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Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 20: Volatility Smiles Multiple Choice Test Bank: Questions with Answers 1. 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 t
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  Hull: Options, Futures, and Other Derivatives, Ninth EditionChapter 20: Volatility Smiles Multiple Choie !est an#: $uestions %ith &ns%ers 1.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 axisB.istorical volatility is on the horizontal axis and strike price is on the vertical axis!.Implied volatility is on the vertical axis and strike price is on the horizontal axis .istorical volatility is on the vertical axis and 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 of the following is true? A.'olatility smile for (uropean puts is the same as for (uropean calls B.'olatility smile for (uropean puts is the same as for American puts !.'olatility smile for (uropean calls is the same as for American calls .'olatility smile for American puts is the same as for 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 following is true when the tails of a future foreign currency distri*ution are compared with those of a lognormal distri*ution with the same mean and standard deviation? A.+he left tail and right tail are thinnerB.+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# Both tails of the foreign currency distri*ution are fatter. +his leads to a -shaped smile./.Which of the following is true when the tails of a future stock price distri*ution are compared with those of a lognormal distri*ution with the same mean and standard deviation? A.+he left 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 forforeign currency options? A.!urrencies are traded in dierent countries at dierent times of theday B.!urrencies tend to have low volatilities!.+he activities of central *anks causes occasional 2umps in theexchange 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 itwas 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 15699.Why do traders use volatility smiles for pricing options?A.+o allow for nonlognormality of the pro*a*ility distri*ution of futureasset 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 one4uity?A.;ptions closetothemoney have the lowest implied volatilityB.;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*oveAnswer# !  +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 putoptions have a low strike price. ence ! is correct.5.What does the shape of the volatility smile reveal a*out call options on acurrency?A.;ptions closetothemoney have the lowest implied volatilityB.;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*oveAnswer# is correct. +he volatility smile for currency options is -shaped. 1<.Which of the following is =;+ true?A.A volatility surface provides more information than a single volatility smileB.A volatility surface is used to determine the implied volatility of an option that does not trade actively!.A volatility surface can *e determined from a single volatility smile using interpolation .A volatility surface incorporates information a*out options with dierent maturity dates Answer# !A volatility surface re4uires a knowledge of how implied volatilities vary with option maturity. ! is therefore not true.11.A volatility surface is a ta*le showing the relationship *etween which of the followingA.Implied volatility> time to maturity> and strike priceB.Implied volatility> historical volatility> and time to maturity!.istorical volatility> strike price> and time to maturity .=one of the a*ove   Answer# AA volatility surface is a lookup ta*le showing implied volatilities as a function of strike price and time to maturity.1&.Which of the following causes a volatility smile that is a frown?A.+here is a small pro*a*ility of a large stock price decrease in one weekB.+here is a small pro*a*ility of a large stock price increase in one week!.+he outcome of a lawsuit $roughly e4ual chance of *eing favora*le or unfavora*le% will create a large movement up or down in one week .=one of the a*ove Answer# !As shown at the end of the chapter the situation in ! leads to a @frown1,.Which of the following could *e a result of @crashopho*ia?A.igh volatilities for inthemoney callsB.igh volatilities for inthemoney puts!.igh volatilities for atthemoney calls .ow volatilities for atthemoney puts Answer# A!rashopho*ia is the word used to descri*e a possi*le @pho*ia that traders might have that the market will crash. It would lead to outofthemoney put options with low strike prices having high values and therefore high implied volatilities. Inthemoney call options have the same implied volatilities as the corresponding outofthemoney put options. ence they also have high implied volatilities and the correct answer is A.1/.Which of the following is true for (uropean call and put options?A.If they have the same strike price> they have the same implied volatilityB.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 must 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
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