derivative

问题如下：

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