Can someone please help me out with the solution to problem number 14 on Swap Markets and Contract on page 124 of Schweser’s. I don’t really get it how they have solved this one.
The value of a swap (or any derivative, for that matter) is:
Value = PV(what you will receive) − PV(what you will pay)
Here, the bank is paying 5% fixed on €800,000: 1¼% (= €10,000) in 70 days and 1¼% in 160 days, plus the principal in 160 days. The present value is:
0.9900(€10,000) + 0.9736(€810,000) = €798,517
In USD, that’s:
€798,517 / (€0.75/$) = $1,064,688.
The bank is receiving LIBOR on $1,000,000: 1.05% (= 4.2%/4 = $10,500) in 70 days, plus the equivalent of par ($1,000,000) in 70 days. (They don’t receive the par payment in 70 days, but when the floating rate resets, the present value (70 days from today) of the interest plus principal will be $1,000,000.) The present value is:
0.9923($1,010,500) = $1,002,719.
So their value is:
$1,002,719 − $1,064,688 = −$61,969
Note that we use the (USD) LIBOR rates to discount the USD payments, and the Eurobor rates to discount the EUR payments.
I wrote an article on valuing currency swaps that may be of some help here: http://financialexamhelp123.com/valuing-currency-swaps/
Makes a lot of sense now and the article actually helped. Thank you Mr. Campbell!
You’re quite welcome.