Curtin University - FINANCE INVE3000

Multiple Choice Questions

1) Which of the following is assumed by the Black-Scholes-Merton model?

a)    The return from the stock in a short period of time is lognormal.
b)    The stock price at a future time is lognormal.
c)    The stock price at a future time is normal.
 d)    None of the above.

2.    A one-year call option on a stock with a strike price of $30 costs $3; a one- year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price below which the trader makes a profit is:

a) $25
b) $28
c) $26
d) $20

3.    Which of the following statements is true?

a)    The Black-Scholes-Merton model is used to price all vanilla options, because it is an exact closed form, analytical formula.
b)    The Black-Scholes-Merton price of a European vanilla option is an expected value of the asset.
c)    The Black-Scholes-Merton price of a European vanilla option is the expected profit from the option.
d)    The    Black-Scholes-Merton    model    allows    an    option    to    be    priced assuming the investment is risky.
e)    None of the above.

4.    An investor has a portfolio consisting of one European vanilla option only. The portfolio has a negative delta and a negative gamma. What is the option position in the portfolio?

a)    Long Call option
b)    Long Put option
c)    Short Call option
d)    Short Put option
e)    It is impossible to have negative delta and negative gamma from a single European vanilla option.

5.    What does N(x) denote?

a)    The area under a normal distribution from zero to x.
b)    The area under a normal distribution up to x.
c)    The area under a normal distribution beyond x.
d)    The area under the normal distribution between –x and x.

6.    You sell a European vanilla Put option with a strike price of $100, and you receive $10 in premium. No delta hedge was traded. Under what circumstances does the seller make a profit?
 
a)    Current spot price (St) is less than 90.
b)    Terminal spot price (ST) is less than 90.
c)    Current spot price (St) is greater than 90.
d)    Terminal spot price (ST) is greater than 90.
e)    Terminal spot price (ST) is greater than 110.

7.    You buy a European vanilla Call option with a strike price of $50, and you pay $2 in premium. No delta hedge was traded. Under what circumstances do you make a profit?

a)    Current spot price (St) is less than 48.
b)    Terminal spot price (ST) is less than 48.
c)    Current spot price (St) is greater than 52.
d)    Terminal spot price (ST) is greater than 50.
e)    Terminal spot price (ST) is greater than 52.

8.    Which of the following are always positively related to the price of a European call option on a stock? (Circle three)

a)    The stock price
b)    The strike price
c)    The time to expiration
d)    The volatility
e)    The risk-free rate
f)    Dividends

9.    Which of the following are always positively related to the price of an American put option on a stock? (Circle two)

a)    The stock price
b)    The strike price
c)    The time to expiration
d)    The volatility
e)    The risk-free rate
f)    Dividends

10.    Which statement is correct?

a)    The vega of a call option is negative and the vega of a put option is positive.
b)    The vega of a call option is positive and the vega of a put option is negative.
c)    The vega of a call option and a put option are both positive.
d)    The vega of a call option and a put option are both negative.
e)    None of the above
 
11.    The  of an option of an underlying asset is the approximate rate of change of the option’s value with respect to the risk-free interest rate.

a)    vega
b)    theta
c)    gamma
d)    rho
e)    delta

12.    Which of the following European vanilla option strategies benefits from an increase in volatility of the underlying asset price?

a)    Short straddle
b)    Short strangle
c)    Short butterfly
d)    All of the above
e)    None of the above

13.    Which of the following European vanilla option strategies benefits from lower market volatility in the underlying asset price?

a)    Long straddle
b)    Long box spread
c)    Long butterfly
d)    All of the above
e)    None of the above

14.    The     of an option is the ratio of the change in the delta of the option to the change in the spot price of the underlying asset.

a)    Delta
b)    Gamma
c)    Vega
d)    Theta
e)    None of the above
 

15.    An investor buys a call option on a futures for gold. The contract size is
100 ounces. The strike price is 1,800. The investors exercises the option when the futures price is 1,840 and the most recent settlement price is 1,838. Which answer is true?

a)    The investor receives a long position in the contract and $4,000.
b)    The investor receives a short position in the contract and pays $3,800.
c)    The investor receives a long position in the contract and $3,800.
d)    The investor receives a short position in the contract and receives $3,800.
e)    None of the above

16.    An investor buys a put option on a futures contract. Which answer is true?

a)    The investor takes a long position in the futures if he/she exercises the put option.
b)    The investor takes a short position in the future if he/she exercises the put option.
c)    The investor takes a short position in the futures if he/she does not exercise the put option.
d)    The investor can choose whether to go long or short when he/she exercises the put option.
e)    None of the above

17.    An investor has a portfolio consisting of one European vanilla option only. The portfolio has a positive delta and a negative gamma. What is the option position in the portfolio?

a)    Long Call option
b)    Long Put option
c)    Short Call option
d)    Short Put option
e)    It is impossible to have positive delta and negative gamma from a single European vanilla option.

18.    The price of the underlying asset is expected to follow a one-step binominal process spanning six months. If u=1.07 and d = u-1, and the riskless interest rate for one year is 5% p.a., what is the current price of a European vanilla Call option expiring in one-year with an end of period value of Vu = $2.50 in the up-state and a value of Vd = $0.90 in the down state?

a) 0.67
b) 0.98
c) 1.97
 d) 1.92
e) 1.39

19.    What is the lower bound for the price of a three-year European vanilla Call option on a non-dividend paying stock when the stock price is $50, the strike price is $45, and the risk-free interest rate is 3% p.a. continuously compounded?

a)$0
b) $0.70
c) $8.87
d)$5
e)None of the above

20.    What is the lower bound for the price of a three-year European vanilla Put option on a non-dividend paying stock when the stock price is $50, the strike price is $55, and the risk-free interest rate is 3% p.a. continuously compounded?

a)$0
b) $0.27
c) $9.30
d)$5
e)None of the above