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Ryoooh · 2020年10月21日

问一道题：NO.PZ2019052801000039

问题如下：

A farmer plans to sell 50,000 tons of soybeans in six months, he decides to purchase 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：

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

x100 tons per contract = $52478

请问老师，这一题的仓储成本为什么是用连续复利计算呢？我就只是按年化的单利计算的

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品职答疑小助手雍 · 2021年08月29日

嗨，爱思考的PZer你好：

首先，这题求的是future的价值，也就是一个未来的价格，所以不需要求仓储成本的PV，只需要计算从目前到期货到期日需要花费多少仓储成本（FV）就可以了。

因为这个仓储成本是和期间的价值复合的过程，所以只能通过508*e^((5%+1.5%)*0.5)这样来求未来豆子本身的价值和仓储话费总和的FV。

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努力的时光都是限量版，加油！

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品职答疑小助手雍 · 2020年10月22日

嗨，爱思考的PZer你好：

这个其实可以算是固定套公式来做的了，不过复利或者连续复利，答案差别也不会特别大。不要用单利来计算。

一般来说FV和PV之间的转换，我个人是建议用复利或者连续复利的。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

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AliciaLi · 2021年08月29日

这里仓储cost每年是508*1.5%，怎么算他的pv啊，他这是半年的仓储成本，能详细列一下式子吗

AliciaLi · 2021年08月29日

仓储成本pv是不是这么算：（1.5%/2 * 508）* e^(5%*0.5)=3.81

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