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##### Draw a payoff diagram for each of the following portfolios:

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Options Homework;Fall 2014;3. Draw a payoff diagram for each of the following portfolios;a. Buy a put X = \$20, buy a call X = \$30.;b. Buy a put X = \$50 (which costs \$16.12), sell a put X = \$45 (which costs \$12.52), sell a;put X = \$40 (which costs \$9.26), buy a put X = \$30 (which costs \$4.02). Draw the gross;and net payoff diagram for this portfolio.;4. A stock currently trades at \$45, but may increase to \$60 or fall to \$35 over the next;year. The risk-free rate is 5%. Using the binomial method, value a call option and a put;option, both with X= \$50. Then verify that the prices you obtained satisfy put/call parity.;Suppose that the actual market price of the call option with X = \$50 was \$5.;Demonstrate that you could engage in arbitrage to take advantage of this mispricing. You;need to show the up-front profit and show that your position is risk-free over the year.;5. A stock trades at \$40. Over the next six months it could go up to \$48 or down to \$33.;In the subsequent six-month period, if the stock starts at \$48 it could go all the way to;\$60 or it could fall to \$39. If the stock starts at \$33, it could go up to \$38 or it might fall;to \$27. Value a put option on this stock with X = \$40 and a call option with X = \$36.;Assume an annual risk-free rate of 4%.

Paper#28247 | Written in 18-Jul-2015

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