Hull: Options, Futures and Other Derivatives, Eighth Edition Chapter 15: The Black-choles-!ert Black-choles-!erton on !odel !ultiple Choice Test Bank: "uestions 1. Which Which of the following following is assumed assumed by the Black-Sch Black-Scholes oles-Mert -Merton on model? model? A. The return return from from the stock stock in a short short eriod eriod of time is lognormal lognormal B. The stock stock rice rice at a future future time time is lognor lognormal mal !. The stock stock rice rice at a future future time time is norm normal al ". #one #one of of the the abo$ abo$e e %. The original original Black-Scholes Black-Scholes and and Merton Merton aers on stock stock otion ricing were ublished in which year? A. 1&'( B. 1&') !. 1&*) ". 1&*( (. Which Which of the follow following ing is a de+nit de+nition ion of $olatil $olatility ity A. The standard standard de$iation de$iation of of the return, return, measured measured with continuous continuous comounding, in one year B. The $ariance $ariance of the return, return, measured measured with continuous continuous comounding, comounding, in in one year !. The standar standard d de$iation de$iation of of the stock stock rice rice in one year year ". The $arianc $ariance e of the stock stock rice rice in one one year ). A stock rice rice is 1. /olatility /olatility is estimated estimated to be %0 er year. year. What is an estimate of the standard de$iation of the change in the stock rice in one week? A. .(' B. %.** !. (.% ". .* 2. What What does does #345 #345 deno denote? te? A. The area under under a normal normal distribution distribution from from 6ero to x under a normal normal distribution distribution u to 4 B. The area under under a normal normal distribution distribution beyond 4 C. The area under D. The area under under the normal normal distribution distribution between - x and and 4 . Which of the following following is true true for a one-year call otion on a stock stock that ays di$idends e$ery three months? A. 7t is ne$er ne$er otimal otimal to e4erc e4ercise ise the otio otion n early B. 7t can be otima otimall to e4erc e4ercise ise the otio otion n at any time time !. 7t is only only e$er otimal otimal to e4ercise e4ercise the otion immediately after after an e4e4di$idend date ". #one #one of of the the abo$ abo$e e
*. What is the number of trading days in a year usually assumed for e8uities? A. (2 B. %2% !. %% ". %*% '. The risk-free rate is 20 and the e4ected return on a non-di$idend-aying stock is 1%0. Which of the following is a way of $aluing a deri$ati$e? A. Assume that the e4ected growth rate for the stock rice is 1*0 and discount the e4ected ayo9 at 1%0 B. Assuming that the e4ected growth rate for the stock rice is 20 and discounting the e4ected ayo9 at 1%0 !. Assuming that the e4ected growth rate for the stock rice is 20 and discounting the e4ected ayo9 at 20 ". Assuming that the e4ected growth rate for the stock rice is 1%0 and discounting the e4ected ayo9 at 20 &. When there are two di$idends on a stock, Black:s aro4imation sets the $alue of an American call otion e8ual to which of the following A. The $alue of a ;uroean otion maturing ; B. istorical $olatilities for stock otions trading on !B>; !. 7mlied $olatilities for otions trading on the S@ 2 inde4 ". istorical $olatilities for otions trading on the S@ 2 inde4 11.What was the original Black-Scholes-Merton model designed to $alue? A. A ;uroean otion on a stock ro$iding no di$idends B. A ;uroean or American otion on a stock ro$iding no di$idends !. A ;uroean otion on any stock ". A ;uroean or American otion on any stock 1%.A stock ro$ides an e4ected return of 10 er year and has a $olatility of %0 er year. What is the e4ected $alue of the continuously comounded return in one year? A. 0 B. '0 !. 10 ". 1%0
1(.An in$estor has earned %0, 1%0 and -10 on e8uity in$estments in
successi$e years 3annually comounded5. This is e8ui$alent to earning which of the following annually comounded rates for the three year eriod. A. 1.((0 B. 1.%(0 !. 1.1(0 ". .&(0 1).Which of the following is #>T true? A. isk-neutral $aluation ro$ides rices that are only correct in a world where in$estors are risk-neutral B. >tions can be $alued based on the assumtion that in$estors are risk neutral !. 7n risk-neutral $aluation the e4ected return on all in$estment assets is set e8ual to the risk-free rate ". 7n risk-neutral $aluation the risk-free rate is used to discount e4ected cash Cows 12.Which of the following is a way of e4tending the Black-Scholes-Merton formula to $alue a ;uroean call otion on a stock aying a single di$idend? A. educe the maturity of the otion so that it e8uals the time of the di$idend B. Subtract the di$idend from the stock rice !. Add the di$idend to the stock rice ". Subtract the resent $alue of the di$idend from the stock rice 1.When the Black-Scholes-Merton and binomial tree models are used to $alue an otion on a non-di$idend-aying stock, which of the following is true? A. The binomial tree rice con$erges to a rice slightly abo$e the BlackScholes-Merton rice as the number of time stes is increased B. The binomial tree rice con$erges to a rice slightly below the BlackScholes-Merton rice as the number of time stes is increased !. ;ither A or B can be true ". The binomial tree rice con$erges to the Black-Scholes-Merton rice as the number of time stes is increased 1*.When the non-di$idend aying stock rice is %, the strike rice is %, the risk-free rate is 0, the $olatility is %0 and the time to maturity is ( months which of the following is the rice of a ;uroean call otion on the stock A. %#3.15-1&.*#3.%5 B. %#3.%5-1&.*#3.15 !. 1&.*#3.%5-%#3.15 ". 1&.*#3.15-%#3.%5
1'.When the non-di$idend aying stock rice is %, the strike rice is %, the risk-free rate is 20, the $olatility is %0 and the time to maturity is ( months which of the following is the rice of a ;uroean ut otion on the stock A. 1&.*#3-.15-%#3-.%5 B. %#3-.15-%#3-.%5 !. 1&.*#3-.%5-%#3-.15 ". %#3-.%5-%#3-.15 1&.A stock rice is %, %%, 1&, %1, %), and %) on si4 successi$e Dridays. Which of the following is closest to the $olatility er annum estimated from this data? A. 20 B. 0 !. *0 ". '0 %.The $olatility of a stock is 1'0 er year. Which of the following is closest to the $olatility er month? A. 1.20 B. (.0 !. 2.%0 ". .(0
