Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/
Author of a study manual for exam FM available at:
http://smartURL.it/krzysioFM (paper) or http://smartURL.it/krzysioFMe (electronic)
Instructor for online seminar for exam FM: http://smartURL.it/onlineactuary
If you find these exercises useful, please consider making a tax-deductible donation to
the Actuarial Program at Illinois State University:
http://smartURL.it/donateISUactuary
May 2005 Casualty Actuarial Society Course 8 Examination, Problem No. 25
(multiple choice answers added), also Dr. Ostaszewski’s online exercise No. 103
posted May 5, 2007
ABC Insurance Company has entered into a 10-year swap with XYZ Insurance
Company. Under the terms of the swap, ABC receives interest at 4% per annum in Swiss
francs and pays interest at 8% per annum in U.S. dollars. Interest payments are
exchanged once per year. The principal amounts are 10 million dollars and 13 million
francs. Suppose that XYZ declares bankruptcy at the end of year 7, right before the swap
payment is to be made. The exchange rate at the end of year 7 is $0.80 per franc. Assume
that forward rates are realized and, at the end of year 7, the interest rate is 4% per annum
in Swiss francs and 9% per annum in U.S. dollars for all maturities. All interest rates are
quoted with annual compounding. Calculate the cost to ABC at the end of year 7 due to
XYZ’s bankruptcy.
A. $0
B. $270,000
C. $816,000
D. $1,570,000
E. $10,816,000
Solution.
The cost to ABC is the difference between what it is owed in remaining payments by
XYZ, and what it owes to XYZ. At the end of year 7, ABC is owed the following amount
in Swiss francs (using the interest rates prevailing then and cash flows promised):
0.04 ⋅13,000,000 ⋅ a4 4% + 13,000,000 ⋅1.04 −3.
The exchange rate is then 0.80 dollars per franc, so that the amount owed ABC in U.S.
dollars is
(
)
0.80 ⋅ 0.04 ⋅13,000,000 ⋅ a4 4% + 13,000,000 ⋅1.04 −3 = 10,816,000.
The amount ABC owes XYZ, in U.S. dollars, is
0.08 ⋅10,000,000 ⋅ a4 9% + 10,000,000 ⋅1.09 −3 ≈ 10,546,870.53.
The net amount owed ABC is
$10,816,000 − $10,546,870.53 = $269,129.47.
Answer B.
© Copyright 2006 by Krzysztof Ostaszewski.
All rights reserved. Reproduction in whole or in part without express written
permission from the author is strictly prohibited.
Exercises from the past actuarial examinations are copyrighted by the Society of
Actuaries and/or Casualty Actuarial Society and are used here with permission.