THE UNIVERSITY OF IOWA
22S.175 Exam 1
Monday
February 22, 2010
6:30 – 8:30 PM
106 GLH
Write legibly.
Show your steps.
Explain your reasoning.
Simplify your answers.
Each question is worth 10 points.
Total =
100
points.
1.
The riskfree interest rate is constant through time.
The time0 price for a 2year 105strike European call option on a dividendpaying stock
is 4.
The time0 price for a 2year 105strike European put option on the same stock is 6.
The time0 forward price for a forward contract that delivers one share of the stock at
time 2 is 100.
Determine the continuously compounded riskfree interest rate.
2. A oneperiod securities market model is given by
S
(0) = [1 1 1],
S
(1,
Ω
)
=
21
.
6 0
00
.
8
001
.
5
x
⎡
⎤
⎢
⎥
⎢
⎥
⎢
⎥
⎣
⎦
.
(The jth column of the matrix gives the jth security’s prices in the three states of nature
at time 1.
The securities pay no dividends.)
Determine the range of values for
x
so that this model is arbitrage free.
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 Spring '08
 Tang,Q
 Probability theory, Riskfree interest rate

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