EBF 473 - Spring 2016 – Final Exam – Name: ___________________________________ The firs ! "#esi$ns are 20 p$ins ea%h& N$e ha here is als$ here is a sixh' exra %re(i' "#esi$n )$rh ! p$ins& Gamma= Γ=(1/2π) 0.5 exp(-d2/2)/ (Sσ(T-t) (Sσ(T-t) 0.5).
Put call parity P = ! "e -rt - S
*f a +aria,le is (isri,#e( n$rmall. )ih mean # an( san(ar( (e+iai$n /' -#/ is (isri,#e( n$rmall. )ih mean 0 an( san(ar( (e+iai$n (e+ iai$n 1& The pri%e $f a %all $pi$n $n 5eaher 5eaher (eri+ai+es is (eri+e( as f$ll$)s: e he n#m,er $f san(ar( (e+iai$ns he srie pri%e is a)a. fr$m he mean& #=-0.0$% $ ! 0.22%2-0.50%!0.& price =#'σ.
The Bla%-Sh$les $pi$n pri%ing f$rm#la is (S "Tt)=S(d)- Pt(T-t)"(d- σ(T-t) 0.5) *+ere d=,(l (S/P t(T-t)"))/( σ(T-t) 0.5)!0.5 σ(T-t) σ(T-t)0.5
*mpli%i +$laili. firs g#ess f$rm#la σ1=((S((105/100)!.02)'(2/.5)) 0.5
*mpli%i +$laili. #p(ae f$rm#la σ2= σ1 ,(1-'(3true4)) '(2π) 0.5 exp(d2/2)/,S 0 (T) 0.5
8 N$rmal 9isri,#i$n %har: -3 -2&; -2& -2&7 -2&6 -2&! -2&4 -2&3 -2&2 -2&1 -2 -1&; -1& -1&7 -1&6 -1&!
N 0&0013 0&001; 0&0026 0&003! 0&0047 0&0062 0&002 0&0107 0&013; 0&017; 0&022 0&027 0&03!; 0&0446 0&0!4 0&066
-1&! -1&4 -1&3 -1&2 -1&1 -1 -0&; -0& -0&7 -0&6 -0&! -0&4 -0&3 -0&2 -0&1 0
N 0&066 0&00 0&0;6 0&11!1 0&13!7 0&1!7 0&141 0&211; 0&2420 0&2743 0&30! 0&3446 0&321 0&4207 0&4602 0&!000
1
igh n$)' i sells f$r ?!! per share& @$# are an $pi$ns )rier' an( .$# ha+e )rien 2000 %all $pi$ns a a srie pri%e $f ?!0 $n
%allher=$sii$n
6elta 7 call 0&704 0&72!
171&
s$%=$sii$n9ela
Gamma 7 call 0&004; 0&00!!
2 <$ ,a% $ pr$,lem 1 an( #se he Bla%-Sh$les e"#ai$n $ pri%e a %all $pi$n )ih a srie $f 60& 9ela 0&72! =ri%e 24&0244
3 8ll in+es$rs ha+e #ili. CExpe%e( *n%$me – ! D arian%e $f *n%$me& The. %an in+es in eiher a safe asse $r s$% $f Briish =er$le#m& Briish =er$le#m s$% has an expe%e( pa.$ff $f F an( a +arian%e $f 0&1& There are 2! shares Briish =er$le#m $#san(ing& The ineres rae is 0' an( all asses pa. $ff nex peri$(&
There are 20 in+es$rs' ,# $nl. 10 are Briish =er$le#m fans )h$ hin F2& The $her 10 in+es$rs are >$.al 9#%h Shell fans )h$ hin F 1& 5ha is he mare pri%e $f Briish =er$le#m G$) m#%h s$% ($es ea%h >$.al 9#%h Shell fan ,#. Ea%h Briish =er$le#m fan
arian%e &1"2 C H - "= I "F – &1!"2 H – "= I "F – 0&!"2 -- ae (eri+ai+e )ih respe% $ " 0 -= I F – " "F–= J 102-= I 101-= J 30 – 20= Kare =ri%e: J 2! 2! 30 – 20= 2! – 30 -20= -! -20= 9ar:et Price = .25 ;P 1D2-1D0&2! = 1.<5 ;P = 1D1-1D0&2! = 0.<5
4 The l$ng-r#n %$s $f $il is ;0& The pri%e sep siLe is 1&1!& The iniial pri%e $f gas is $ne sep ,el$) he l$ng-r#n %$s& The )ell pr$(#%es #nis $f gas in he firs peri$( $f (rilling an( 6 in he se%$n( peri$( $f (rilling& The %$s $f (rilling in he firs peri$( is 700& The r$.al. rae )ill ,e 1!A& e he sep %$effi%ien 7' s$ ha he pr$,a,l. $f an #p m$+e is 0&!7-S7& 5ha is he +al#e $f he $pi$n if .$# exer%ise i in he firs peri$( an( (rill n$) mean price
step size
initai size
2nd period size
90
1.15
8
6
1st period initial price
2nd period Pr (up
Pr(do!n
78.26
0.57 Price (up 90.00 %e&enue s 5#0.00
0.#$ Price(do! n 68.05
81.00
61.25
*+pecte d %e&enue s 262.29
1#8.7#
Initial position step rom mean "1
%e&enue s 626.09 %oyalties 9$.91 'ost o drillin 700.00 )et re&enues
"167.8$ ,otal re&enue to producer i drill no! 2#$.20
#08.$2
1st period producti on costs 700
step coefcie nt
royal ty rate
7
0.15
,otal re&enue to lando!n er i drill no! 166.#5
! @$# are ,#.ing a srip $f %all $pi$ns $n Man#ar. an( Fe,r#ar. G99 in *r#s' >#ssia yes, it’s cold there in the winter )ih a srie pri%e $f 7000& The expe%e( +al#e $f G99s f$r Man#ar. in *r#s is 32!0& The san(ar( (e+iai$n is 700& *n Fe,r#ar. he expe%e( +al#e is 200 )ih a san(ar( (e+iai$n $f 600& The %$rrelai$n ,e)een hese )$ m$nhs is 0&& $mp#e he pri%e $f his srip& srie 7000 %lim$s 32!0 %lim$ 60!0 s(s 700 600 rh$ 0&000 s( 1&2337eI03 0&7700 @ 0&1317 pri%e 162&!173
200
