為什麼這個題目不是用e計算？

NO.PZ2024061801000098

问题如下：

Consider the following information:

$1 million notional value, semiannual, 18-month maturity.

Spot SOFR rates: 6 months, 2.6%; 12 months, 2.65%; 18 months, 2.75%.

The fixed rate is 2.8%, with semiannual payments.

Which of the following amounts is closest to the value of the swap to the floating rate payer, assuming that it is currently the floating-rate reset date?

选项：

−$1,026.

$1,026.

−$12,416.

$12,416.

解释：

但為什麼這題不是用e計算？？是因為SOFR嗎？

之前做其他相似題目，例如下面這題是也用e計算。swap 不是都用e計算嗎？

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1 个答案

李坏_品职助教 · 2025年05月04日

嗨，努力学习的PZer你好：

这个题目是swap，利率互换。利率互换其实用离散复利计算就可以了。题库里有个别swap的计算题用了e，其实是不规范的，当然结果相差很小。

你说的e那是连续复利，是用于equity index forward或者option的题目。

如果题目特别要求用continuously compounding，那是让你用e计算的意思，如果没有这个要求，那swap不需要用e计算。

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其它问题这个答案的格式有问题 fixe= ($14,000 / 1.0260.5) + ($14,000 / 1.02651) + [($1,000,000 + $14,000) /1.02751.5] = $13,821 + $13,639 + $973,566 = $1,001,026

2025-04-27 09:49 1 · 回答

NO.PZ2024061801000098 问题如下 Consir the following information:$1 million notionvalue, semiannual, 18-month maturity.Spot SOFR rates: 6 months, 2.6%; 12 months, 2.65%; 18 months, 2.75%.The fixerate is 2.8%, with semiannupayments.Whiof the following amounts is closest to the value of the swto the floating rate payer, assuming thit is currently the floating-rate reset te? A.−$1,026. B.$1,026. C.−$12,416. $12,416. B fixe= ($14,000 / 1.0260.5) + ($14,000 / 1.02651) + [($1,000,000 + $14,000) /1.02751.5] = $13,821 + $13,639 + $973,566 = $1,001,026Note thwe are a (semiannual) reset te, so the floating-rate portion ha value equto the notionamount.Vsw= (Bfixe− Bfloating) = $1,001,026 − $1,000,000 = $1,026 为什么 “we are a (semiannual) reset te, so the floating-rate portion ha value equto the notionamount.\"? present value of floating要怎么计算呢？

2025-04-23 12:38 1 · 回答