不懂

问题如下：

Sonal Johnson is a risk manager for a bank. She manages the bank’s risks using a combination of swaps and forward rate agreements (FRAs).

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

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%.

One of the bank’s investments is exposed to movements in the Japanese yen, and Johnson desires to hedge the currency exposure. She prices a one-year fixed-for-fixed currency swap involving yen and US dollars, with a quarterly reset. Johnson uses the interest rate data presented in Exhibit 3 to price the currency swap.

Johnson next reviews an equity swap with an annual reset that the bank entered into six months ago as the receive-fixed, pay-equity party. Selected data regarding the equity swap, which is linked to an equity index, are presented in Exhibit 4. At the time of initiation, the underlying equity index was trading at 100.00.

The equity index is currently trading at 103.00, and relevant US spot rates, along with their associated present value factors, are presented in Exhibit 5.

Johnson reviews a 6 x 9 FRA that the bank entered into 90 days ago as the pay-fixed/ receive-floating party. Selected data for the FRA are presented in Exhibit 6, and current Libor data are presented in Exhibit 7. Based on her interest rate forecast, Johnson also considers whether the bank should enter into new positions in 1 x 4 and 2 x 5 FRAs.

Three months later, the 6 x 9 FRA in Exhibit 6 reaches expiration, at which time the three-month US dollar Libor is 1.10% and the six-month US dollar Libor is 1.20%. Johnson determines that the appropriate discount rate for the FRA settlement cash flows is 1.10%.

Based on Exhibit 6 and the three-month US dollar Libor at expiration, the payment amount that the bank will receive to settle the 6 x 9 FRA is closest to:

选项：

$19,945.

$24,925.

$39,781.

解释：

A is correct.

Given a three-month US dollar Libor of 1.10% at expiration, the settlement amount for the bank as the pay-fixed (receive-floating) party is calculated as

Settlement amount pay-fixed (receive floating)

= NA × {[L_m – FRA₀ ]t_m }/[1 + D_m t_m ]}.

Settlement amount pay-fixed (receive floating)

=$20,000,000 × {[0.011 – 0.0070] × (90/360)]/[1 + 0.011(90/360)]}.

Settlement amount pay-fixed (receive floating)

=$20,000,000 × (0.001)/1.00275 = $19,945.15.

中文解析：

本题考察的是在FRA到期时刻求value。仍然使用画图法。

向上箭头为：NP

向下箭头为：$\frac{NP\times\left[1+0.7\%\times{\displaystyle\frac{90}{360}}\right]}{1+1.1\%\times{\displaystyle\frac{90}{360}}}$

令向上箭头-向下箭头得到此时的value，其中NP=20,000,000