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lcrcp3 · 2023年10月08日

如题

NO.PZ2023041003000021

问题如下:

Johnson prices a three-year Libor-based interest rate swap with annual resets using the present value factors presented in Exhibit 1.

Exhibit 1 Present Value Factors

Johnson also uses the present value factors in Exhibit 1 to value an interest rate swap that the bank entered into one year ago as the receive-floating party. Selected data for the swap are presented in Exhibit 2. Johnson notes that the current equilib­rium two-year fixed swap rate is 1.12%.

Exhibit 2 Selected Data on Fixed for Floating Interest Rate Swap

From the bank’s perspective, using data from Exhibit 1, the current value of the swap described in Exhibit 2 is closest to

选项:

A.

-$2,951,963.

B.

-$1,849,897.

C.

-$1,943,000.

解释:

The value of a swap from the perspective of the receive-fixed party is calculated as


The swap has two years remaining until expiration. The sum of the present values for Years 1 and 2 is


Given the current equilibrium two-year swap rate of 1.12% and the fixed swap rate at initiation of 3.00%, the swap value per dollar notional is calculated as

V = (0.03 - 0.0112)1.967975 = 0.036998

The current value of the swap, from the perspective of the receive-fixed party, is $50,000,000 x 0.036998 = $1,849,897.

From the perspective of the bank, as the receive-floating party, the value of the swap is -$1,849,897.



1.画时间轴的话,折现因子归属到底是哪种?我认为应该是1,时间越长利率越高,折现因子就越小,0.965136应该对应第三年。

2.现在是站在1这个时间点,还有两年到期,算PV的和不应该是第2年和第3年的和吗?怎么会是第1年和第2年,把前两年的和加一起最后站在的不是2时间点吗?

2 个答案

李坏_品职助教 · 2023年10月09日

嗨,努力学习的PZer你好:


对,是一样的,days to maturity意思就是还剩几天到期。days=90那就代表90天后收到的1美元,现在的现值是present value factor这么多。

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

李坏_品职助教 · 2023年10月08日

嗨,从没放弃的小努力你好:


present value factors意思是,预计1年后收到的1美元,现在的现值=0.990099。预计2年后收到的1美元,现在现值=0.977876. 这个不是第几年的意思,他给的就是对应期限的现金流在当前的现值。


swap还剩2年到期,也就是现在是已经比刚签订Swap合约的时候过去1年了,未来的现金流只剩下两笔:1年后的现金流和2年后的现金流。



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就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

lcrcp3 · 2023年10月08日

那这种给maturity的方式,和有的题给的是days to maturity:90 180 270 360,这两种给法表达的意思一样吗?