连续函数，和离散函数的推导

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：

$35412.

$76634.

$50217.

$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

红色圈出来的是老师上课讲的公式，在这种离散情况下，PVCost在t0时刻到底怎么求，是不是题目得告诉具体cost金额，那除以的利率和时间呢？连续函数怎么用上面这个公式类似推导出来

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1 个答案

李坏_品职助教 · 2024年05月18日

嗨，努力学习的PZer你好：

离散复利的情况下，PVcost0 = 未来的成本 / (1+无风险利率)^T。

比如预计在2个月之后会产生1块钱的持有成本，那么PVcost0 = 1 / [(1+无风险利率)^(2/12)].

连续复利的情况下，FP = S0 * e^[(无风险利率+C)*T]，这里的时间间隔T也和离散复利一样，是年化的。

C指的是比率形式的年化持有成本率，题目会直接告诉我们年化的持有成本率是1%，那么连续复利的公式里面C=1%.

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NO.PZ2019052801000039 问题如下 A farmer plans to sell 50,000 tons of soybeans in six months, he cis to short futures contracts to hee against the priline. The current priof soybeans is $ 508/ton, the contrasize is 100 tons, the storage cost for the soybeans is 1.5% per year. The continuously compounrate is 5%, what's the prifor the futures contra? A.$35412. B.$76634. C.$50217. $52478. 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}=524.78FP=S0e(r+C)×T=508e(0.05+0.015)×0.5=524.78x100 tons per contra= $52478 以下是我的解题思路按老师讲的大原则，FP=S0+cost-income，同时期货定价和远期定价一样，所以通过期初V0=0构建公式。FP/(e^R*T)=s0(1+1.5%)^0.5请问以上哪里不对呢？

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连续函数，和离散函数的推导

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