Homework Set 2
STAT GU4265 & GR5265 – Stochastic Methods in Finance
Irene Hueter
1.
Consider a onestep binomial model for two noarbitrage assets
X
and
Y
with parameters
0
< d <
1
< u,
and initial price
X
Y
(0) = 1
.
We cannot assume that the dollar prices of
X
and
Y
are correlated.
(a) Find the price and the hedge of a contract
V
that pays off
V
1
= max(
X
1
, Y
1
)
.
(b) Compute the price of the contract
V
using both martingale measures
P
Y
and
P
X
.
(
Hint
: In the case that there is no perfect hedge for this model, find the hedging portfolio
that minimizes the variance of the difference between the value of the contract and the value
of the hedging portfolio.)
2.
Consider an American contract
V
that pays off max(6$
τ
, S
τ
) = max(6
, S
$
)
·
$
τ
at exercise
time
τ
≤
2 in a twostep binomial model with parameters
u
= 2
, d
=
1
2
, r
=
1
4
,
and
S
$
= 4
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 Spring '16
 Yuchong Zhang

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