CFA题目分享：二级Derivatives PP题分享-1

An analyst values a fixed-for-fixed currency swap by building a portfolio to replicate the swap cash flows using the following bonds:

If the current exchange rate is $1.10/€1, the no-arbitrage value (in $ millions) of the swap is closest to:

A –1.64.

B 1.64.

C 1.80.

解析：

A.Incorrect because the answer corresponds to the value of swap in € (not in $), and the currency swap legs are inverted.

V_CS = €62 million – $70 million /($1.10/€1) = –$1.636363 million ~ –$1.64 million.

B.Incorrect because the answer corresponds to the value of swap in € (not in $).

V_CS = $70 million / ($1.10/€1) – €62 million = $1.636363 million ~ $1.64 million.

C.Correct because the value of the currency swap, expressed in $, is computed as follows:

V_CS = V_$ – S₀ × V_€, where

V_CS = value of the currency swap in $;

V_$ = value of $-denominated bond;

V_€ = value of €-denominated bond; and

S₀ = spot exchange rate in $/€.

V_CS = $70 million – $1.10/€1 × €62 million = $1.80 million.

The value of a fixed-for-fixed currency swap, V_CS, is the difference in the price of two bonds. That is, the value of a currency swap is simply the value of a bond in currency a (V_a) less the value of a bond in currency b (V_b), expressed in terms of currency a, as follows:

V_CS = V_a – S₀ × V_b

Here, S₀ is the spot exchange rate at time 0.