Question 1

Which of the following causes a volatility smile that is a ``frown``?

Accepted Answer

A)  There is a small probability of a large stock price decrease in one week 
B)  There is a small probability of a large stock price increase in one week 
C)  The outcome of a lawsuit (roughly equal chance of being favorable or unfavorable) will create a large movement up or down in one week 
D)  None of the above 
A)  There is a small probability of a large stock price decrease in one week 
B)  There is a small probability of a large stock price increase in one week 
C)  The outcome of a lawsuit (roughly equal chance of being favorable or unfavorable) will create a large movement up or down in one week 
D)  None of the above C

Question 2

The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 6 months are 20% and 22%.The implied volatilities for strike prices of 1.1 and 1.2 when the time to maturity is 1 year are 18.8% and 20.2%.Using linear interpolation,what is the implied volatility for a strike price of 1.12 and a time to maturity of 10 months?

Accepted Answer

A)  19.24% 
B)  19.52% 
C)  20.48% 
D)  19.96% 
A)  19.24% 
B)  19.52% 
C)  20.48% 
D)  19.96% B

Question 3

If the volatility implied from an at-the-money put currency option were used to price other put options on the currency,which of the following would be true?

Accepted Answer

A)  Out-of-the money and in-the-money prices would be too high 
B)  Out-of-the money and in-the-money prices would be too low 
C)  Out-of-the-money option prices would be too high and in-the-money option prices would be too low 
D)  Out-of-the-money option prices would be too low and in-the-money option prices would be too high 
A)  Out-of-the money and in-the-money prices would be too high 
B)  Out-of-the money and in-the-money prices would be too low 
C)  Out-of-the-money option prices would be too high and in-the-money option prices would be too low 
D)  Out-of-the-money option prices would be too low and in-the-money option prices would be too high B

Question 4

Why do traders use volatility smiles for pricing options?

Accepted Answer

A)  To allow for non-lognormality of the probability distribution of future asset price 
B)  Because it is consistent with recent market moves 
C)  As a tool to reflect their views about extreme market moves 
D)  Because extreme market moves are always more likely than Black-Scholes-Merton assumes 
A)  To allow for non-lognormality of the probability distribution of future asset price 
B)  Because it is consistent with recent market moves 
C)  As a tool to reflect their views about extreme market moves 
D)  Because extreme market moves are always more likely than Black-Scholes-Merton assumes

Question 5

Which of the following could be a result of "crashophobia"?

Accepted Answer

A)  High volatilities for in-the-money calls 
B)  High volatilities for in-the-money puts 
C)  High volatilities for at-the-money calls 
D)  Low volatilities for at-the-money puts 
A)  High volatilities for in-the-money calls 
B)  High volatilities for in-the-money puts 
C)  High volatilities for at-the-money calls 
D)  Low volatilities for at-the-money puts

Question 6

What does the shape of the volatility smile reveal about call options on a currency?

Accepted Answer

A)  Options close-to-the-money have the lowest implied volatility 
B)  Options deep-in-the-money have a relatively high implied volatility 
C)  Options deep-out-of-the-money have a relatively high implied volatility 
D)  All of the above 
A)  Options close-to-the-money have the lowest implied volatility 
B)  Options deep-in-the-money have a relatively high implied volatility 
C)  Options deep-out-of-the-money have a relatively high implied volatility 
D)  All of the above

Question 7

If the volatility implied from an at-the-money put stock option were used to price other put options on the stock,which of the following would be true?

Accepted Answer

A)  Out-of-the money and in-the-money prices would be too high 
B)  Out-of-the money and in-the-money prices would be too low 
C)  Out-of-the-money option prices would be too high and in-the-money option prices would be too low 
D)  Out-of-the-money option prices would be too low and in-the-money option prices would be too high 
A)  Out-of-the money and in-the-money prices would be too high 
B)  Out-of-the money and in-the-money prices would be too low 
C)  Out-of-the-money option prices would be too high and in-the-money option prices would be too low 
D)  Out-of-the-money option prices would be too low and in-the-money option prices would be too high

Question 8

Which of the following is true?

Accepted Answer

A)  Volatility smile for European puts is the same as for European calls 
B)  Volatility smile for European puts is the same as for American puts 
C)  Volatility smile for European calls is the same as for American calls 
D)  Volatility smile for American puts is the same as for American calls 
A)  Volatility smile for European puts is the same as for European calls 
B)  Volatility smile for European puts is the same as for American puts 
C)  Volatility smile for European calls is the same as for American calls 
D)  Volatility smile for American puts is the same as for American calls

Question 9

Which of the following is true as time to maturity increases?

Accepted Answer

A)  The volatility smile for currency options tends to become more pronounced 
B)  The volatility smile for currency options tends to become less pronounced 
C)  The volatility smile for currency options first becomes less pronounced and then becomes more pronounced 
D)  The volatility smile for currency options remains approximately the same 
A)  The volatility smile for currency options tends to become more pronounced 
B)  The volatility smile for currency options tends to become less pronounced 
C)  The volatility smile for currency options first becomes less pronounced and then becomes more pronounced 
D)  The volatility smile for currency options remains approximately the same

Question 10

Which of the following is true of a volatility smile?

Accepted Answer

A)  Implied volatility is on the horizontal axis and strike price is on the vertical axis 
B)  Historical volatility is on the horizontal axis and strike price is on the vertical axis 
C)  Implied volatility is on the vertical axis and strike price is on the horizontal axis 
D)  Historical volatility is on the vertical axis and strike price is on the horizontal axis 
A)  Implied volatility is on the horizontal axis and strike price is on the vertical axis 
B)  Historical volatility is on the horizontal axis and strike price is on the vertical axis 
C)  Implied volatility is on the vertical axis and strike price is on the horizontal axis 
D)  Historical volatility is on the vertical axis and strike price is on the horizontal axis

Question 11

Which of the following is true about daily exchange rate moves?

Accepted Answer

A)  Four standard deviation daily moves in an exchange rate happen less frequently than they would do if changes were normally distributed 
B)  Four standard deviation daily movements in an exchange rate happen more frequently than three standard deviation moves in the exchange rate 
C)  The frequency of six standard deviation daily movements in an exchange rate is about once every 100 years 
D)  None of the above 
A)  Four standard deviation daily moves in an exchange rate happen less frequently than they would do if changes were normally distributed 
B)  Four standard deviation daily movements in an exchange rate happen more frequently than three standard deviation moves in the exchange rate 
C)  The frequency of six standard deviation daily movements in an exchange rate is about once every 100 years 
D)  None of the above

Question 12

Which of the following is true when the tails of a future foreign currency distribution are compared with those of a lognormal distribution with the same mean and standard deviation?

Accepted Answer

A)  The left tail and right tail are thinner 
B)  The left tail is thinner and the right tail is fatter 
C)  The right tail is thinner and the left tail is fatter 
D)  Both tails are fatter 
A)  The left tail and right tail are thinner 
B)  The left tail is thinner and the right tail is fatter 
C)  The right tail is thinner and the left tail is fatter 
D)  Both tails are fatter

Question 13

The daily percentage change in an exchange rate is compared to a normal distribution with the same mean and standard deviation.Which of the following is true

Accepted Answer

A)  Both small and large exchange rate moves are more likely than with the normal distribution 
B)  Small exchange rate moves are less likely and large exchange rate moves are more likely than with the normal distribution 
C)  Large exchange rate moves are less likely and small exchange rate moves are more likely than with the normal distribution 
D)  Both small and large exchange rate moves are less likely than with the normal distribution 
A)  Both small and large exchange rate moves are more likely than with the normal distribution 
B)  Small exchange rate moves are less likely and large exchange rate moves are more likely than with the normal distribution 
C)  Large exchange rate moves are less likely and small exchange rate moves are more likely than with the normal distribution 
D)  Both small and large exchange rate moves are less likely than with the normal distribution

Question 14

Which of the following is true?

Accepted Answer

A)  The volatility skew for equities is much more pronounced now than it was in 1985. 
B)  The volatility skew for equities has a positive gradient 
C)  The volatility skew for equities is consistent with the Black-Scholes-Merton model. 
D)  The volatility skew for equities is similar to that for foreign currencies. 
A)  The volatility skew for equities is much more pronounced now than it was in 1985. 
B)  The volatility skew for equities has a positive gradient 
C)  The volatility skew for equities is consistent with the Black-Scholes-Merton model. 
D)  The volatility skew for equities is similar to that for foreign currencies.

Question 15

Which of the following is true for European call and put options?

Accepted Answer

A)  If they have the same strike price, they have the same implied volatility 
B)  If they have the same time to maturity, they have the same implied volatility 
C)  If they have the same strike price and time to maturity, they have the same implied volatility 
D)  None of the above 
A)  If they have the same strike price, they have the same implied volatility 
B)  If they have the same time to maturity, they have the same implied volatility 
C)  If they have the same strike price and time to maturity, they have the same implied volatility 
D)  None of the above

Question 16

Which of the following could cause the volatility smile typically seen for foreign currency options?

Accepted Answer

A)  Currencies are traded in different countries at different times of the day 
B)  Currencies tend to have low volatilities 
C)  The activities of central banks causes occasional jumps in the exchange rate 
D)  Interest rates may be different in the two countries 
A)  Currencies are traded in different countries at different times of the day 
B)  Currencies tend to have low volatilities 
C)  The activities of central banks causes occasional jumps in the exchange rate 
D)  Interest rates may be different in the two countries

Question 17

A volatility surface is a table showing the relationship between which of the following

Accepted Answer

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)  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

Question 18

Which of the following is NOT true?

Accepted Answer

A)  A volatility surface provides more information than a single volatility smile 
B)  A volatility surface is used to determine the implied volatility of an option that does not trade actively 
C)  A volatility surface can be determined from a single volatility smile using interpolation 
D)  A volatility surface incorporates information about options with different maturity dates 
A)  A volatility surface provides more information than a single volatility smile 
B)  A volatility surface is used to determine the implied volatility of an option that does not trade actively 
C)  A volatility surface can be determined from a single volatility smile using interpolation 
D)  A volatility surface incorporates information about options with different maturity dates

Question 19

Which of the following is true when the tails of a future stock price distribution are compared with those of a lognormal distribution with the same mean and standard deviation?

Accepted Answer

A)  The left tail and right tail are thinner 
B)  The left tail is thinner and the right tail is fatter 
C)  The right tail is thinner and the left tail is fatter 
D)  Both tails are fatter 
A)  The left tail and right tail are thinner 
B)  The left tail is thinner and the right tail is fatter 
C)  The right tail is thinner and the left tail is fatter 
D)  Both tails are fatter

Question 20

What does the shape of the volatility smile reveal about put options on equity?

Accepted Answer

A)  Options close-to-the-money have the lowest implied volatility 
B)  Options deep-in-the-money have a relatively high implied volatility 
C)  Options deep-out-of-the-money have a relatively high implied volatility 
D)  All of the above 
A)  Options close-to-the-money have the lowest implied volatility 
B)  Options deep-in-the-money have a relatively high implied volatility 
C)  Options deep-out-of-the-money have a relatively high implied volatility 
D)  All of the above

Exam 20: Volatility Smiles

Which of the following causes a volatility smile that is a ``frown``?

If the volatility implied from an at-the-money put currency option were used to price other put options on the currency,which of the following would be true?

Why do traders use volatility smiles for pricing options?

Which of the following could be a result of "crashophobia"?

What does the shape of the volatility smile reveal about call options on a currency?

If the volatility implied from an at-the-money put stock option were used to price other put options on the stock,which of the following would be true?

Which of the following is true?

Which of the following is true as time to maturity increases?

Which of the following is true of a volatility smile?

Which of the following is true about daily exchange rate moves?

Which of the following is true when the tails of a future foreign currency distribution are compared with those of a lognormal distribution with the same mean and standard deviation?

The daily percentage change in an exchange rate is compared to a normal distribution with the same mean and standard deviation.Which of the following is true

Which of the following is true?

Which of the following is true for European call and put options?

Which of the following could cause the volatility smile typically seen for foreign currency options?

A volatility surface is a table showing the relationship between which of the following

Which of the following is NOT true?

Which of the following is true when the tails of a future stock price distribution are compared with those of a lognormal distribution with the same mean and standard deviation?

What does the shape of the volatility smile reveal about put options on equity?

Introduction

Futures Markets and Central Counterparties

Hedging Strategies Using Futures

Interest Rates

Determination of Forward and Futures Prices

Interest Rate Futures

Swaps

Securitization and the Credit Crisis of 2007

Xvas

Mechanics of Options Markets

Properties of Stock Options

Trading Strategies Involving Options

Binomial Trees

Wiener Processes and Itos Lemma

The Black-Scholes-Merton Model

Employee Stock Options

Options on Stock Indices and Currencies

Futures Options and Blacks Model

The Greek Letters

Basic Numerical Procedures

Value at Risk and Expected Shortfall

Estimating Volatilities and Correlations

Credit Risk

Credit Derivatives

Exotic Options

Filters