Question 1

Vega tends to be high for which of the following

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?

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

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?

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?

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?

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?

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?

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?

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

Accepted Answer

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

Question 11

What does vega measure?

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?

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?

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?

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?

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?

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?

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?

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

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?

Accepted Answer

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

Quiz 19: The Greek Letters