Question

Suppose term of the structure of interest rate is flat in both US and Japan. The Japanese rate is 5% per annum and US rate is 10% per annum (both with continuous compounding). A financial enter a currency swap: (a) received 6% per annum in yen and (b) 9% per annum in dollars and (c) exchange once a year (d) the principal $10 million (dollars) and $1200 (yen). Life of swap is equal to two years and the exchange rate is S=110 yen/per dollar. What is the value of the swap (in terms of bond prices)?

Answer 1

Given info:- swap life = 2 years

Dollar Bond Cash flow:-
1st year Paid amount (in million) = $10*9% =$0.9
2nd year paid amount (in million) =Principal +Interest

=10+0.9 =$10.9
Value of Dollar bond is  
(BD) = 0.9e^-0.1*1 + 10.9e^-0.1*2 = 9.7385

Yen Bond Cash flow:-
1st year Paid amount (in million) = 1200*6% =72
2nd year paid amount (in million) =Principal +Interest =1200+72 = 1272
Value of Yen bond is  
(By) =72 e^-0.05*1+ 1272e^-0.05*2 = 1219.44

Here Exchange rate is 110 Yen =$1
So, 1219.44 Yen = 1219.44/110 = $11.09
Value of swap in dollars is
Vswap = 11.09 -9.74 = 1.35 million