互换题目

问题如下：

Sixty days ago, a European company entered into a receive-fixed GBP, pay-fixed EUR swap with the following specifications:

Currently, long positions in the associated bonds with unit face value are priced at EUR 1.06 and GBP 0.97, respectively. If the current exchange rate is 0.91 GBP/EUR, the value of the swap to the European company is closest to:

选项：

A.A.GBP 250,500. B.B.GBP 396,000. C.C.GBP 693,057.

解释：

A Correct because the value of a fixed-for-fixed currency swap at some future point in time, say Time t, is simply the difference in a pair of fixed-rate bonds, one expressed in currency a [here GBP] and one expressed in currency b [here EUR]. To express the bonds in the same currency units, we convert the currency b bond into units of currency a through a spot foreign exchange transaction at a new rate S_t. The value of a 'receive currency a, pay currency b' (fixed-for-fixed) swap at any time t expressed in terms of currency a is the difference in bond values: V_CS = V_a – S_tV_b.

Moreover, the NA (or par value) of the bond denominated in currency a (NA_a) must equal the spot exchange rate S₀ times the notional amount (or par value) of the bond denominated in currency b (NA_b). That is, NA_a = S₀ × NA_b = 0.88 × 5,000,000 = GBP 4,400,000.

Finally, the value of each fixed-rate bond can be computed by multiplying the notional amount in that currency by the value of a long position in a bond with face value equal to one unit of that currency (the values given in the question).

Hence, V_CS = (4,400,000 × 1.06) – [0.91 × (5,000,000 × 0.97)] = 4,664,000 – 4,413,500 = GBP 250,500.

B Incorrect because it uses the exchange rate at initiation, rather than after 60 days, to convert the EUR fixed-rate bond value to GBP, yielding:

V_CS = (4,400,000 × 1.06) – [0.88 × (5,000,000 × 0.97)] = 4,664,000 – 4,268,000 = GBP 396,000.

C Incorrect because it misinterprets the stated exchange rates as EUR per GBP, rather than GBP per EUR, i.e., concluding that S₀ = 1/0.88 = 1.1363636 (GBP/EUR) and S_t = 1/0.91 = 1.0989011 (GBP/EUR). This yields:

NA_a = S₀ × NA_b = 1.1363636 × 5,000,000 = GBP 5,681,818 and

V_CS = (5,681,818 × 1.06) – [1.0989011 × (5,000,000 × 0.97)] ≈ 6,022,727 – 5,329,670 = GBP 693,057.