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Elsa陆艳 · 2022年02月18日

Estimate the futures price on August 1

NO.PZ2020021204000036

问题如下:

Assume that the bond that will be cheapest to deliver in a Treasury bond futures contract pays semi-annual coupons at the rate of 10% per annum on May 1 and November 1 and will be delivered on September 1. The bond's quoted price on August 1 is 130.00 and its conversion factor is 1.2341. Estimate the futures price on August 1 assuming that all interest rates are 4% (continuously compounded).

选项:

解释:

There are 92 days between May 1 and August 1 (30, 30,31, and 1 in May, June, July, and August, respectively) and 184 days between May 1 and November 1 (30, 30, 31, 31, 30, 31, 1 in May, June, July, August, September, October, and November, respectively). The dirty price of the bond is therefore:

130 + 5 X 92/184 = 132.5

No coupons will be paid in the 31-day period between August 1 and September 1. The time to delivery is 31/365 = 0.0849 years. The dirty futures price is therefore:

132.5e0.0849X0.04=132.9509

The accrued interest on September 1 is 5 X 123/184= 3.3423. The clean futures price is therefore:

132.9509 - 3.3423 = 129.6086

Dividing by the conversion factor we obtain the estimated futures price as:

129.6086/1.2341= 105.0227

老师您好,我有点没理解全这个题目,题目不是让估计8月1日的价格吗?我以为clean+5月-8月的AI,就可以结束了,为什么求到了9月的?

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品职答疑小助手雍 · 2022年02月18日

同学你好,首先这个期货是9月1号交割的期货,一切对期货价格的估计都是对9月1号的价格的估计。

所以给的是8月1号的债券的报价130,需要用AI和CF推算的是9月1号交割的期货 的价格。

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