What is the difference between entering a long forward position when the forward price is $100 and taking a long position in a call option with a strike price of $100?

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

1. What is the difference between entering a long forward position when the forward price is $100 and taking a long position in a call option with a strike price of $100?

2. A European call option that expires in 6 months and has a strike price of $30 sells for

$3. The stock price is $30, the risk-free rate is 0%, and a $2 dividend is expected in 4 months.

 

(a) Using put-call parity, what must be the price of a 6-month European put option on the stock with a strike price of $30?

(b) Suppose the put option has price $6 instead. Carefully explain the available arbitrage strategy and find the profit (be sure to show the strategy has no risk).

 

3. You sell a put with strike price $15 for $4 and buy a put with strike price $25 for $10.

 

(a) Draw the payoff and profit diagrams of this spread. Is this a bull or bear spread?

(b) What is the largest attainable profit? What is the largest possible loss?

(c) What is the break-even price?

(d) Fill in the following table to show your profit for various ending values of the underlying asset:

 

4. You own 1000 American call options (10 option contracts) on a non-dividend-paying stock whose current price is $25. The strike price is $20 and the maturity is 1 year. The 1-year risk-free rate is 5%. Your friend urges you to exercise now and get $5000 ($5 ×1000) because he’s sure the stock price will drop. Carefully describe an alternate strategy that is guaranteed, no matter what happens, to pay out even more in present value (and report that value).

5. You sell a European call with strike K and expiration time T and buy a European put on the same asset with the same strike and expiration. The put costs $5. If the strike K is equal to the current forward price (for a forward contract on the asset with

 

delivery time T ), how much must you have received from selling the call? [Hint: what does put-call parity tell you?]

 

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