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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 putcall parity condition. If so indicate clearly which securities you would buy and sell and
indicate the amount of your riskfree arbitrage profit.
2. Suppose a twomonth European put option on a nondividendpaying stock is currently selling for $2 and that the
stock price is $47, the strike price is $50, and the riskfree 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, riskfree 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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View Full Document4. A stock is currently selling for $100. The current price of a 6month call option on the stock with an exercise
price of $105 is selling for $12. The riskfree interest rate is 5%, compounded continuously.
a) Assuming there is no dividend paid on the stock, compute the price of a 6month 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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 Spring '11
 mazaheri
 Management

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