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学习王 · 2023年10月26日

为什么不用长期国债定价公式呢

  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

为什么不用长期国债定价公式呢

FP=（FP bond）*（1+r）^t-AI T-FVCoupon


underlying是bond呀

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1 个答案

pzqa35 · 2023年10月26日

嗨，从没放弃的小努力你好：


这道题是说H这个人卖出了5个bond的远期，这个远期在0时刻的价格是146，在到期三个月前是价格是148，都是按照面值的百分比来报价，问现在他手上的合约价值是多少？所以这道题是在t时刻求价值，不是在0时刻定价。我们需要搞清楚什么是定价什么是valuation，定价就是在0时刻签订合约时约定的未来买卖商品的价格，用的是定价的公式，valuation时在t时刻我们需要知道我们签的合约有多少价值，用的是valuation公式。

那么这道题就是在到期前三个月求valuation，已经告诉了我们在到期前三个月的价格FPt=148，那么我们可以采用重新估值法来求即可，因为时short方，所以valuation=[（146-148）/100]/(1+0.15%)0.25*100000000*5=-9996253. 计算略微差异为小数点保存位置不一样。

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