011 - 11 Option Payoffs and Option Strategies Answers to...

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73 Answers to Questions and Problems 1. Consider a call option with an exercise price of $80 and a cost of $5. Graph the profits and losses at expira- tion for various stock prices. 11 Option Payoffs and Option Strategies
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74 CHAPTER 11 OPTION PAYOFFS AND OPTION STRATEGIES 2. Consider a put option with an exercise price of $80 and a cost of $4. Graph the profits and losses at expiration for various stock prices. .
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ANSWERS TO QUESTIONS AND PROBLEMS 75 3. For the call and put in questions 1 and 2, graph the profits and losses at expiration for a straddle comprising these two options. If the stock price is $80 at expiration, what will be the profit or loss? At what stock price (or prices) will the straddle have a zero profit? With a stock price at $80 at expiration, neither the call nor the put can be exercised. Both expire worthless, giving a total loss of $9. The straddle breaks even (has a zero profit) if the stock price is either $71 or $89. 4. A call option has an exercise price of $70 and is at expiration. The option costs $4, and the underlying stock trades for $75. Assuming a perfect market, how would you respond if the call is an American option? State exactly how you might transact. How does your answer differ if the option is European? With these prices, an arbitrage opportunity exists because the call price does not equal the maximum of zero or the stock price minus the exercise price. To exploit this mispricing, a trader should buy the call and exercise it for a total out-of-pocket cost of $74. At the same time, the trader should sell the stock and deliver the stock just acquired through exercise for a $75 cash inflow. This produces a riskless profit without invest- ment of $1. Because the option is at expiration, both the American and European options have the same right to exercise. Therefore, the American or European character of the option has no effect on the trading strategy. 5. A stock trades for $120. A put on this stock has an exercise price of $140 and is about to expire. The put trades for $22. How would you respond to this set of prices? Explain. At expiration, the put price must equal the maximum of zero or the exercise price minus the stock price to avoid arbitrage. Therefore, the put price should be $20 in this situation, but it trades for $22.
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76 CHAPTER 11 OPTION PAYOFFS AND OPTION STRATEGIES This difference gives rise to an arbitrage opportunity, because the put is priced too high relative to its theoret- ical value. To exploit this, the trader should simply sell the put and receive $22. Now the option can be exer- cised against the trader or not. If it is not exercised, the put expires worthless, the obligation is complete, and the trader retains the $22 as total profit. However, the purchaser of the option may choose to exercise imme- diately. In this case, the seller of the put must buy the stock for the exercise price of $140. The trader then sells the stock for $120 in the market, giving a $20 loss on the exercise. But the put seller already received $22,
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011 - 11 Option Payoffs and Option Strategies Answers to...

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