interest of 0.20 in three
months (futures contract expiration) to the adjusted price of the futures
contract gives a total price of 112.70.
This difference means that the futures contract
is overpriced by 112.70 - 112.1640 = 0.5360. The available arbitrage profit is
the present value of this difference: 0.5360/(1.003)0.25= 0.5356.
这题答案里,他先算了无套利fp,但根据公式应该要减去accrued interest at futures contract expiration的0.2才对呀。 请问这里为什么不减呢?
我有看有问必答里的其他答案,还是有点迷惑。就是我该如何判断什么情况下要减去什么情况下要加上呢?
而且根据公式qfp= fp/cf, 其中的fp也是根据现货计算得出= (bo+ai0)x (1+rf)-ait-fvc