Krzys’ Ostaszewski, http://math.illinoisstate.edu/krzysio/krzys.html
http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
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Spring 2006 Casualty Actuarial Society Course 8 Examination, Problem No. 20
(multiple choice answers added) and Dr. Ostaszewski’s online exercise No. 94 posted
March 3, 2007
A currency swap has a remaining life of 15 months. The swap involves exchanging
annual euro interest for dollar interest. The principal amounts are also exchanged at the
end of the life of the swap. You are given the following additional information:
• The swap involves exchanging interest at 11% on 25 million euro for interest at 8% on
$30 million once a year.
• The term structure of interest rates in both Europe and the United States is currently flat.
• If the swap were negotiated today, the interest rates exchanged would be 8% in euros
and 6% in dollars.
• All interest rates are quoted with annual compounding.
• The current exchange rate (dollars per euro) is 1.25.
Calculate the value of the swap (in dollars) to the party paying dollars.
A. $2000000 B. $2390000 C. $2510000 D. $2640000 E. $2750000
Solution.
The value of the remaining payments in euros is (valued in euros)
0.11⋅ 25000000 1.11⋅ 25000000
+
≈ 27902397.20.
3
15
1.08 12
1.08 12
The value of the remaining payments in dollars is (valued in dollars)
0.08 ⋅ 30000000 1.08 ⋅ 30000000
+
≈ 32489294.80.
3
15
1.06 12
1.06 12
The value of the swap to the party paying dollars is
⎛ 0.11⋅ 25000000 1.11⋅ 25000000 ⎞ ⎛ 0.08 ⋅ 30000000 1.08 ⋅ 30000000 ⎞
1.25 ⋅ ⎜
+
+
⎟ −⎜
⎟≈
3
15
3
15
⎜⎝
⎟⎠ ⎜⎝
⎟⎠
12
12
12
12
1.06
1.08
1.08
1.06
≈ 1.25 ⋅ 27902397.20 − 32489294.80 ≈ 2388701.70.
Answer B.
© Copyright 2007 by Krzysztof Ostaszewski.
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Exercises from the past actuarial examinations are copyrighted by the Society of
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