MGTC71-PS3A - UNIVERSITY OF TORONTO AT SCARBOROUGH...

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UNIVERSITY OF TORONTO AT SCARBOROUGH DEPARTMENT OF MANAGEMENT MGTC71: Introduction to Derivatives Markets Problem SET – 3 1.The following are European call and put prices for a stock on November 9 (today): Last transaction Prices ($) Calls Puts Strike Price Dec Mar June Dec Mar June 65 3 4 5/8 -- 2 -- 4 The maturity dates of the options are on Fridays preceding the third Saturday in each month which is 37 days from now (for the December options). You may assume that the annual risk free interest rate is 7%. The stock closed at 65 1/4 on November 9. a) is there a violation of the put-call parity condition. If so indicate clearly which securities you would buy and sell and indicate the amount of your risk-free arbitrage profit. 2. Suppose a two-month European put option on a non-dividend-paying stock is currently selling for $2 and that the stock price is $47, the strike price is $50, and the risk-free interest rate is 6% (C.C.). a) Is there an opportunity for arbitrage? Design a strategy to exploit this arbitrage? b) If the stock pays a dividend of $2/per share in 1 month, would the above market prices still provide an arbitrage opportunity? 3. You own a call option on Microsoft with an expiration date of 6 months from now. Microsoft is going to start paying a large dividend every quarter to shareholders. (Investors are indifferent to Microsoft paying the dividend and retaining the cash in the company - thus there is no stock movement at the time of the announcement.) a) What do you expect to happen to the price of the call option you own? What about a put option if you owned that? (Assume that volatility, exercise price and interest rates remain constant). b) Assume you are selling Microsoft put options to investors. You would like to sell or write a put option with a strike price of $65 with 4 months to maturity. How can you use a combination of Microsoft’s stock, risk-free bonds and Microsoft call options to hedge the risk you would have from selling put options? Be precise: (Drawing some graphs may help you solve this problem - but still decide what securities you should buy or sell.) Assume that risk free interest rate is 6%, and a call with a strike price of $65.00 sells for $2.75. The current stock price is $62.00. c) What is the minimum amount you should charge for this put option that you will sell?
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4. A stock is currently selling for $100. The current price of a 6-month call option on the stock with an exercise price of $105 is selling for $12. The risk-free interest rate is 5%, compounded continuously. a) Assuming there is no dividend paid on the stock, compute the price of a 6-month put option on the stock with exercise price equal to $105. b) Imagine that the put is selling in the market for $13. Is there an arbitrage opportunity? If so, execute a strategy to
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MGTC71-PS3A - UNIVERSITY OF TORONTO AT SCARBOROUGH...

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