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
Solution:
The correct answer is (c) 4.73.
For complete solution, refer the excel sheet.
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.
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.) Select
one:
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
Solution
N(d1) = 0.7915
Since the call is overpriced, therefore to make the arbitrage profit, we should buy 791 shares and
short 1,000 calls.
3. Which of the following variables in the Black-Scholes-Merton option pricing model is the
most difficult to obtain? Select one:
a. the volatility
b. the risk-free rate
c. the stock price
d. the time to expiration
e. the exercise price
Solution
The correct answer is (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
Solution
The correct answer is (a) when the number of time period is large.
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
Solution
The correct answer is (a) the volatility can change
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
Solution
The correct answer is (b)
Reason: It is not necessary true that implied volatility equals historical volatility if the option is
correctly priced as implied volatility is calculated for future and there are several factors that can
affect the volatility.
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).
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
Solution
The correct answer would be 37 - 30 - 2.89 = 4.11
But this answer is not given in question. Kindly cross check with posted question.
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
Solution
The correct answer is (d) the insurance is more costly.
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
Solution
The correct answer is (b). Transaction costs tend to be high
13. A synthetic long call position can be created with which of the following sets of transactions.
Select one:
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
Solution
The correct answer is (e). The synthetic long call is purchase of stock with simultaneous
purchase of Put.
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
Solution
The correct answer is (e). The synthetic short put is short sale of security with simultaneous
purchase of call.
