STAT/ACTSC 446/846
Assignment #3 (due November 9, 2007)
Note:
When handing in your assignment, please use a cover page showing only your UWID number and section (lecture)
number. Please write your name on the first actual page of your assignment. ACTSC/STAT 846 students: please indicate on
the cover page that you are a graduate student by writing “846”.
Recall that assignments must be handed in at MC 6028 before 3pm.
If you want to use Excel for some of the problems (e.g., (4) and (5)), you are welcome to do so. In that case, hand in a copy
of your spreadsheet and explain which approach/formulas you used.
(1) (This is a variant on Exercise 5.5 of
Financial Economics
(FE).) A oneperiod arbitragefree model
has two assets with the following price evolution: for asset 1,
S
1
(0) = 10
.
8 and
S
1
(1
, ω
1
) = 12, while
S
1
(1
, ω
2
) = 8; for asset 2,
S
2
(0) = 10 and
S
2
(1
, ω
1
) =
a
, where
a >
0 is a constant to be determined,
while
S
2
(1
, ω
2
) = 3. In addition, you are told that a call option on asset 1 with a strike price of 9
has a price of 2.1.
a) Compute the stateprice vector implicit in this model and determine
a
.
b) Show that the implied interest rate for this model is 0 (hint: construct a riskless portfolio whose
payoff is always 1 and find its time 0 value).
c) Determine the riskneutral probabilities for this model.
d) The price of a call option on asset 2 is 2.8. What is the strike price of this option?
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 Fall '09
 Adam
 Strike price, MC 6028

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