Deck 20: Volatility Smiles

Question 1

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?

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

Answer 1

B
The volatility smile for currency options shows that at-the-money options have lower implied volatilities than out-of-the-money and in-the-money options.This means that using at-the- money implied volatilities for out-of-the-money or in-the-money options would lead to the volatility being too low so that there would be underpricing.

Question 2

Which of the following is true of a volatility smile?

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

Answer 2

C
A volatility smile shows implied volatility (which is on the vertical axis)as a function of the strike price (which is on the horizontal axis).

Question 3

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

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

Answer 3

B
The volatility smile tends to become less pronounced as the time to maturity increases.(This does not mean that its impact on prices becomes less pronounced.)

Question 4

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?

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 5

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

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 6

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?

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 7

Which of the following is NOT true?

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 8

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?

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 9

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

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 10

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

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 11

Why do traders use volatility smiles for pricing options?

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 12

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?

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

Question 13

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

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 14

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

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 15

Which of the following is true?

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 16

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

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

Question 17

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

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 18

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

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 19

Which of the following is true?

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 20

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

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