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徐威廉 · 2024年10月28日

这个解释里面DV01为什么都要除以100?

NO.PZ2023100703000108

问题如下:

A derivatives trader at an investment bank is considering how to hedge a relatively illiquid 7-year USD interest-rate swap the bank just entered into as the fixed-rate payer. The trader recognizes that any profit resulting from the bid-ask spread may be lost if the trade is hedged with another illiquid 7-year swap and considers using the more liquid 5-year and 10-year USD interest-rate swaps as a hedge. To evaluate this possible hedge, the trader runs a two-variable regression model using changes in the 5-year and 10-year swap rates to explain changes in the 7-year swap rate. The regression model, regression results, and information about the swaps are given below:


What are the correct notional amounts of 5-year and 10-year swaps needed to hedge a USD 100 million notional amount of 7-year swaps?

选项:

A.USD 23.76 million of 5-year swaps, and USD 65.81 million of 10-year swaps B.USD 24.71 million of 5-year swaps, and USD 65.36 million of 10-year swaps C.USD 34.03 million of 5-year swaps, and USD 47.74 million of 10-year swaps D.USD 68.85 million of 5-year swaps, and USD 36.52 million of 10-year swaps

解释:

C is correct.

To determine the notional amount of the 5-year and 10-year swaps required to hedge USD 100 million notional of a 7-year swap it must be understood that the

P&L of the position is given by:

-F7*(DV017/100)*Δyt7 – F5*(DV015/100)*Δyt5 – F10*(DV0110/100)*Δyt10

In a perfect hedge this P&L would equal zero.Substituting the predicted change in the 7-year swap rate from the regression equation into the P&L equation given above, and retaining only the terms related to the changes in the 5-year and 10-year swap rates gives the following equation for the P&L:

[-F7*(DV017/100)*β5 – F5*(DV015/100)]*Δyt5 + [-F7*(DV017/100)*β10 – F10*(DV0110/100)]*Δyt10

Now set the terms inside the brackets equal to zero so the P&L is not dependent on changes in the 5-year and 10-year swap rates. This leaves:

F5 = -F7 * (DV017/DV015) * β5

F10 = -F7 * (DV017/DV0110) * β10

Now, using the information derived from the regression and the DV01s, the notional amounts of the 5-year and 10-year swaps can be calculated.

F5 = -100* (0.084/0.061) * 0.2471 = -34.03, USD 34.03 million as the fixed-rate receiver

F10 = -100* (0.084/0.115) * 0.6536 = -47.74, USD 47.74 million as fixed-rate receiver

A is incorrect. The ratio of fixed rates is used instead of the ratio of DV01s in the formula.

F5 = -100* (0.02492/0.02591) * 0.2471 = -23.76, USD 23.76 million as the fixed-rate receiver

F10 = -100* (0.02492/0.02475) * 0.6536 = -65.81, USD 65.81 million as fixed-rate receiver

B is incorrect. This answer choice simply multiplies the Betas and the initial notional amount.

D is incorrect. This answer choice uses the ratio of DV01s but not the betas, then divides by 2 since the position is a butterfly.

F5 = -100* (0.084/0.061) / 2 = -68.85, USD 68.85 million as the fixed-rate receiver

F10 = -100* (0.084/0.115) / 2 = -36.52, USD 36.52 million as the fixed-rate receiver

这个解释里面DV01为什么都要除以100?

2 个答案
已采纳答案

李坏_品职助教 · 2024年10月29日

嗨,努力学习的PZer你好:


因为DV01的默认数据是百分比。比如表格中的0.061的DV01 实际上应该是0.061%的意思。那也就是5年期的DV01 / 100.

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虽然现在很辛苦,但努力过的感觉真的很好,加油!

徐威廉 · 2024年10月31日

这好无聊啊,考试的时候DV01也是这样吗?

李坏_品职助教 · 2024年10月31日

嗨,爱思考的PZer你好:


这个题目确实出的不够严谨,正式考试中 会给你写出来DV01 (%)这样。这就是告诉你,DV01数字的单位是百分比。


如果不写%的话,也得看作是百分比的形式。

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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!

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