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Problem Set 3 Solutions
Econ 136, Fall 2009
A note about grading:
5: no major or minor errors
4: no more than a few minor errors
3: a major or many minor errors
2: multiple major errors
1: multiple major errors and portions left blank
0: blank or never turned in.
1.
Dynamic Trading
a)
As before, we price using LOOP by 1) calculating the payoff of the asset, 2) constructing
a replicating portfolio, 3) pricing the asset using the price of the replicating portfolio.

Calculate the payoff.
S
is the statecontingent payoff and equals the number of heads, and
X
= 0.2, so using the formula for the call payoff we get
State
S
Put payoff: max (SX, 0)
2 Heads
2
max (20.2, 0) = 1.8
1 Head
1
max (10.2, 0) = 0.8
0 Heads
0
max (00.2, 0) = 0

Create a replicating portfolio. From lecture, we know (first four columns):
State
AD1
AD2
AD3
Call Option
1.8*AD1 + 0.8AD2 + 0*AD3
2 Heads
1
0
0
1.8
1.8
1 Head
0
1
0
0.8
0.8
0 Heads
0
0
1
0
0
Price
0.25
0.50
0.25
?
1.8*0.25 + 0.8*0.5 = 0.85
We can replicate the payoff of the call option by constructing a portfolio of 1.8 shares of AD1
and 0.8 shares of AD2.

Price the call using LOOP. The price of the replicating portfolio is 1.8*0.25 + 0.8*0.5 =
0.85. This is the price at date zero for buying the call option.
b)
To construct a dynamic trading strategy directly for the put option, we need to work
backwards on the event tree. There are three time periods: t=0, 1, 2.
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 Fall '08
 SZEIDL

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