Krzys’ Ostaszewski, http://www.math.ilstu.edu/krzysio/, Exercise 112, 7/7/7
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The current price of a stock is $50. The stock value either increases by 6% or decreases
by 5% in six months. The risk-free interest rate is 4% per annum with continuous
compounding. Determine the value of a six-month European call option with a strike
price of $52.
A. $0.63
B. $0.64
C. $0.65
D. $0.66
E. $0.67
Solution.
The risk-neutral probability of the up move is
1
!0.04
" 0.95
e2
p=
# 0.638194.
1.06 " 0.95
In the case of the up move the stock price will be $50 !1.06 = $53, and in the case of the
down move it will be $50 ! 0.95 = $47.50. The call will pay $1 in the case of the up
move, and $0 in the case of the down move. The value of the call is therefore
p ! $1! e
Answer A.
"0.04!
1
2
# $0.63.
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