为什么这里的T=1/12

问题如下：

Ace serves as a futures commission merchant to assist several of its commodity trading adviser (CTA) clients to clear and settle their futures margin positions with the futures exchange. Ace is reviewing the copper futures market for a CTA client considering a long copper futures position for the first time. Details of the copper futures market are as follows:

Today’s copper spot price is $4.25 per pound, and the constant risk-free rate is 1.875%. Each contract has a $10 storage cost payable at the end of the month.

Which of the following statements best characterizes the margin exposure profile of Ace’s CTA client if it enters a one-month copper futures contract?

选项：

A.The CTA will be expected to post $10,000 initial margin and would receive a margin call if the copper futures price were to immediately fall below $4.10 per pound or below a price of $102,425 per contract. B.The CTA would be expected to post $10,000 in initial margin and would receive a margin call at any time over the life of the contract if the copper futures price were to immediately fall below $3.86 per pound or below a price of $96,425 per contract. C.The CTA will be expected to post $10,000 initial margin, but we cannot determine the exact futures price at which a margin call will occur as the futures MTM is settled each day and the contract value resets to zero.

解释：

Solution

A is correct.

The CTA will face a margin call if the copper contract price falls by more than $4,000, or $0.16 (= $4,000/25,000) per pound. We may solve for the price at which the CTA receives a margin call by first solving for the initial futures contract price, f₀(T), at contract inception as follows: f₀(T) = [S₀ + PV₀(C)](1+r)^T.

Solve for PV₀(C) per pound as follows: PV₀(C) = $9.98 (= $10[1.01875^–(1/12)]).

Substitute PV₀(C) = $9.98 into Equation 4 to solve for f₀(T):

f₀(T) = [($4.25 × 25,000) + $9.98](1.01875 ^(1/12))

f₀(T) = $106,425 per contract (≈ $4.257 per pound).

So, $106,425 − $4,000 = $102,425 per contract, and $4.257 − $0.16 = $4.10 per pound.

B is incorrect as it assumes there is no maintenance margin, and while C may be true under some circumstances, the change in A is immediate (occurs at trade inception).

中文解析：

由表格可知该铜期货合约的初始保证金是10,000.维持保证金是6,000.

因此当保证金水平低于6,000时，会收到追加保证金的通知，即期货合约价格下降的空间为4,000美元，即每磅允许下跌0.16美元(= 4,000/25,000美元)。

计算期货合约的价格f₀(T)：

f₀(T) = (S₀) (1 + r) ^T+FV(C) = [(4.25 x 25000) (1.01875 ^(1/12))]+10 =106,425

因此当合约价格低于102,425美元（每份合同106,425美元- 4,000美元= 102,425美元）时，需要追加保证金。

另外，由于每份合同是106,425美元，对应的是每磅4.257美元。

因此当价格低于4.10美元（每磅4.257美元- 0.16美元= 4.10美元）时，会收到保证金催收电话。