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Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 23: Estimating Volatilities and Correlations Multiple Choice Test Bank: Questions with Answers 1. How many parameters are necessary to define an EWMA model A. B. C. D. 1 2 3 4 Answer: A One parameter (lambda) is necessary to define an EWMA model. 2. How many parameters are necessary to define a GARCH (1,1) model A. B. C. D. 1 2 3 4 Answer: C Three parameters (omega, alpha, and beta) are necessary to define a GARCH (1,1) m
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  Hull: Options, Futures, and Other Derivatives, Ninth Edition Chapter 23: Estimating Volatilities and Correlations Multiple Choice est !an : #uestions $ith %ns$ers 1. How many parameters are necessary to defne an EWMA modelA.1B.2C.3D.4Answer: AOne parameter lam!da #s necessary to defne an EWMA model. 2. How many parameters are necessary to defne a $A%CH 1&1 modelA.1B.2C.3D.4Answer: C '(ree parameters ome)a& alp(a& and !eta are necessary to defne a $A%CH 1&1 model. 3. At t(e end o* '(+rsday& t(e est#mated ,olat#l#ty o* asset A #s 2- per day. D+r#n) r#day asset A prod+ces a ret+rn o* 3-. An EWMA model w#t( lam!da e/+al to 0. #s +sed. W(at #s an est#mate o* t(e ,olat#l#ty o* asset A at t(e endo* r#day A.2.0-B.2.10-C.2.12-D.2.14- Answer: C '(e ,ar#ance rate #s 0.0.02 2 50.10.03 2 6 0.00047. '(e ,olat#l#ty per day #s t(e s/+are root o* t(#s or 2.12-. 4. At t(e end o* '(+rsday& t(e est#mated ,olat#l#ty o* asset B #s 1- per day. D+r#n) r#day asset B prod+ces a ret+rn o* 8ero. An EWMA model w#t( lam!da e/+al to 0. #s +sed. W(at #s an est#mate o* t(e ,olat#l#ty o* asset A att(e end o* r#day A.0.-B.0.7-C.0.2-D.0.0-   Answer: B '(e ,ar#ance rate #s 0.0.01 2 50.10.0 2 6 0.0000. '(e ,olat#l#ty per day #s t(e s/+are root o* t(#s or 0.7-. 7. At t(e end o* '(+rsday& t(e est#mated co,ar#ance !etween assets A and B #s 0.0001. D+r#n) r#day asset A prod+ces a ret+rn o* 3- and asset B prod+ces aret+rn o* 8ero. An EWMA model w#t( lam!da e/+al to 0. #s +sed. W(at #s an est#mate o* t(e co,ar#ance at t(e end o* r#dayA.0.00000B.0.00001C.0.000100D.0.00007 Answer: A '(e co,ar#ance #s 0.0.000150.10.030 6 0.00000. 9. W(#c( o* t(e *ollow#n) #s a defn#t#on o* t(e co,ar#ance !etween  and ;A.Correlat#on !etween  and ; t#mes ,ar#ance o*  t#mes ,ar#ance o* ;B.<ar#ance o*  t#mes t(e ,ar#ance o* ;C.Correlat#on !etween  and ; d#,#ded !y t(e prod+ct o* t(e standard de,#at#on o*  and t(e standard de,#at#on o* ;D.Correlat#on !etween  and ; t#mes standard de,#at#on o*  t#mes standard de,#at#on o* ; Answer: DCo,ar#ance #s t(e coe=c#ent o* correlat#on m+lt#pl#ed !y t(e prod+ct o* t(etwo standard de,#at#ons. >. W(at does EWMA stand *orA.E/+ally we#)(ted mo,#n) a,era)eB.E/+ally we#)(ted med#an appro?#mat#onC.E?ponent#ally we#)(ted mo,#n) a,era)eD.E?ponent#ally we#)(ted med#an a,era)e Answer: CEWMA stands *or e?ponent#ally we#)(ted mo,#n) a,era)e . W(#c( o* t(e *ollow#n) #s tr+e w(en t(e parameter lam!da e/+als 0.7A.'(e we#)(t )#,en to t(e most recent o!ser,at#on #s 0.7B.'(e we#)(t )#,en to t(e o!ser,at#on one day a)o #s 7- o* t(e we#)(t )#,en to t(e o!ser,at#on two days a)oC.'(e we#)(ts )#,en to o!ser,at#ons add +p to 0.7  D.'(e we#)(ts )#,en to t(e o!ser,at#on two days a)o #s 7- o* t(e we#)(t )#,en to t(e o!ser,at#on one day a)o Answer: D '(e we#)(ts )#,en to o!ser,at#ons )o down !y 7- *or eac( day we )o !ac@ #n t#me. . W(#c( o* t(e *ollow#n) #s tr+e o* ma?#m+m l#@el#(ood met(odsA.'(ey calc+late t(e ma?#m+m poss#!le ,al+es *or parametersB.'(ey calc+late parameters t(at )#,e t(e (#)(est pro!a!#l#ty o* past data occ+rr#n)C.'(ey calc+late ,al+es *or @ey ,ar#a!les t(at are most l#@ely to occ+r #n t(e *+t+reD.'(ey #n,ol,e a m+lt#,ar#ate re)ress#on analys#sAnswer: BMa?#m+m l#@el#(ood met(ods are concerned w#t( est#mat#n) parameter,al+es !y searc(#n) *or t(e ,al+es t(at ma?#m#8e t(e c(ance o* o!ser,ed data occ+rr#n). 10. * t(e ,olat#l#ty *or a port*ol#o #s 20- per year& w(at #s t(e ,olat#l#ty per /+arterA.20-B.10-C.7-D.2- Answer: B  '(e ,olat#l#ty per /+arter #s 1.025.02.0  =× or 10-. 11. W(#c( o* t(e *ollow#n) #s tr+eA.$A%CH models #ncorporate mean re,ers#on EWMA models do not B.EWMA models #ncorporate mean re,ers#on $A%CH models do notC.Bot( $A%CH and EWMA models #ncorporate mean re,ers#onD.e#t(er $A%CH nor EWMA models #ncorporate mean re,ers#onAnswer: A$A%CH models #ncorporate mean re,ers#on EWMA models do not. 12. W(#c( o* t(e *ollow#n) #s tr+eA.All opt#on #mpl#ed ,olat#l#t#es tend to mo,e !y t(e same a!o+t *rom oneday to t(e ne?tB.'(e #mpl#ed ,olat#l#t#es o* lon)dated opt#ons tend to mo,e !y more t(an t(e #mpl#ed ,olat#l#t#es o* s(ortdated opt#onsC.'(e #mpl#ed ,olat#l#t#es o* s(ortdated opt#ons tend to mo,e !y more t(an t(e #mpl#ed ,olat#l#t#es o* lon)dated opt#ons  D. omet#mes C #s tr+e and somet#mes D #s tr+eAnswer: CW(en t(ere #s a s(oc@ ca+s#n) an #ncrease or decrease #n ,olat#l#ty #ts #mpact tends to d#sappear   o,er t#me. '(#s #s t(e eFect o* mean re,ers#on. '(e res+lt #s t(at t(e #ncrease or decrease ,olat#l#ty (as most eFect on t(e #mpl#ed ,olat#l#t#es o* s(ortdated opt#ons. 13. W(#c( o* t(e *ollow#n) #s tr+e o* a pos#t#,e sem#defn#te ,ar#anceco,ar#ance matr#?A.All elements o* t(e matr#? are pos#t#,eB.'(e determ#nant o* t(e matr#? #s pos#t#,eC.'(e matr#? #s symmetr#cD.'(e matr#? #s #nternally cons#stentAnswer: D '(e correlat#ons !etween many d#Ferent ,ar#a!les are not #nternally cons#stent +nless t(e ,ar#anceco,ar#ance matr#? #s pos#t#,e sem#defn#te. 14. W(#c( o* t(e *ollow#n) #s tr+eA.<olat#l#t#es and correlat#ons decreased #n t(e second (al* o* 200B.<olat#l#t#es and correlat#ons #ncreased #n t(e second (al* o* 200C.<olat#l#t#es decreased and correlat#ons #ncreased #n t(e second (al* o* 200D.<olat#l#t#es #ncreased and correlat#ons decreased #n t(e second (al* o* 200Answer: BAs t(e *o+r#nde? e?ample #n t(e c(apter s(ows& !ot( ,olat#l#t#es and correlat#ons #ncreased #n t(e second (al* o* 200 17.  '(e parameters #n a $A%CH 1&1 model are: ome)a 60.000002& alp(a6 0.04& and !eta 6 0.7. '(e c+rrent est#mate o* t(e ,olat#l#ty le,el #s 1- per day. * we o!ser,e a c(an)e #n t(e ,al+e o* t(e ,ar#a!le e/+al to 2-& (ow does t(e est#mate o* t(e ,olat#l#ty c(an)eA.1.29-B.1.19-C.1.09-D.1.03-Answer: C '(e new ,ar#ance rate #s 0.00000250.040.02 2 50.70.01 2 6 0.000113.  '(e new ,olat#l#ty #s t(e s/+are root o* t(#s or 1.09- 19.  '(e parameters #n a $A%CH 1&1 model are: ome)a 60.000002& alp(a6 0.04& and !eta 6 0.7. W(#c( o* t(e *ollow#n) #s t(e closest to t(e lon) r+n
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