STAT/ACTSC 446/846
Assignment #3 (due March 13th, 2009) Over 50 marks
Note:
Recall that, when handing in your assignment, you are requested to use a cover page showing only your UWID number and your
section (846 students: also write “846” on the cover page) and to write your full name on the next page.
Assignments must be handed in during the TAs office hours in MC 6095
before or on the due date (see the Calendar on UWACE for
details).
This assignment looks long but answers are often shorter than the question!
Problem 1:
[4marks]
The initial value
S
0
of the index is 20. The index is modeled in a one period framework with time step T=1 year:
ω
1
ω
2
S
1
19
25
The riskfree rate
r
(annual rate, continuously compounded) is 5%. A company sells indexlinked contracts with a maturity
T
= 1 year for which an initial investment of $1000 yields a payoff given by
1000 max
parenleftbigg
1 +
G
,
0
.
9
S
T
S
0
parenrightbigg
at maturity, where
S
T
is the value of the index at time
T
and
k >
0.
G
is a minimum guaranteed rate.
(a)[
2pts]
Calculate the risk neutral probability. And find the price by calculating the expectation of the discounted payoff
under the risk neutral probability.
(b)[
1pt]
If
G
= 0, is the contract priced fairly (that is, is the initial investment of $1000 equal to the noarbitrage price of
this derivative contract)? Justify your answer.
(c)[
1pt]
Which value of
G
gives a fairly priced index linked contract?
Problem 2:
[6marks]
Consider a market model with
T
= 2, i.e.
t
= 0
,
1
,
2, and riskless interest rate
r
=
1
4
(
effective interest rate per period, but
you will also get full credit if you considered a continuously compounded interest rate since the question was ambiguous.
), and
one risky asset whose prices are described by the following diagram:
S
2
= 12
ω
1
S
1
= 8
3
4
d57
d115
d115
d115
d115
d115
d115
d115
d115
d115
d115
1
4
d37
d75
d75
d75
d75
d75
d75
d75
d75
d75
d75
S
2
= 6
ω
2
S
0
= 5
2
5
d67
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
d7
3
5
d27
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
d55
S
2
= 6
ω
3
S
1
= 4
2
7
d57
d115
d115
d115
d115
d115
d115
d115
d115
d115
d115
5
7
d37
d75
d75
d75
d75
d75
d75
d75
d75
d75
d75
S
2
= 3
ω
4
(Do not use decimal approximations in calculations.)
1. (2pt) Compute a hedge for the European put option with the exercise price equal to 5.
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 Spring '09
 idk..
 market model, uu uu uu

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