Question 1:

Consider the one step trinomial model from lecture with the following parameters:

S

0

= 100

S

u

= 110

S

m

= 100

S

d

= 90

p

u

= 0

.

4

p

d

= 0

.

3

M

0

= 1

M

u

=

M

d

=

M

m

= 1

.

05

Find all possible no-arbitrage values of a call option with strike

K

= 100.

Question 2:

Consider the following modification to the multistep binomial tree from lecture:

S

n

+1

=

S

n

e

t

+

tx

n

+1

where

x

n

takes values of 1 or

1 with probabilities

p

and 1

p

.

i) Find

p

such that the

N

-period logarithmic return has expected value (

1

2

2

)

T

.

ii) Find the risk-neutral branching probability. When using the risk-neutral probability, what is the

expectation of the

N

-period logarithmic return in the limit as

N

?

1

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