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?
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
老师好，
1、计算卖出和买入之间的利息要看利息是在每个月何时付？因为课程里讲的是卖出pool后当月的利息拿不到，所以要减去，但是这里又计算的是利息的AI。之所以计算AI就是因为这道题是月中交易，利息又是月末支付？如果月末交易，月末支付利息是不是就不用计算AI？
2、“and interest and principal payments on the pool during the month of the roll would amount to 0.4% of the par value. ”遇到了一道dollar roll和repo不同的题，其中一个不同说的是dollar roll不支付利息，这里咋又支付利息了呢？
而且利息支出为啥不是｛（1000万*0.4%）/12｝再安AI计算？
所有题目的利率不都是年化吗？4万应该是一年的利息支出吧？
