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天才出于勤奋 · 2023年07月14日

不明白为什么cost也是用连续利率算

  1. FRM I
  2. Financial Markets And Products

NO.PZ2019052801000039

问题如下：

A farmer plans to sell 50,000 tons of soybeans in six months, he decides to short futures contracts to hedge against the price deline. The current price of soybeans is $ 508/ton, the contract size is 100 tons, the storage cost for the soybeans is 1.5% per year. The continuously compounded rate is 5%, what's the price for the futures contract ?

选项：

A.

$35412.

B.

$76634.

C.

$50217.

D.

$52478.

解释：

D is correct.

考点：远期合约定价

解析：

FP  =S0e(r+C)×T=508e(0.05+0.015)×0.5=524.78FP\;=S_0e^{(r+C)\times T}=508e^{(0.05+0.015)\times0.5}=524.78

x100 tons per contract = $52478

cost的算法为什么不是508*1.5%/2 然后加上508再乘e^5%*0.5

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3 个答案

品职答疑小助手雍 · 2023年07月15日

离散算法按连续复利这个变换一下就好了，508*（1+1.5%）^0.5 *（1+5%）^0.5

你的计算过程对storage cost默认了一个semi annual compounding，对利率有没有这样做，不统一。最好还是统一一致。

品职答疑小助手雍 · 2023年07月14日

折现这种事情一般都是看题目要求的，本题给了连续复利的折现率就直接用连续复利了。

有些题目确实也会直接单独给一个金额，甚至可能不折现。所以主要还是看题面描述

天才出于勤奋 · 2023年07月14日

那可不可以这么理解，如果这道题是离散利率，计算就是508*1.5%/2 然后加上508再乘（1+5%）^0.5。

品职答疑小助手雍 · 2023年07月14日

同学你好，cost每天都会产生，连续复利折现很正常，类似的公式讲义210页左右有讲。

天才出于勤奋 · 2023年07月14日

那是不是如果折现是离散利率，cost也用离散算。cost和折现保持一样的算法？

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