FINC 6680

Which of the following describes a call option?

A. The right to buy an asset for a certain price

B. The obligation to buy an asset for a certain price

C. The right to sell an asset for a certain price

D. The obligation to sell an asset for a certain price

A

An investor has exchange-traded put options to sell 100 shares for $20. There is a $1 cash

dividend during the life of the option. Which of the following is then the position of the

investor?

A. The investor has put options to sell 100 shares for $20

B. The investor has put options to sell 100 shares for $19

C. The investor has put options to sell 105 shares for $19

D. The investor has put options to sell 105 shares for $19.05

A

When the stock price increases with all else remaining the same, which of the following is

true?

A. Both calls and puts increase in value

B. Both calls and puts decrease in value

C. Calls increase in value while puts decrease in value

D. Puts increase in value while calls decrease in value

C

When volatility increases with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value

B. Both calls and puts decrease in value

C. Calls increase in value while puts decrease in value

D. Puts increase in value while calls decrease in value

A

When dividends increase with all else remaining the same, which of the following is true?

A. Both calls and puts increase in value

B. Both calls and puts decrease in value

C. Calls increase in value while puts decrease in value

D. Puts increase in value while calls decrease in value

D

The price of a European call option on a non-dividend-paying stock with a strike price of

$50 is $6. The stock price is $51, the continuously compounded risk-free rate (all

maturities) is 6% and the time to maturity is one year. What is the price of a one-year

European put option on the stock with a strike price of $50?

A. $9.91

B. $7.00

C. $6.00

D. $2.09

D

A European call and a European put on a stock have the same strike price and time to

maturity. At 10:00am on a certain day, the price of the call is $3 and the price of the put is

$4. At 10:01am news reaches the market that has no effect on the stock price or interest

rates, but increases volatilities. As a result, the price of the call changes to $4.50. Which of

the following is correct?

A. The put price increases to $6.00

B. The put price decreases to $2.00

C. The put price increases to $5.50

D. It is possible that there is no effect on the price

C

Which of the following can be used to create a long position in a European put option on a

stock?

A. Buy a call option on the stock and buy the stock

B. Buy a call on the stock and short the stock

C. Sell a call option on the stock and buy the stock

D. Sell a call option on the stock and sell the stock

B

Which of the following creates a bull spread?

A. Buy a low strike price call and sell a high strike price call

B. Buy a high strike price call and sell a low strike price call

C. Buy a low strike price call and sell a high strike price put

D. Buy a low strike price put and sell a high strike price call

A

How can a straddle be created?

A. Buy one call and one put with the same strike price and same expiration date

B. Buy one call and one put with different strike prices and same expiration date

C. Buy one call and two puts with the same strike price and expiration date

D. Buy two calls and one put with the same strike price and expiration date

A

Which of the following describes a protective put?

A. A long put option on a stock plus a long position in the stock

B. A long put option on a stock plus a short position in the stock

C. A short put option on a stock plus a short call option on the stock

D. A short put option on a stock plus a long position in the stock

A

Which of the following describes a covered call?

A. A long call option on a stock plus a long position in the stock

B. A long call option on a stock plus a short put option on the stock

C. A short call option on a stock plus a short position in the stock

D. A short call option on a stock plus a long position in the stock

D

In a binomial tree created to value an option on a stock, the expected return on stock is

A. Zero

B. The return required by the market

C. The risk-free rate

D. It is impossible to know without more information

C

What is the number of trading days in a year usually assumed for equities?

A. 365

B. 252

C. 262

D. 272

B

Which of the following is measured by the VIX index

A. Implied volatilities for stock options trading on the CBOE

B. Historical volatilities for stock options trading on CBOE

C. Implied volatilities for options trading on the S&P 500 index

D. Historical volatilities for options trading on the S&P 500 index

C

When the Black-Scholes-Merton and binomial tree models are used to value an option on

a non-dividend-paying stock, which of the following is true?

A. The binomial tree price converges to a price slightly above the Black-Scholes-

Merton price as the number of time steps is increased

B. The binomial tree price converges to a price slightly below the Black-Scholes-

Merton price as the number of time steps is increased

C. Either A or B can be true

D. The binomial tree price converges to the Black-Scholes-Merton price as the

number of time steps is increased

D

Which of the following is true?

A. An employee stock option is usually held to maturity

B. An employee stock option tend to be exercised earlier than an exchange-

traded option with the same terms

C. An employee stock options tend to be exercised later than an exchange-traded

option with the same terms

B

Which of the following is true about the practice of backdating a stock options grant?

A. It is illegal

B. It is illegal in the majority of states in the U.S., but not all states

C. It is illegal in roughly half the states in the U.S.

D. It is unethical, but not illegal

A

Which of the following defines the vesting period?

A. The period during which employee stock options can be exercised

B. The period during which the options are issued

C. The period during which the strike price of the options equals the stock price

D. The period during which employee stock options cannot be exercised

D

Which of the following ensures that managers are rewarded only when a company

performs better than its competitors?

A. A constant strike price for executive stock options

B. A strike price that increases with time

C. A strike price that changes in line with an index of stock prices

D. A strike price that is tied to reported profit

C

What does gamma measure?

A. The rate of change of delta with the asset price

B. The rate of change of the portfolio value with the passage of time

C. The sensitivity of a portfolio value to interest rate changes

D. None of the above

A

A call option on a stock has a delta of 0.3. A trader has sold 1,000 options. What position

should the trader take to hedge the position?

A. Sell 300 shares

B. Buy 300 shares

C. Sell 700 shares

D. Buy 700 shares

B

What does theta measure?

A. The rate of change of delta with the asset price

B. The rate of change of the portfolio value with the passage of time

C. The sensitivity of a portfolio value to interest rate changes

D. None of the above

B

What does gamma measure?

A. The rate of change of delta with the asset price

B. The rate of change of the portfolio value with the passage of time

C. The sensitivity of a portfolio value to interest rate changes

D. None of the above

A

What does vega measure?

A. The rate of change of delta with the asset price

B. The rate of change of the portfolio value with the passage of time

C. The sensitivity of a portfolio value to interest rate changes

D. None of the above

D

Maintaining a delta-neutral portfolio is an example of which of the following

A. Stop-loss strategy

B. Dynamic hedging

C. Hedge and forget strategy

D. Static hedging

B

Gamma tends to be high for which of the following

A. At-the money options

B. Out-of-the money options

C. In-the-money options

D. Options with a long time to maturity

A

A volatility surface used in Practitioner Black-Scholes model is a table showing the

relationship between which of the following

A. Implied volatility, time to maturity, and strike price

B. Implied volatility, historical volatility, and time to maturity

C. Historical volatility, strike price, and time to maturity

D. None of the above

A

What are the assumptions of Black-Scholes Model?

Assumptions on the market:

No arbitrage opportunities

• Possible to borrow and lend at risk-free rate

• No short selling restrictions

• No transaction costs

• Trading is continuous

Assumptions on the asset

• The underlying is a non-dividend paying stock

• Return on the underlying in very short time intervals is normally distributed and follows the geometric Brownian motion

Assumption on the option

• Option is European style

Name three US Index Options. State if they are European or American and if they are

settled in cash or the underlying

S&P 500 index options (SPX): European

S&P 100 index options (OEX) American

Dow Jones Industrial Average options (DJX) European

Under the assumptions of the Black-Scholes model, volatility is constant. In reality, we

observe that volatility depends on moneyness. What is the reason of this volatility smile?

The Black-Scholes model assumes a lognormal distribution of underlying asset returns

In reality: the implied distribution has fatter tails → higher probability of unlikely events and

higher price of deep-out-of(in)-the money options → volatility smile

Discuss, what would be your approach how to value

A. American options

Binomial Tree

European Options

Black-Scholes Model

Binomial tree

The current price of a non-dividend paying stock is $30. Use a two-step tree to value a

European call option on the stock with a strike price of $32 that expires in 6 months. Each

step is 3 months, the risk free rate is 8% per annum with continuous compounding. What

is the option price when u = 1.1 and d = 0.9. (6 point)

$1.49