Hull_ofod9e_multiplechoice_questions_only_ch21.doc

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Hull: Options, Futures, and other Derivatives, Ninth Edition Chapter 21: Basic Numerical Procedures Multiple Choice est Ban!: "uestions 1. How many nodes nodes are are there at the end of a Cox-Ros Cox-Ross-Rubin s-Rubinstein stein ve-step binomial tree? A. 4 . ! C. " #. $ %. &hi'h of the followin( followin( 'annot 'annot be estimated estimated from from a sin(le binomial tree? tree? A. delta . (amma C. theta #. ve(a ). &hi'h of the the followin( is true for u in in a Cox-Ross-R Cox-Ross-Rubinstein ubinstein binomial binomial tree? tree? A. *t depends depends on the the interes interestt rate and and the volatil volatility ity . *t depends depends on the the volatilit volatility y but not the the intere interest st rate C. *t depends depends on the intere interest st rate but but not the volatil volatility ity #. *t depends on neither neither the interest rate nor the volatility volatility 4. How many di+erent di+erent paths are are there throu(h throu(h a Cox-Ros Cox-Ross-Rubi s-Rubinstein nstein tree tree with four-steps? A. ! . , C. 1% #. 1" !. &hen we move from from assumin( no dividends dividends to assumin( assumin( a 'onstant dividend dividend yield whi'h of the followin( is true for a Cox Ross Rubinstein tree? A. he para paramet meters ers u and and p 'han( 'han(e e . p 'han( 'han(es es but but u does does not not C. u 'han( 'han(es es but but p does does not not #. /eith /either er p nor nor u 'han 'han(es (es ". &hen the sto'0 pri'e pri'e is % and and the present present value of dividends dividends is % whi'h of the followin( is the re'ommended way of 'onstru'tin( a tree? A. #raw a tree tree for an initial sto'0 sto'0 pri'e of % and and subtra't subtra't the present present value of future dividends at ea'h node . #raw a tree tree for an initial sto'0 sto'0 pri'e of %% and and subtra't subtra't the present present value of future dividends at ea'h node C. #raw a tree tree with an initial sto'0 sto'0 pri'e of of 12 and add the present present value value of future dividends at ea'h node #. #raw a tree tree with an initial initial sto'0 pri'e pri'e of 12 and add add % at ea'h node node $. &hat is the re'ommended re'ommended way of ma0in( interest interest rates a fun'tion fun'tion of of time in a Cox Ross Rubinstein tree? A. 3a0e u a fun'tion of time . 3a0e p a fun'tion of time C. 3a0e u and p a fun'tion of time #. 3a0e the len(ths of the time steps uneual 2. &hat is the re'ommended way of ma0in( volatility a fun'tion of time in a Cox Ross Rubinstein tree? A. 3a0e u a fun'tion of time . 3a0e p a fun'tion of time C. 3a0e u and p a fun'tion of time #. 3a0e the len(ths of the time steps uneual ,. A binomial tree pri'es an Ameri'an option at 5).1% and the 'orrespondin( 6uropean option at 5).4. he la'0-7'holes pri'e of the 6uropean option is 5%.,2. &hat is the 'ontrol variate pri'e of the Ameri'an option? A. 5)." . 5).12 C. 5%., #. 5).2 1.he 'hapter dis'usses an alternative to the Cox Ross Rubinstein tree. *n this alternative whi'h of the followin( are true8 A. he relationship between u and d is8 u91:d . he relationship between u and d is8 u-191-d C. he probabilities on the tree are all .! #. /one of the above 11.&hi'h of the followin( 'annot be valued by 3onte Carlo simulation A. 6uropean options . Ameri'an options C. Asian options ;i.e. options on the avera(e sto'0 pri'e< #. An option whi'h provides a payo+ of 51 if the sto'0 pri'e is (reater than the stri0e pri'e at maturity 1%.&hi'h of the followin( is true? A. he impli'it nite di+eren'e method relates pri'es at one node to three pri'es at nodes at a later time . he impli'it nite di+eren'e method relates pri'es at one node to three pri'es at nodes at an earlier time C. he impli'it nite di+eren'e method relates pri'es at one node to three pri'es at nodes at the same time #. /one of the above 1).&hi'h of the followin( is true? A. he impli'it nite di+eren'e method is euivalent to usin( a trinomial tree . he expli'it nite di+eren'e method is euivalent to usin( a trinomial tree C. oth methods are euivalent to usin( a trinomial tree #. /either method is euivalent to usin( a trinomial tree 14.he standard deviation of the values of an option 'al'ulated usin( 1 3onte Carlo trials is 4.!. he avera(e of the values is %. &hat is the standard error of this as an estimate of the option pri'e? A. 4.! . .4! C. .4! #. .4! 1!.he values of a sto'0 pri'e at the end of the se'ond time step are 52 51 51%!. he 'orrespondin( values of an option are 5 5! and 5% respe'tively. &hat is an estimate of (amma? A. .1)" . .14" C. .1!" #. .1"" 1".&hat is the di+eren'e between valuin( an Ameri'an and a 6uropean option usin( a tree? A. he value of u is hi(her for Ameri'an options . he value of u is lower for Ameri'an options C. he time steps for Ameri'an options are not eual #. *t is ne'essary to do two 'al'ulations at nodes where the option is in the money 1$.A 6uropean option on a sto'0 with a 0nown dollar dividend is valued by settin( the sto'0 pri'e variable eual to the sto'0 pri'e minus the present value of the dividend in the la'0-7'holes-3erton formula. A se'ond pri'e 'an be obtained usin( the tree buildin( pro'edure in the 'hapter. &hi'h of the followin( is true when a very lar(e number of time steps are used in the tree? A. he rst pri'e is hi(her than the se'ond pri'e . he rst pri'e is lower than the se'ond pri'e C. he rst pri'e is sometimes hi(her and sometimes lower than the se'ond pri'e #. he two pri'es are almost exa'tly the same 12.&hi'h of the followin( is possible in a modied Cox Ross Rubinstein binomial tree? A. he interest rate and volatility 'an both be fun'tions of time . he interest rate or the volatility 'an be a fun'tion of time but not both C. he interest rate 'an be a fun'tion of time but the volatility 'annot #. he interest rate and volatility must be 'onstant 1,.&hi'h of the followin( des'ribes the way that the parameters in a binomial tree are 'hosen? A. he expe'ted return durin( ea'h time step is the ris0-free rate . he standard deviation of the return in ea'h time step is for small time steps almost exa'tly eual to the volatility per annum times the suare root of the len(th of the time step in years C. he tree re'ombines #. All of the above %.&hi'h of the followin( 'an be valued without usin( a numeri'al pro'edure su'h as a binomial tree? A. Ameri'an put options on a non-dividend payin( sto'0 . Ameri'an 'all options on a non-dividend payin( to'0 C. Ameri'an 'all options on a 'urren'y #. Ameri'an put options on futures