Question 1

Gamma tends to be high for which of the following?

Accepted Answer

Gamma 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

B

Question 3

What does vega measure?

Accepted Answer

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

Question 4

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

Accepted Answer

Vega is not a letter in the Greek alphabet.

Question 5

What does theta measure?

Accepted Answer

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

Question 6

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 7

Which of the following is true for a call option on a non-dividend-paying stock?

Accepted Answer

The answer of Which of the following is true for...

Question 8

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

Delta measures the sensitivity of an option's price to changes in the price of the underlying stock. Since the delta of the call option is 0.3, it means that for every $1 increase in the price of the stock, the option price will increase by $0.30. 
To hedge the position, the trader needs to take an opposite position in the underlying stock. Since the trader has sold 1,000 call options, he is short the options and needs to buy the stock to hedge his position. 
The trader should buy 300 shares of the stock, which is calculated as: 
Delta of option x Number of options sold x Price of the stock 
= 0.3 x 1,000 x Price of the stock 
= 300 x Price of the stock 
This will effectively hedge the trader's position and protect against any adverse price movements in the stock.

Question 9

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 0.5F1F1F1S1F1F1F10S² = 0.5×500×3²=$2,250.

Question 10

What does rho measure?

Accepted Answer

Rho measures the sensitivity of a portfolio value to changes in interest rates. Option A refers to delta, Option B refers to theta, and Option D refers to none of the above.

Question 11

Vega tends to be high for which of the following?

Accepted Answer

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

Question 12

When the interest rate is zero which of the following is true for a delta-neutral portfolio with a positive gamma?

Accepted Answer

The answer of When the interest rate is zero which...

Question 13

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 put option is always negative and equal in absolute value to the delta of the corresponding call option minus one. Therefore, the delta of the put option in this case is (-0.4)-1 = -1.4. However, since the delta cannot be less than -1 or greater than 1, the answer closest to this is -0.6, which is choice C.

Question 14

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

Accepted Answer

A delta-neutral portfolio is one in which the overall delta value is zero, meaning that the portfolio is not sensitive to small changes in the underlying asset's price. A long position in call options plus a short position in the underlying stock (A) and a long position in put options and a long position in the underlying stock (C) are both examples of delta-neutral portfolios. A long position in a put option and a long position in a call option (D) can also be considered a delta-neutral portfolio if the strike prices are the same. However, a short position in call options plus a short position in the underlying stock (B) is not delta-neutral, as the overall delta value would be negative.

Question 15

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 16

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 17

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 of a one-year futures on the index?

Accepted Answer

The delta of a futures contract is 1, as it represents a one-to-one relationship with the underlying asset. Therefore, we need to calculate the futures price to determine the delta with respect to the index. 
Based on the information given, we know that the futures price must be equal to the spot price compounded at the risk-free rate minus the present value of the dividend. 
Therefore, the futures price is:
Index price * (1 + r) - Dividend
= Index price * (1.05) - Index price * (0.02)
= Index price * (1.03)
The delta of the futures contract with respect to the index is the futures price divided by the index price:
Delta = Futures price / Index price = (Index price * (1.03)) / Index price = 1.03 
Therefore, the delta is 1.03, which is closest to answer choice C.

Question 18

Which of the following is NOT true about gamma?

Accepted Answer

A big positive value for gamma actually indicates that a big movement in the asset price in either direction will lead to a large profit, not a loss.

Question 19

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

Accepted Answer

Maintaining a delta-neutral portfolio involves continuously adjusting the hedge ratio to keep the portfolio's overall delta (sensitivity to changes in the underlying asset's price) at zero. This is achieved through dynamic hedging, which involves rebalancing the portfolio regularly to maintain the desired hedge ratio. Stop-loss strategy involves setting a predetermined sell order to limit losses. Hedge and forget strategy involves hedging against potential risks and then leaving the position unchanged indefinitely. Static hedging involves establishing a hedge position that is fixed for a specific period.

Question 20

What does gamma measure?

Accepted Answer

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

Quiz 17: The Greek Letters