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计算结果不一样

NO.PZ2023040401000106

问题如下：

Baywhite observes that one-month MRR is 1.2% and two-month MRR is 1.5%. Which of the following rates is closest to the forward rate that Baywhite would expect on 1m1m forward rate agreement?

选项：

1.80%

1.35%

3.55%

解释：

A is correct. The APR of the monthly compounded two-month rate is 1.499%. Dividing (1.01499/12)2 by (1.012/12) equals 1.001499. Subtracting 1 and then multiplying by 12 gives 1.7982%. Thus, the approximate forward rate is 1.80%.

B is incorrect because this is a simple average of the two spot rates.

C is incorrect because this result is derived from simply dividing (1.01499/12) by (1.012/12), then subtracting 1, and then multiplying by 12.

为什么我按老师讲解算出来的不是1.8%？

嗨，努力学习的PZer你好：

题目告诉你1个月的市场利率是1.2%，2个月的市场利率是1.5%，让你求出1-2这个期间的远期利率。

题目给的条件都默认是年化利率，我们需要转化成月度利率。

也就是现在0-2的复利是：(1+1.5% / 12)^2，这里(1+1.2%/12)表示1个月的复利，期限是2个月，所以括号外面是2次方。

0-1的复利是：(1+1.2% / 12),

1-2的复利是：(1+x / 12)，

0-2的复利应该是和(0-1的复利) × (1-2的复利)相等的，所以（1+1.5% / 12)^2 = (1+1.2% / 12) × (1+x / 12)，可以求出x = 1.8%.

如果你算的结果不是1.8%，可能是用了连续复利（也就是e的r*t次方那种）。此题的期限很短，都是1个月、2个月，所以用离散复利即可。

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虽然现在很辛苦，但努力过的感觉真的很好，加油！

计算结果不一样

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