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沐沐的方盒 · 2023年10月05日

麻烦老师用画图法帮忙求一遍过程，谢谢

  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

如题，麻烦老师用画图法帮忙求一遍过程

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2 个答案

李坏_品职助教 · 2023年10月06日

嗨，爱思考的PZer你好：


如果按照课上画图法（不推荐），图里面的FP就是题目里的F0.

所以Value = (Bt + AIt - PVCt) - (F0+AI_T) / (1+rf)^(90/360) ，但题目没有给出AIt的相关信息，所以无法直接求出答案。还是要借助重新定价法找到如下的关系：

也就是用Ft去代替Bt和AI_t，然后才能得出最终答案。(Ft + AI_T) / (1+rf)^(90/360) = (Bt + AIt - PVCt)，

所以value = (Bt + AIt - PVCt) - (F0+AI_T) / (1+rf)^(90/360)

= (Ft+AI_T) / (1+rf)^(90/360) - (F0 + AI_T) / (1+rf)^(90/360)，这里AI_T抵消了，结果和重新定价完全一样。

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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

李坏_品职助教 · 2023年10月06日

嗨，从没放弃的小努力你好：


这个题问的是Forward的Value，直接套公式是最快的。如果画图：

首先F0的意思是0时刻签订的远期合约在T时刻的结算价格。Ft表示假设在t时刻重新签订的远期合约在T时刻的结算价格。

所谓的value实际上就是问你从0时刻到t时刻，这个合约价值变动了多少？那也就是Ft-F0, 但是这俩都是T时刻的结算价，所以要从T时刻折现3个月。最后取负号（short），然后乘以5（因为有5份合约）。



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就算太阳没有迎着我们而来，我们正在朝着它而去，加油！

沐沐的方盒 · 2023年10月06日

老师你这个不是李老师上课讲的画图大法，你这还是重新定价法啊

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