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Branson · 2024年04月09日

买卖的报价

  1. FRM I
  2. Valuation And Risk Models

NO.PZ2020011303000037

问题如下：

In a dollar roll a USD 10,000,000 30-year 6% pool is sold for 103.25 and bought for 102.80. The settlement is on the fourteenth of the month for both months. The interest is paid at the end of the month. The proceeds of the sale can be invested at 4% per year (compounded monthly), and interest and principal payments on the pool during the month of the roll would amount to 0.4% of the par value. What is the value of the roll?

选项：

解释：

USD selling price is 10,325,000 + 10,000,000 × (14/30) × (0.06/12) = 10,348,333.

USD buying price is 10,280,000 + 10,000,000 × (14/30) × (0.06/12) = 10,303,333.

Investment of proceeds yields in USD 10,348,333 × 0.04/12 = 34,494.

Payments on the pool would be USD 40,000.

The value of the roll (USD) is

10,348,333 − 10,303,333 + 34,494 − 40,000 = 39,494


有一个dollar rool，面值10m，30年，6%利息的资产池，卖价是103.25，买价是102.8。每月的14号进行结算，利息每个月月底进行支付。卖了之后可以以4%年利率，每月复利来进行再投资。资产池每月需要支付的利息和本金是面值的0.4%。求这个dollar roll的价格？

真实的买卖价格需要考虑accrual interest：

USD selling price is 10,325,000 + 10,000,000 × (14/30) × (0.06/12) = 10,348,333.

USD buying price is 10,280,000 + 10,000,000 × (14/30) × (0.06/12) = 10,303,333.

卖价可以以4%月利率再进行投资，那么投资1个月的利息是：

Investment of proceeds yields in USD 10,348,333 × 0.04/12 = 34,494.

支付的利息与本金：

Payments on the pool would be USD 40,000.

The value of the roll (USD)：

10,348,333 − 10,303,333 + 34,494 − 40,000 = 39,494

Selling price 103.25 = 10,325,000

Buying price 102.80 = 10,280,000


为什么不是 10.325 Million 和 10.28 Million？

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1 个答案

pzqa27 · 2024年04月10日

嗨，爱思考的PZer你好：


因为常规的报价（就像本题第一句话的那种直说price）都是clean price，但是由于settlement的时间距离上一个付息日（上个月底）晚了14天，所以交割的是等了14天的债券，其中就包含了递延的利息，也就是6%年化coupon的14天的利息（和clean price合起来就是dirty price），也就是本题价格加上的部分。

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