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kan1223 · 2022年01月08日

请教老师，这道题的148/146都站在一个时间点上吗？

  1. CFA II
  2. Derivative

NO.PZ2019010402000059

问题如下：

One months ago, Harvey took a short position in five 10-year Canadian government bond forward contracts, with each contract having a contract notional value of 100 million CAD. when the contracts were purchased, the contracts had a price of CAD 146 (quoted as a percentage of par). Now, the contracts have three months left to expiration, and have a price of CAD 148. The annualized three-month interest rate is 0.15%. The value of the forward contract is :

选项：

A.

- CAD9,996,500

B.

CAD9,996,500

C.

CAD1,999,300

解释：

A is correct

本题考察的是重新定价法求远期合约的价值。

For the long position:

Vt =PV[Ft -F0 ]=(148-146)/(1+0.0015)90/360 = 1.9993

1.9993/100 * 100,000,000 * 5= CAD9,996,500

本题求解的是short position，因此取负号为 - CAD9,996,500

when the contracts were purchased, the contracts had a price of CAD 146 (quoted as a percentage of par). Now, the contracts have three months left to expiration, and have a price of CAD 148. 


Vt =PV[Ft -F0 ]=(148-146)/(1+0.0015)90/360 = 1.9993


如上，做题时我理解这个买的时候146，时间点是T0, 然后148是三个月以后的，也就是T3, 然后应该把148往前折现了，再与146作差，就得出value，我哪里理解错了，请老师解答下，谢谢。


另外，什么时候是用 1+0.15%* 90/360, 这样的利率表达形式是不是只有swap一种情况？



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1 个答案

lynn_品职助教 · 2022年01月08日

嗨，从没放弃的小努力你好：


假设现在是时刻T0，那么148是站在3个月后的，然后，146是购买时的价格，也就是说3个月后，合约的long方可以赚得148-146=2。考题求T0时刻这份合约short方的价值，将3个月的2折现到T0，再加个负号即可。同学的思路错在146并不是现在的合约报价，所以根据题目给的已知信息，应该将T3时刻的合约价值折现到T0。

(1+0.15%)* 90/360 这种利率表达形式，同学是问年化利率去年华的方式嘛？衍生品中，所有涉及libor的，如FRA，利率互换，interest rate option等，都是单利，去年化形式都是这种。

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