这个解释里面DV01为什么都要除以100？

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)*Δy_t⁷ – F⁵*(DV01⁵/100)*Δy_t⁵ – F¹⁰*(DV01¹⁰/100)*Δy_t¹⁰

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)]*Δy_t⁵ + [-F⁷*(DV01⁷/100)*β¹⁰ – F¹⁰*(DV01¹⁰/100)]*Δy_t¹⁰

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