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蜗牛也是牛Megan · 2025年05月04日

画图法怎么做

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?

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