We are currently working on payoff diagrams in my intro to investments class. Was wondering if anyone could help me draw a payoff diagram to the following problems. Is there any easy way to do this?

OPTIONS
(3) Determine the payoff at maturity for the following portfolio: A long forward contract on a stock (with a forward price = F0) and a long European put on the same stock with the same maturity as the forward and a strike price X = F0. Show that this portfolio has the same payoffs as a European call on the stock with a strike price of F0. Draw the payoffs of each the contracts (i.e. the forward, the put and the call) on the same diagram.

(4) A trader buys a call option with a strike price of \$45 and a put option with a strike price of \$40. Both options have the same maturity. The call costs \$3 and the put costs \$4. Draw a diagram showing the payoff and the profits to holding these options.

FUTURES
(5) Assume that the risk-free rate is 9% per year with continuous compounding and that the dividend yield on a stock index varies throughout the year. In February, May, August and November dividends are paid at a rate of 5% per year. In other months, dividends are paid a rate of 2% per year. Suppose that the value of the index on July 31, 2006 is 300. What is the futures price for a contract deliverable on December 31, 2006? Hint: You need to calculate the average dividend yield.

(6) Suppose that the risk free interest rate is 10% per year with continuous compounding and that the dividend yield on a stock index is 4% per year. The level of the index is 400, and the futures price for a contract deliverable in four months is 405. Is this an arbitrage opportunity? If so, what positions would you take?

### Comments (9)

isnt this sort of cheating?

i guess it could be considered in the grey area.. help if you want to..if not no reason to post.

I think I figured out the payoff diagram to number 4.

It looks like this:

http://img482.imageshack.us/img482/1545/payoffxm3.jpg

sorry, i wont help

My head hurts

I don't think guiding someone on the right track would be considered "cheating", not unless you write out the complete answers with work shown. It is just simply helping someone out, just as if they were to work with a friend or go to a TA for help. And who better to ask than the "best" in finance.

Anyways, Im in the same type of class and we have just begun covering this topic, so Im afraid I would not be the most credible source for an answer. But goodluck

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haha, I really hope that kid was joking that refused to help because he considered it cheating. wow.

5

I calculated my average dividend yield to be (4/12)5+(8/12)2 = 3% Value of the index on July 31st is 300. They want me to calculate from end of July to end of December this is 5 months, so T = 5/12?

Anyone know the equation to figure out the futures price of the contract ?

bump 