Hull_OFOD9e_MultipleChoice_Questions_and_Answers_Ch20.doc

Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 20: Volatility Smiles Multiple Choie !est "an#: $uestions %ith &ns%ers

1. Which of of the follow following ing is true true of a volat volatility ility smile? smile? A. Implied Implied volatilit volatility y is on the horizontal horizontal axis axis and strike strike price is on the vertical axis B. istorical istorical volatil volatility ity is on the horizontal horizontal axis axis and strike strike price is on the vertical axis !. Implied Implied volatilit volatility y is on the vertical vertical axis and strike strike price price is on the horizontal axis ". istorical volatility volatility is on the vertical vertical axis and strike strike price is on the horizontal axis Answer# ! 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%. &. Which Which of the the follo followi wing ng is true? true? A. 'olatility olatility smile smile for (uropean (uropean puts is the same same as for (uropean (uropean calls B. 'olatility olatility smile smile for (uropean (uropean puts is the same same as for American American puts !. 'olatility smile smile for (uropean (uropean calls calls is the same as for for American calls ". 'olatility smile smile for American American puts is the same as for American American calls Answer# A )ut call parity shows that the volatility smile for ( uropean puts should *e exactly the same as that for (uropean calls. +he volatility smile for American options is usually close to *ut not exactly the same as that for (uropean options. ,. Which of the follow following ing is true when the tails tails of a future future foreign foreign currency currency distri*ution are compared with those of a lognormal distri*ution with the same mean and standard deviation? A. +he left left tail tail and right tail are thinner B. +he left left tail is is thinner thinner and the the right tail tail is fatter fatter !. +he right right tail tail is thinner thinner and the the left left tail is fatter fatter ". Both Both tails tails are are fatt fatter er Answer# " Both tails of the th e foreign currency distri*ution are fatter. fatter. +his leads to a - shaped smile. /. Which of the the following following is true true when the tails tails of a future future stock stock price price distri*ution are compared with those of a lognormal distri*ution with the same mean and standard deviation? A. +he left left tail tail and right tail are thinner

B. +he left tail is thinner and the right tail is fatter !. +he right tail is thinner and the left tail is fatter ". Both tails are fatter Answer# !  +he left tail is fatter and the right tail is thinner. 0. Which of the following could cause the volatility smile typically seen for foreign currency options? A. !urrencies are traded in dierent countries at dierent times of the day B. !urrencies tend to have low volatilities !. +he activities of central *anks causes occasional 2umps in the exchange rate ". Interest rates may *e dierent in the two countries Answer# !  +he possi*ility of 2umps in the exchange rate makes extreme exchange rates more likely and is consistent with the volatility smile that is o*served. 3. Which of the following is true? A. +he volatility skew for e4uities is much more pronounced now than it was in 1560. B. +he volatility skew for e4uities has a positive gradient !. +he volatility skew for e4uities is consistent with the Black7choles 8erton model. ". +he volatility skew for e4uities is similar to that for foreign currencies. Answer# A  +here was very little volatility skew or smile for e4uities prior to the crash of 1569 9. Why do traders use volatility smiles for pricing options? A. +o allow for nonlognormality of the pro*a*ility distri*ution of future asset price B. Because it is consistent with recent market moves !. As a tool to re:ect their views a*out extreme market moves ". Because extreme market moves are always more likely than Black 7choles8erton assumes Answer# A 'olatility smiles allow for the fact that the assumptions underlying the Black 7choles8erton model do not hold exactly. +he B78 assumptions imply a lognormally distri*uted future asset price.

6. What does the shape of the volatility smile reveal a*out put options on e4uity? A. ;ptions closetothemoney have the lowest implied volatility B. ;ptions deepinthemoney have a relatively high implied volatility !. ;ptions deepoutofthemoney have a relatively high implied volatility ". All of the a*ove Answer# !  +he volatility smile shows that lowstrikeprice options have high implied volatilities relative to atthemoney options. ighstrikeprice options have low implied volatilities relative to atthemoney options. ;ut ofthemoney put options have a low strike price. ence ! is correct. 5. What does the shape of the volatility smile reveal a*out call options on a currency? A. ;ptions closetothemoney have the lowest implied volatility B. ;ptions deepinthemoney have a relatively high implied volatility !. ;ptions deepoutofthemoney have a relatively high implied volatility ". All of the a*ove Answer# " " is correct. +he volatility smile for currency options is -shaped. 1 they have the same implied volatility B. If they have the same time to maturity> they have the same implied volatility !. If they have the same strike price and time to maturity> they have the same implied volatility ". =one of the a*ove Answer# ! If a (uropean call and put option have the same strike price and time to maturity putcall parity shows that they mu st have the same implied volatility. ;therwise there are ar*itrage opportunities. 10.Which of the following is true a*out daily exchange rate moves? A. Cour standard deviation daily moves in an exchange rate happen less

fre4uently than they would do if changes were normally distri*uted B. Cour standard deviation daily movements in an exchange rate happen more fre4uently than three standard deviation moves in the exchange rate !. +he fre4uency of six standard deviation daily movements in an exchange rate is a*out once every 1 B> and ! are not true. arge daily exchange rate moves happen more fre4uently than they would if they were normally distri*uted. By deDnition a four standard deviation move occurs less fre4uently than a three standard deviation move. A six standard deviation move happens more fre4uency than once every 1