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Shutong · 2024年05月05日

到期时间怎么看出来？

  1. CFA II
  2. Derivative

NO.PZ2023020101000005

问题如下：

Ryan Parisi is a managing director in the derivatives group at High Ridge Partners, an investment management firm. Parisi specializes in advising institutional clients on the use of forward contracts in their portfolio management strategies. Parisi is preparing a response to questions from one of the firm’s US-based clients: Leslie Sheroda. Todd Curry, an intern in the derivatives group, will assist Parisi.

Leslie Sheroda oversees both equity and fixed-income portfolios for a pension fund. One month (30 days) ago, Sheroda had indicated that the pension fund expected a large inflow of cash in 60 days. In order to hedge against a potential rise in equity values over this period, Parisi advised Sheroda to enter into a long forward contract on the UAX 300 Index expiring in 60 days.

Prior to the meeting, Parisi shows the spot price of the UAX 300 index in Exhibit 1 to Curry and asks how the 30-day forward price will relate to the current level of the index. Curry compares the spot index to the forward price.

Exhibit 1: Selected Financial Information for Sheroda Meeting

Assuming a 360-day year, the value of Sheroda’s forward contract on the UAX index is closest to:

选项：

A.

USD 52.18

B.

USD 49.16

C.

USD 50.71

解释：

The 30-day forward price is Ft(T) = S0e(rc–γ)T = 1450.82e(0.0392–0.025)(30/360) = 1,452.54.

Vt(T) = PVt,T[Ft(T) – F0(T)] = e–0.0392(30/360)(1,452.54 – 1,403.22) = 49.16

题目说一个月前，两个月后有一笔金额需要hedge；又说要用60的contract来hedge，到期时间和折现计算时间，怎么看？

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1 个答案

李坏_品职助教 · 2024年05月06日

嗨，爱思考的PZer你好：


题目第二段说“One month (30 days) ago, Sheroda had indicated”，就是30天之前，也就是在t=-30的时刻，预计60天之后会有一大笔现金流入。所以在-30的时候，这个人做了一笔期限为60天的股票远期合约（a long forward contract on the UAX 300 Index expiring in 60 days.）


合约是t=-30时刻签订的，现在是t=0时刻，合约到期日是t=30时刻。


现在问你，在t=0的时刻，这个股票远期合约的value是多少？

首先要计算t=0时刻的30天的Ft(T)，因为再过30天，股票远期合约就到期了。

Ft(T) = 现在的股票指数1450.82 * e^[(rf - dividend yield)*30/360] = 1,452.54.

而原来在-30时刻签订60天期限的合约时，远期价格F0(T)是1403.22，二者作差得到的结果是在t=30时刻的价值，再折现30天到t=0时刻即可得到现在的value。

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