PROBLEM SET 6 (Team work)
Problem 1: Pricing of an option portfolio (20 points)
Consider a portfolio that consist of one share of stock XYZ, one unit of a put option
written on stock XYZ, and a short position in a call option written on stock XYZ. Both
the call and the put options have the same expiration date (1 year from today) and the
same strike price ($45). The price of stock XYZ evolves according to a binomial process.
The stock is currently trading at $45 and it is known that at the end of one year, the price
will be either $60 (in the “up” state) or $30 (in the “down” state).
1.
(
10 points
) What should be the current price of the option portfolio? Assume
that the riskfree interest rate is 8% per annum with continuous compounding.
2.
(
10 points
) Using a diagram, show how the
net
payoff (i.e., the profit/loss) of
the option portfolio varies as the stock price at the expiration date varies
between $0 and $75. Please, label the axes and the key points in the diagram
clearly.
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 Spring '11
 john
 Options, Investment and Portfolio Management, stock xyz

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