1.The following information is given about options on the stock of a certain company. S0 = 23 X = 20 rc = 0.09 T = 0.5 s2 = 0.15 No dividends are expected. What value does the Black-Scholes-Merton model predict for the call? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 cents.)
a. 5.35
b. 1.10
c. 4.73
d. 6.50
e. none of the above
2. The following information is given about options on the stock of a certain company. S0 = 23 X = 20 rc = 0.09 T = 0.5 s2 = 0.15 No dividends are expected. Use this information to answer questions 1 and 2. Suppose you feel that the call is overpriced. What strategy should you use to exploit the apparent misvaluation? (Due to differences in rounding your calculations may be slightly different. "none of the above" should be selected only if your answer is different by more than 10 shares.)
a. buy 791 shares, sell 1,000 calls
b. buy 705 shares, sell 1,000 calls
c. sell short 791 shares, buy 1,000 calls
d. sell short 705 shares, buy 1,000 calls
e. none of the above
3. Which of the following variables in the Black-Scholes-Merton option pricing model is the most difficult to obtain?
a. the volatility
b. the risk-free rate
c. the stock price
d. the time to expiration
e. the exercise price
4.The binomial price will theoretically equal the Black-Scholes-Merton price under which of the following conditions?
a. when the number of time periods is large
b. when the option is at-the-money
c. when the option is in-the-money
d. when the option is out-of-the-money
e. none of the above
5.What is the reason for executing a gamma hedge?
a. the volatility can change
b. the stock price can make a large move
c. the stock price moves are too small for a delta hedge to work
d. there is no true risk-free rate
e. none of the above
6.Which of the following statements about the volatility is not true?
a. the implied volatility often differs across options with different exercise prices
b. the implied volatility equals the historical volatility if the option is correctly priced
c. the implied volatility is determined by trial and error
d. the implied volatility is nearly linearly related to the option price
e. none of the above
7. Consider a stock priced at $30 with a standard deviation of 0.3. The risk-free rate is 0.05. There are put and call options available at exercise prices of 30 and a time to expiration of six months. The calls are priced at $2.89 and the puts cost $2.15. There are no
dividends on the stock and the options are European. Assume that all transactions consist of 100 shares or one contract (100 options). Use this information to answer questions 7 and 8. What is your profit if you buy a call, hold it to expiration and the stock price at expiration is $37?
a. $32.89
b. $30.00
c. $27.11
d. $32.15
11. Which of the following statements is true about the purchase of a protective put at a higher exercise price relative to a lower exercise price?
a. the breakeven is lower
b. the maximum loss is greater
c. the insurance is less costly
d. the insurance is more costly
e. none of the above
12. What is the disadvantage of a strategy of rolling over a covered call to avoid exercise?
a. the call premium is essentially thrown away
b. transaction costs tend to be high
c. the stock will incur losses
d. the call is more expensive when rolled over
e. none of the above
13. A synthetic long call position can be created with which of the following sets of transactions.
a. borrow the present value of the strike price, sell stock, sell put
b. lend the present value of the strike price, sell stock, buy put
c. sell put, buy stock, lend the present value of the strike price
d. buy stock, buy put, borrow the present value of the strike price
e. none of the above creates a synthetic long call position
14. A synthetic short put position can be created with which of the following sets of transactions.
a. borrow the present value of the strike price, sell stock, sell call
b. lend the present value of the strike price, sell stock, buy call
c. sell call, buy stock, lend the present value of the strike price
d. buy stock, buy call, borrow the present value of the strike price
e. none of the above creates a synthetic long call position