STOR 890, Spring 2011, Homework 2
Note:
Try these problems yourselves and contribute to the class discussion on Thur. 3/3.
(1) Consider a binomial model with
T
= 2 where the stock has an initial price of $100 and can go
up 15% or down 5% in each period. The price of a European call option on this stock with strike
price $115 and maturity
T
= 2 is $5.424. What should be the initial value of a riskfree security
that pays $1 at
t
= 1? We assume a constant interest rate
r
.
(2) A European call option and put option on a stock both have a strike price of $20 and an
expiration date in three months. Both sell for $3. The riskfree annual interest rate is 10%, the
current stock price is $19, and a $1 dividend is expected in one month.
Identify an arbitrage
opportunity open to a trader.
(3) Consider a twoperiod binomial tree with
S
(0) = $50,
r
= 2%. After one period the price of
the stock can go up to $55 or drop to $47, and it will pay (in both cases) a dividend of $3. If it
goes up the first period, then it can go up to $58 or down to $48 the second period. If it goes down
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 Spring '08
 Staff
 $55, $41, $47, $58

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