Question 1

Vega 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 short time to maturity

Accepted Answer

Vega tends to be high for at-the-money options.

Question 2

A call option on a non-dividend-paying stock has a strike price of $30 and a time to maturity of six months.The risk-free rate is 4% and the volatility is 25%.The stock price is $28.What is the delta of the option?
A)N(-0.1342)
B)N(-0.1888)
C)N(-0.2034)
D)N(-0.2241)

Accepted Answer

The delta is N(d₁)where $d _ { 1 } = \frac { \ln \left( S _ { 0 } / K \right) + \left( r + \sigma ^ { 2 } / 2 \right) T } { \sigma \sqrt { T } }$ In this case $d _ { 1 } = \frac { \ln ( 28 / 30 ) + \left( 0.04 + 0.25 ^ { 2 } / 2 \right) \times 0.5 } { 0.25 \sqrt { 0.5 } } = - 0.1888$

Question 3

Which of the following is true for a long position in an option
A)Both gamma and vega are negative
B)Gamma is negative and vega is positive
C)Gamma is positive and vega is negative
D)Both gamma and vega are positive

Accepted Answer

Gamma and vega are both positive for a long position in an option.It does not matter whether the option is a call or a put.

Question 4

Which of the following is true for a call option on a non-dividend-paying stock when the stock's price equals the strike price?
A)It has a delta of 0.5
B)It has a delta less than 0.5
C)It has a delta greater than 0.5
D)Delta can be greater than or less than 0.5

Accepted Answer

The delta is N(d₁)where $d _ { 1 } = \frac { \ln \left( S _ { 0 } / K \right) + \left( r + \sigma ^ { 2 } / 2 \right) T } { \sigma \sqrt { T } }$ From this it can be seen that,when S₀ = K,d₁ is $\frac { \left( r + \sigma ^ { 2 } / 2 \right) \sqrt { T } } { \sigma }$ This is always positive.Hence delta is always greater than 0.5.

Question 5

Which of the following is NOT a letter in the Greek alphabet?
A)delta
B)rho
C)vega
D)gamma

Accepted Answer

Vega,although it is referred to a "Greek letter" by option traders,is not a letter in the Greek alphabet.

Question 6

A trader uses a stop-loss strategy to hedge a short position in a three-month call option with a strike price of 0.7000 on an exchange rate.The current exchange rate is 0.6950 and value of the option is 0.1.The trader covers the option when the exchange rate reaches 0.7005 and uncovers (i.e.,assumes a naked position)if the exchange rate falls to 0.6995.Which of the following is NOT true?
A)The exchange rate trading might cost nothing so that the trader gains 0.1 for each option sold
B)The exchange rate trading might cost considerably more than 0.1 for each option sold so that the trader loses money
C)The present value of the gain or loss from the exchange rate trading should be about 0.1 on average for each option sold
D)The hedge works reasonably well

Accepted Answer

A good hedging system will ensure that the cost of selling an option is close to its theoretical value.The stop-loss hedging procedure does not have this property.It can lead to the option costing nothing or costing considerably more than its theoretical value.On average the cost of the option is its Black-Scholes value,but there is a wide variation.D is the correct answer.

Question 7

The risk-free rate is 5% and the dividend yield on an index is 2%.Which of the following is the delta with respect to the index for a one-year futures on the index?
A)0.98
B)1.05
C)1.03
D)1.02

Accepted Answer

The futures price is given by F₀=S₀e(r-q)T Hence the delta of the futures with respect to the spot is e???q??.In this case,this is e^{(0.05-0.03)×1}=1.03

Question 8

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

Accepted Answer

Gamma measure the rate of change of delta with the asset price.

Question 9

A portfolio of derivatives on a stock has a delta of 2400 and a gamma of -10.An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded.What position in the option is necessary to make the portfolio gamma neutral?
A)Long position in 250 options
B)Short position in 250 options
C)Long position in 20 options
D)Short position in 20 options

Accepted Answer

The options must have a gamma of +10 to neutralize the gamma of the portfolio.Each option has a gamma of 0.04.Hence a long position of 10/0.04 = 250 options is required.

Question 10

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

Accepted Answer

Gamma tends to be high for at-the-money options.

Question 11

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

Accepted Answer

Vega measures the rate of change of the value of the portfolio value with volatility.

Question 12

Which of the following could NOT be a delta-neutral portfolio?
A)A long position in call options plus a short position in the underlying stock
B)A short position in call options plus a short position in the underlying stock
C)A long position in put options and a long position in the underlying stock
D)A long position in a put option and a long position in a call option

Accepted Answer

Calls have a positive delta.Puts have a negative delta.A long stock position has a positive delta.A short stock position has a negative delta.B cannot be delta neutral (i.e.,have a delta of zero)because both parts of the portfolio have a negative delta.

Question 13

Which of the following is true?
A)The delta of a European put equals minus the delta of a European call
B)The delta of a European put equals the delta of a European call
C)The gamma of a European put equals minus the gamma of a European call
D)The gamma of a European put equals the gamma of a European call

Accepted Answer

The delta of a put on a non-dividend-paying stock equals the delta of the call minus one.The gamma of a put equals the gamma of call even when there are dividends.

Question 14

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

Accepted Answer

When the stock price increases by a small amount,the option price increases by 30% of this amount.The trader therefore has a hedged position if he or she buys 300 shares.For small changes the gain or loss on the stock position is equal and opposite to the loss or gain on the option position.

Question 15

The gamma of a delta-neutral portfolio is 500.What is the impact of a jump of $3 in the price of the underlying asset?
A)A gain of $2,250
B)A loss of $2,250
C)A gain of $750
D)A loss of $750

Accepted Answer

The change in the value is a gain of $ 0.5 \Gamma \Delta S^{2} $ = 0.5×500×3²=$2,250.

Question 16

The delta of a call option on a non-dividend-paying stock is 0.4.What is the delta of the corresponding put option?
A)-0.4
B)0.4
C)-0.6
D)0.6

Accepted Answer

The delta of a call option is N(d₁)and the delta of a put is N(d₁)-1.When N(d₁)= 0.4,N(d₁)-1 is -0.6.

Question 17

What does rho 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

Accepted Answer

Rho measures the rate of change of the value of the portfolio with interest rates.(Usually a parallel shift in interest rates is considered.)

Question 18

Which of the following is NOT true about gamma?
A)A highly positive or highly negative value of gamma indicates that a portfolio needs frequent rebalancing to stay delta neutral
B)The magnitude of gamma is a measure of the curvature of the portfolio value as a function of the underlying asset price
C)A big positive value for gamma indicates that a big movement in the asset price in either direction will lead to a loss
D)A long position in either a call or a put has a positive gamma

Accepted Answer

C is not true.The change in the value is a gain of $ 0.5 Г \Delta S^{2} $.There is a gain from a big movement when gamma is positive and a loss from a big movement when gamma is negative.

Question 19

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

Accepted Answer

Delta-neutral hedging is an example of dynamic hedging.The hedge has to be adjusted periodically.(In theory,to maintain a delta-neutral hedge,the hedge must be adjusted continuously.)

Question 20

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

Accepted Answer

Theta measures the rate of change in the value of a portfolio with the passage of time.

Quiz 19: The Greek Letters

Vega tends to be high for which of the following

A call option on a non-dividend-paying stock has a strike price of $30 and a time to maturity of six months.The risk-free rate is 4% and the volatility is 25%.The stock price is $28.What is the delta of the option?

Which of the following is true for a long position in an option

Which of the following is true for a call option on a non-dividend-paying stock when the stock's price equals the strike price?

Which of the following is NOT a letter in the Greek alphabet?

The risk-free rate is 5% and the dividend yield on an index is 2%.Which of the following is the delta with respect to the index for a one-year futures on the index?

What does gamma measure?

A portfolio of derivatives on a stock has a delta of 2400 and a gamma of -10.An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded.What position in the option is necessary to make the portfolio gamma neutral?

Gamma tends to be high for which of the following

What does vega measure?

Which of the following could NOT be a delta-neutral portfolio?

Which of the following is true?

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?

The gamma of a delta-neutral portfolio is 500.What is the impact of a jump of $3 in the price of the underlying asset?

The delta of a call option on a non-dividend-paying stock is 0.4.What is the delta of the corresponding put option?

What does rho measure?

Which of the following is NOT true about gamma?

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

What does theta measure?