Problem Set 3
Ec 136, Fall 2009
This problem set is due on September 24, Thursday, in class. Sorry, no late
problem sets are accepted! All students must submit problem sets individu
ally. Please write your name, section time and GSI on the front page of your
solution.
1. Dynamic trading
In the coin toss economy in lecture 6, consider a call option with strike
X
= 0
:
2
and
expiration in period 2, which is written on the number of heads. Formally, the payo/
of this option is
max (
S
°
X;
0)
where
S
is the total number of heads (
0
,
1
or
2
) and
X
= 0
:
2
. Assume that the two securities traded in the economy are the Head and Tail
assets discussed in class.
(a) According to the LOOP, what is the price of this call option at date zero?
(b) Use backward induction to construct a dynamic trading strategy that replicates the
payo/ of the call option.
(c) Suppose that the coins being tossed are replaced, and that the new coins are not fair,
so that the probability of heads is now
3
=
5
. However, the prices and payo/s of the Head
and Tail security are unchanged. Is the price of the call option a/ected?
2. Present value of car payments
[based on 2006 Spring midterm]
Montague Autos is o/ering interestfree credit on a new car that costs $11,250. The deal
is that you pay down $750 and then $250
a month
for the next 42 months.
Capulet
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 Fall '08
 SZEIDL
 Time Value Of Money, Interest Rate, Mathematical finance

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