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sentimentalbus · 2023年08月25日

进一步确认一下S(t=30天)时的价格

  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

这道题好像没有明确148这个价格到底是S(t=30天)时候的Spot price还是Forward price，如果148是Spot price的话，是不是按照下列的算法会更加科学？


148*(1+0.15%)^90/360=148.0555


根据重新定价法：short position: PVt,T[F0(T)-Ft(T)]= (146-148.0555 )/(1+0.15%)^90/360=-2.05473


-2.05473/100*5*100,000,000=-10,273,647.38?


请问我的思路对吗？

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1 个答案

pzqa35 · 2023年08月28日

嗨，努力学习的PZer你好：


本题考察的是forward contract的valuation，通过题目我们可以发现此题使用重新定价法的计算方式会更为简单一些。可以根据题目已知的数据，将其直接带入公式得Vt =PV[Ft -F0]=(148-146)/(1+0.0015)90/360 = 1.9993，1.9993/100 * 100,000,000 * 5= CAD9,996,500，又因为此题求得是short position，因此取负号为 - CAD9,996,500

同学的疑问在于148这个价格到底是Ft还是St，那么根据题意我们看到题目给的是“the contracts have three months left to expiration, and have a price of CAD 148.”，所以这里给的应该是Ft，同时如果是要给St，那应该说的是underlying asset的价格，在此题里面就应该是government bond的价格，而不是contract的价格。举个简单的例子，我未来要卖出一瓶水，我现在签的合约价格是4个月后以146元去卖，如果用Ft来表述，就是1个月以后这个合约的价格变成了148，如果用St来表述，就是1个月后，我这瓶水的价格是148，所以要判断是Ft还是St，我们需要关注的是这个价格到底说的是forward合约还是说的underlying asset。

----------------------------------------------
虽然现在很辛苦，但努力过的感觉真的很好，加油！

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