23.2

a. The call seller receives $55.50 for writing the call. If the stock price at expiration is $660, the call expires valueless and the investor keeps the entire $55.50 as a profit. If the stock price is $760, the value of the call at expiration is $760 - $720 = $40. In other words, the call seller must deliver a stock worth $760 for an exercise price of only $720. The investor's

net profit is $55.50 - $40-$15.50. The call seller will clear a positive net profit as long as the value of the call at expiration is less than the initial premium received for writing the option; this requires that the stock price remain below $720 + $55.50 = $775.50.

b. The put seller receives $52 for writing the put. If the stock price at expiration is $660, the final value of the put is $720 - $660 = $60. In other words, the put seller must pay an exercise price of $720 for a stock worth only $660. The investor's net profit is $52 $60-$8. If the stock price is $760, the put expires valueless and the put seller keeps the entire $52 as a profit. The put seller will clear a positive net profit as long as the value of the put at expiration is less than the initial premium received for writing the option; this requires that the stock price remain above $720 - $52 = $668.

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net profit is $55.50 - $40-$15.50. The call seller will clear a positive net profit as long as the value of the call at expiration is less than the initial premium received for writing the option; this requires that the stock price remain below $720 + $55.50 = $775.50. b. The put seller receives $52 for writing the put. If the stock price at expiration is $660, the final value of the put is $720 - $660 = $60. In other words, the put seller must pay an exercise price of $720 for a stock worth only $660. The investor's net profit is $52 $60-$8. If the stock price is $760, the put expires valueless and the put seller keeps the entire $52 as a profit. The put seller will clear a positive net profit as long as the value of the put at expiration is less than the initial premium received for writing the option; this requires that the stock price remain above $720 - $52 = $668. 23.3 Put-call parity states that value of stock + value of put = value of call + present value of exercise price. Therefore, in the case of Witterman $60 $55+value of put = $8.05+ 1.04 and value of put = $8.05 +$57.69 - $55 - $10.74. 23.4 The value of a put option is higher when the exercise price is higher. You would be willing to pay more for the right to sell a stock at a high price than the right to sell it at a low price. 23.5 First consider the payoff to the put holder in the lower volatility scenario: Stock price Put value $620 $840 $100 0 In the higher volatility scenario, the value of the stock can be $500 or $960. Now the payoff to the put is