Learning objectives: Describe the types, position variations, and typical underlying assets of options. Explain the specification of exchange-traded stock option contracts, including that of nonstandard products. Describe how trading, commissions, margin requirements, and exercise typically work for exchange-traded options.
Questions:
724.1. A stock with a volatility of 31.0% is currently trading at $47.00 while the risk-free rate is 3.0%. An investor purchases a European straddle with a strike price of $45.00: a straddle is a call and a put on the same stock with identical strike prices and expiration dates. The straddle expires in nine months (0.75 years). The price of the put is $3.50. Among the following choices, which best summarizes the final stock price required (in nine months, at expiration) in order for the trader to realize at least a positive net PROFIT on this trade?
a. Stock to stay inside the interval {$35.00 to $55.00}; i.e., both above $35.00 and below $55.00
b. Stock to stay inside the interval {$37.00 to $57.00}; i.e., both above $37.00 and below $57.00
c. Stock to fall outside the interval {$35.00 to $55.00}; i.e., either below $35.00 or above $55.00
d. Stock to fall outside the interval {$40.00 to $54.00}; i.e., either below $40.00 or above $54.00
724.2. Last week, Peter purchased one contract for 100 call options on StrongDrill Corporation (ticker: SDC) with a strike price of $15.00. The options on SDC are exchange-traded. Today the stock price is $18.00 so Peter's options are "in the money." Consider the impact of the following four corporate actions if they were immediately affected, when the stock price is $18.00:
I. 2-for-1 split
II. 20.0% stock dividend
III. 1-for-5 reverse split
IV. 12.0% one-time cash dividend
Each of the following statements is true EXCEPT which is false?
a. The (II.) stock dividend will have no impact on the strike price or quantity of Peter's option position
b. Peter's intrinsic value in his option position is $300.00 and it will be unchanged by any of the four scenarios
c. Among the four corporate actions, the highest adjusted strike price will be realized by (III.) the 1-for-5 reverse split
d. Among the four corporate actions, this greatest adjusted number of options will be realized by (I.) the 2-for-1 split
724.3. Assume a European call option has an exercise (aka, strike) price, K = $95.00, and a time to expiration of one year. The risk-free rate is 3.0% per annum. The current stock price, S(0) = $110.00 and the stock pays a 3.0% dividend (the dividend happens to equal to the risk-free rate!) and this dividend has an equivalent lump sum present value (PV) over the life of the option equal to $3.35. Consider the following statements about this call option:
I. If the option's value is $20.52, then it's time value is about $5.52
II. If the stock does NOT pay any dividends, the minimum value (lower bound) of this European option would be about $17.81
III. If the stock pays a 3.0% dividend with a discounted present value (over the life of the option) equal to $3.35, then the minimum value of this European option is below its intrinsic value
IV. If this were instead an American option, and if the stock pays a dividend, then it might be optimal to exercise early
Which of the above statements is (are) TRUE?
a. None are true
b. Only I. is true
c. Only II. and IV. are true
d. All are true
Answers here:
Questions:
724.1. A stock with a volatility of 31.0% is currently trading at $47.00 while the risk-free rate is 3.0%. An investor purchases a European straddle with a strike price of $45.00: a straddle is a call and a put on the same stock with identical strike prices and expiration dates. The straddle expires in nine months (0.75 years). The price of the put is $3.50. Among the following choices, which best summarizes the final stock price required (in nine months, at expiration) in order for the trader to realize at least a positive net PROFIT on this trade?
a. Stock to stay inside the interval {$35.00 to $55.00}; i.e., both above $35.00 and below $55.00
b. Stock to stay inside the interval {$37.00 to $57.00}; i.e., both above $37.00 and below $57.00
c. Stock to fall outside the interval {$35.00 to $55.00}; i.e., either below $35.00 or above $55.00
d. Stock to fall outside the interval {$40.00 to $54.00}; i.e., either below $40.00 or above $54.00
724.2. Last week, Peter purchased one contract for 100 call options on StrongDrill Corporation (ticker: SDC) with a strike price of $15.00. The options on SDC are exchange-traded. Today the stock price is $18.00 so Peter's options are "in the money." Consider the impact of the following four corporate actions if they were immediately affected, when the stock price is $18.00:
I. 2-for-1 split
II. 20.0% stock dividend
III. 1-for-5 reverse split
IV. 12.0% one-time cash dividend
Each of the following statements is true EXCEPT which is false?
a. The (II.) stock dividend will have no impact on the strike price or quantity of Peter's option position
b. Peter's intrinsic value in his option position is $300.00 and it will be unchanged by any of the four scenarios
c. Among the four corporate actions, the highest adjusted strike price will be realized by (III.) the 1-for-5 reverse split
d. Among the four corporate actions, this greatest adjusted number of options will be realized by (I.) the 2-for-1 split
724.3. Assume a European call option has an exercise (aka, strike) price, K = $95.00, and a time to expiration of one year. The risk-free rate is 3.0% per annum. The current stock price, S(0) = $110.00 and the stock pays a 3.0% dividend (the dividend happens to equal to the risk-free rate!) and this dividend has an equivalent lump sum present value (PV) over the life of the option equal to $3.35. Consider the following statements about this call option:
I. If the option's value is $20.52, then it's time value is about $5.52
II. If the stock does NOT pay any dividends, the minimum value (lower bound) of this European option would be about $17.81
III. If the stock pays a 3.0% dividend with a discounted present value (over the life of the option) equal to $3.35, then the minimum value of this European option is below its intrinsic value
IV. If this were instead an American option, and if the stock pays a dividend, then it might be optimal to exercise early
Which of the above statements is (are) TRUE?
a. None are true
b. Only I. is true
c. Only II. and IV. are true
d. All are true
Answers here:
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