Question 1

Which of the following is NOT true about gamma?

Accepted Answer

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 
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 C

Question 2

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

A) Sell 300 shares 
B) Buy 300 shares 
C) Sell 700 shares 
D) Buy 700 shares 
A) Sell 300 shares 
B) Buy 300 shares 
C) Sell 700 shares 
D) Buy 700 shares B

Question 3

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

A) -0.4 
B) 0.4 
C) -0.6 
D) 0.6 
A) -0.4 
B) 0.4 
C) -0.6 
D) 0.6 C

Question 4

What does rho measure?

Accepted Answer

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) 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

Question 5

What does gamma measure?

Accepted Answer

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) 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

Question 6

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

Accepted Answer

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 
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

Question 7

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

Accepted Answer

A) delta 
B) rho 
C) vega 
D) gamma 
A) delta 
B) rho 
C) vega 
D) gamma

Question 8

Gamma tends to be high for which of the following

Accepted Answer

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) At-the money options 
B) Out-of-the money options 
C) In-the-money options 
D) Options with a long time to maturity

Question 9

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

Accepted Answer

A) Stop-loss strategy 
B) Dynamic hedging 
C) Hedge and forget strategy 
D) Static hedging 
A) Stop-loss strategy 
B) Dynamic hedging 
C) Hedge and forget strategy 
D) Static hedging

Question 10

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

A) 0.98 
B) 1.05 
C) 1.03 
D) 1.02 
A) 0.98 
B) 1.05 
C) 1.03 
D) 1.02

Question 11

Which of the following is true?

Accepted Answer

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 
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

Question 12

Vega tends to be high for which of the following

Accepted Answer

A) At-the money options 
B) Out-of-the money options 
C) In-the-money options 
D) Options with a short time to maturity 
A) At-the money options 
B) Out-of-the money options 
C) In-the-money options 
D) Options with a short time to maturity

Question 13

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) 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 
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

Question 14

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

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 
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

Question 15

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

A) Long position in 250 options 
B) Short position in 250 options 
C) Long position in 20 options 
D) Short position in 20 options 
A) Long position in 250 options 
B) Short position in 250 options 
C) Long position in 20 options 
D) Short position in 20 options

Question 16

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

A) N(-0.1342) 
B) N(-0.1888) 
C) N(-0.2034) 
D) N(-0.2241) 
A) N(-0.1342) 
B) N(-0.1888) 
C) N(-0.2034) 
D) N(-0.2241)

Question 17

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

Accepted Answer

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 
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

Question 18

What does vega measure?

Accepted Answer

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) 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

Question 19

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

A) A gain of $2,250 
B) A loss of $2,250 
C) A gain of $750 
D) A loss of $750 
A) A gain of $2,250 
B) A loss of $2,250 
C) A gain of $750 
D) A loss of $750

Question 20

What does theta measure?

Accepted Answer

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) 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

Exam 19: The Greek Letters

Which of the following is NOT true about gamma?

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 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?

What does gamma measure?

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

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

Gamma tends to be high for which of the following

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

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?

Which of the following is true?

Vega tends to be high for which of the following

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 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 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

What does vega measure?

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?

What does theta measure?

Introduction

Mechanics of Futures Markets

Hedging Strategies Using Futures

Interest Rates

Determination of Forward and Futures Prices

Interest Rate Futures

Swaps

Securitization and the Credit Crisis of 2007

OIS Discounting, Credit Issues, and Funding Costs

Mechanics of Options Markets

Properties of Stock Options

Trading Strategies Involving Options

Binomial Trees

Wiener Processes and Ito’s Lemma

The Black-Scholes-Merton Model

Employee Stock Options

Options on Stock Indices and Currencies

Futures Options

Volatility Smiles

Basic Numerical Procedures

Value at Risk

Estimating Volatilities and Correlations

Credit Risk

Credit Derivatives

Exotic Options

Filters