Lecture5-07

Lecture5-07 - ! " # $% "&' ) ) * +* ,- .* /*...

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Unformatted text preview: ! " # $% "&' ) ) * +* ,- .* /* 0 ( )! )! )# $" " " " " " " + . ,- .* /* 001 ! " # $% " 34 5 7! %" -" &" 0 % &* % + % &* + ) % &%+ , % &'( ) / % &* . + % &* . % &%( * % &%'' "6 2 882 2 ! " # $% ) 2 " $ ) 14 5 "1 " 13 1 1 9 ! " # $% 34 )/ 6 " % &%'' ) <% " )? -* ''7/89 $" 2 > " -* ''" 0:; <% $ 2 1= &%' ''' % : ! " # $% < > = " S' A ! F'A # TA rA @ " 1 1 1 " 1T ; ! " # $% @& " Time T $ - (ST − F0 0 $ ST − F0 " )7 Transaction Sell forward Buy underlying stock Borrow discounted value of F0 Time 0 0 - S0 F0 (1 + r)T F0 − S0 > 0 (1 + r)T Total 0 ? ! " # $% > @ ) " 3" B$ ) " " 3" B$ A2 A " 1 5 " 5 1 12 " ! " # $% 5 )! ); " ) ); " 1 " 1 21 1 " 1 " 2 2 " 1 " A ! " # $% 7 B )! 15 15 E D9 : 15 /! < ) ) A " /! D " 2 1 :F " 1 D2A8 @ @& " !C " 8 ! " # $% 7 @& )! 15 15 E D2A8 15 /! < ) A " /! D " 2 :F " 1 D2A8 "B @ 5 !C " ! " # $% 15 7 ) S T1 ) F = S (1+r )T %1 3 " 2 F 1 5 r ) $" SC ' TC -( % rC '. ' F C-( %D '. C) . '3 ' 5 '( ' ! " # $% G5 H > > * 5 " F0 = S0erT E 1 " " 2 2 ! " # $% G5 @ I I 2 F0 = (S0 F I )erT " 7 . G E " ? = &. ' =' * 1 9 ! " # $% G5 @ I J q " F0 = S0 e(rFq )T 21 3$ 25 2 : ! " # $% = )! ) K 1 2 ) H = (F0 K )eFrT ) !" 1 ) H = (K F F0 )eFrT 1 " > F0 1 H ; ! " # $% 1 ) 2 ) 2 )% ) )? )? $ " C. &* '' 2 % &''' % &') 02 2 2%& -" 2 2 %" 2- " ? ! " # $% )# "? 12 2 2 ) 2 2 " 1 " A 1 " 1 ) 2 1 ! " # $% ' ) 12 ) 1 " 4 q F0 = S0 e(rFq )T 2 1 1 $ 2 A ! " # $% ' . 0 4 $ )# ) 2 ) 8 " " 2 $ " " $" " 8 ! " # $% 4@ & )? )? F0 > S0e(r-q)T 12 F0 < S0e(r-q)T 2 $ 2 1 12 1 " $ ! " # $% 4@ & . 0 " ) $ 2 " 13 2 " 2 0 15 " 2 " 1 )I1 )/ S0 F0 ! " # $% > ) ) ) rf 2 1 1 2 2 1 2 1 2 F0 = S 0 e )! -G 1 2 -1 $ ( r −rf ) T . G :J :! &- 90 :!> ? :!> 90 % &) 2 ! " # $% G 5! 5 * 1000 1000 units of foreign currency at time zero H 1 - units of foreign currency at time T 1000 e rf T 1000S0 dollars at time zero dollars at time T 1000F0e f rT 1000S0erT dollars at time T 9 ! " # $% > @ u F0 ≤ S0 e(r+u )T 2 " 1 U F0 ≤ (S0+U )erT 2 : ! " # $% 15 > ) )# )# ) " " 1 ) F0 = S0 e(cFy )T 1c " 2 F0 = S0ecT F0 ≤ S0ecT " > ! y ; ! " # $% K 34 )! k $ E 1 )? F0e r T at the risk-free rate and enter into a long futures contract ST " 1 ) ( F 0 e − rT ) e kT = E ( S T ) or F0 = E ( S T ) e ( r − k ) T ? ! " # $% K . ) ! & " ! ! '5 k=r F0 ST ' 5 kLr ' 5 kMr 0 F 0 M E (S T ) F 0 L E (S T ) ...
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This note was uploaded on 12/14/2011 for the course FIN 5515 taught by Professor Staff during the Spring '10 term at FSU.

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