NO.PZ2025040202000046
问题如下:
An investor buys a 1-year futures contract at 104 that expires in six months. The underlying is currently trading at 107, and the annually compounded risk-free rate is 3%. Assuming no other carry cash flows, the forward value of the existing contract is closest to:选项:
A.A.–4.53. B.B.2.96. C.C.4.53.解释:
A Incorrect because the futures prices in
the term PV[Ft – F0] are reversed. Using F0 =
104, S0.5 = 107, r = 3%, and T – t = 0.5, the new forward price
at t is simply Ft = FV(St) = 107(1 + 0.03)0.5 =
108.5931. Therefore: Vt = PV[Ft – F0]
= (104 – 108.5931)/(1 + 0.03)0.5 = –4.5931/1.014889 = –4.5257 ≈ –4.53.
B Incorrect because it assumes Ft =
107, the price of the underlying at six months left to expiration. The
calculation becomes: Vt = PV[Ft – F0]
= (107 – 104)/(1 + 0.03)0.5 = 3/1.014889 = 2.9560 ≈ 2.96.
C Correct because
we have F0 = 104, S0.5 = 107, r = 3%, and T – t
= 0.5. Note that the new forward price at time t is simply Ft =
FV(St) = 107(1 + 0.03)0.5 = 108.5931. Therefore: Vt =
PV[Ft – F0] = (108.5931 – 104)/(1 + 0.03)0.5 =
4.5931/1.014889 = 4.5257 ≈ 4.53. Note that the current forward value is greater
than the difference between the current underlying price of 107 and the initial
forward price of 104 due to interest costs.
这道题用画图法怎么计算?底层资产价格应该没有影响?