Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 83, 12/16/6
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May 2000 Casualty Actuarial Society Course 8 Examination, Problem No. 24
(multiple choice answers added)
You are given the following:
• The risk-free rate is a constant annual 8% compounded continuously.
• The three-month futures price for an asset is $400.
• Dividends on the asset are paid continuously at a constant dividend-yield rate, q, of
2.4% per annum.
What is the current price for the asset, assuming no arbitrage opportunity?
A. $392.08
B. $394.44
C. $389.73
D. $369.25
E. $361.07
Solution.
The basic futures-spot parity formula is F = Se! T . But when the underlying produces
income, its price must be replaced by the current price without that income, e.g., without
the dividend. In this case, the stock will yield dividends continuously at the rate of 2.4%
per annum, and time to futures maturity is 0.25 years, so that its price of without those
dividends is Se!0.024"0.25 . Given that F = $400, T = 0.25 years, ! = 0.08, we obtain
400 = S ! e"0.024!0.25 ! e0.08!0.25 .
Therefore,
S = $400 ! e"0.056!0.25 # $394.44.
Answer B.
© Copyright 2006 by Krzysztof Ostaszewski.
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