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梦梦 · 2024年07月07日

利率互换的bank pay X to A

NO.PZ2020021204000047

问题如下:

Company A can borrow at a fixed rate of 4.3% for five years and at a floating rate of Libor plus 30 basis points. Company B can borrow for five years at a fixed rate of 5.9% and at a floating rate of Libor plus 100 basis points. As a swaps trader you are in touch with both companies and know that Company A wants to borrow at a floating rate and that Company B wants to borrow at a fixed rate. Both companies want to borrow the same amount of money. Design a swap where you will earn 10-basis points, and which will appear equally attractive to both sides.

解释:

The spread between the fixed rates offered to Companies A and B is 5.9% - 4.3% or 1.6%. The spread between the floating rates is 70 basis points or 0.7%. The difference between these two spreads is 1.6% - 0.7% or 0.9%. It should be possible to design a swap where the parties are in aggregate 0.9% better off. The bank (intermediary) wants 0.1%. This leaves 0.4% for each side. We should therefore be able to design a swap where Company A borrows at Libor + 0.3% - 0.4% or Libor - 0.1 % and Company B appears to borrow at 5. 9% - 0.4% = 5.5%. If the bank pays X% to A we require 4.3% + Libor - X% = Libor - 0.1% so that X = 4.4. Similarly, if B pays Y% to the bank, we require Y% + 1% = 5.5% so that Y = 4.5. The swap arrangement is


老师好,1、if bank pays X% to A是什么意思?bank已经拿了0.1%,A和B互分0.4%了,为啥bank还要pay X%to A?

2、蓝色公式没看明白

3 个答案
已采纳答案

李坏_品职助教 · 2024年07月07日

嗨,从没放弃的小努力你好:


我们作为swaps trader(也就是图中的bank)是要分别和A、B两家公司都各签订一份swap。


首先,A公司的最终目标是以浮动利率借款(就是A最终想支付浮动利率),但是A公司的相对优势是在4.3%的固定利率上。所以A先找其他银行支付4.3%的固定利率,为了抵消这个固定利率的影响,我们银行要给A支付固定利率X,然后A公司再给我们银行支付浮动利率libor。(绿色字体部分,就是我们银行与A公司签订的swap)

这样一来,A公司最终的效果就是固定利率被大部分抵消了,剩下了浮动利率libor,达到了A的目标。


由于题目要求进行swap交易之后,银行要分0.1%的好处费,这样留给A公司的好处只有0.4%了。而A公司自己本来支付浮动利率的成本 = libor + 0.3%, 算上swap的0.4%的好处,A最终的利率 = libor + 0.3% - 0.4% = libor - 0.1%.


所以考虑银行支付X给A之后,A支付的最终利率 = 4.3% - X + libor = libor - 0.1%, 所以X = 4.4%


同理,B公司自己支付固定利率成本 = 5.9%, 考虑0.4%的好处之后利率成本 = 5.9%-0.4% = 5.5%.

由于B最终是希望支付固定利率,而B的相对优势是在浮动利率,所以B先找其他银行支付libor + 1%,我们银行给B支付libor,抵消了B的浮动利率,然后B再给我们银行支付Y(红色字体是我们银行与B签订的swap)。如此一来,B最终只剩下固定利率,完成目标。

B最终支付的利率 = libor + 1% + Y - libor = 5.5%,Y = 4.5%.

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

梦梦 · 2024年07月07日

“所以A先找其他银行支付4.3%的固定利率,为了抵消这个固定利率的影响,我们银行要给A支付固定利率X”,1、“其他银行”和“我们银行”不是一家吧?2、为了抵消固定利率的影响,为什么是支付X而不是4.3%?

梦梦 · 2024年07月10日

明白了,就是“我们银行要给A支付固定利率X,然后A公司再给我们银行支付浮动利率libor。(绿色字体部分,就是我们银行与A公司签订的swap)”,所有的题目,如果是这种设计方案的,都是先假设1、节约的利息双方平分;2、和swap tader的浮动利率交易都是libor,而不是libor加/减多少点?

李坏_品职助教 · 2024年07月10日

嗨,从没放弃的小努力你好:


对,是这样的。

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加油吧,让我们一起遇见更好的自己!

梦梦 · 2024年07月10日

好的,谢谢

李坏_品职助教 · 2024年07月08日

嗨,努力学习的PZer你好:


  1. 不是一家。
  2. 因为抵消固定利率并不是为了恰好弥补4.3%,具体是要支付给A多少的固定利率,取决于4.3% - X + libor = libor - 0.1% 这个等式的计算结果。 不是拍脑袋乱定的。

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加油吧,让我们一起遇见更好的自己!

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2024-03-30 08:57 1 · 回答

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2022-05-26 01:01 1 · 回答

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2022-03-20 02:14 1 · 回答