Hanson Laboratory for Advanced Computing University of Illinois at Chicago 851 Morgan St MC 249 Chicago IL 606077045 USA hansonmathuicedu and J J Westman Department of Mathematics University of California Box 951555 Los Angeles CA 900951555 USA jwes ID: 25220
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FloydB.HansonLaboratoryforAdvancedComputingUniversityofIllinoisatChicago851MorganSt.;M/C249Chicago,IL60607-7045,USAhanson@math.uic.eduJ.J.WestmanDepartmentofMathematicsUniversityofCaliforniaBox951555 " : !! 7!*) ) ) , ; ) =( ) ** ) ) * ( &6 ! & ( * & * =.0=" ( )( " " ; %&# ). 0=&#x-359;&#x.900; &#x-359;&#x.900;#(% #&#x-359;&#x.900; &5 * * )#) ! = #&#x-359;&#x.900; * &5 )( !* " * * ! ) 6 ".# 0 #$$%% # 5 #& * *! ( ) ( .)( ( . 0)% ) ) * )( ) & * . 0 * )Theorem2.1. . ! %&9 % 0.1 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.1 0 50 100 150 200 250 300 (sp)Frequency, f (sp)S&P500 Log Returns, DLog(S) 5 #21 6 "#$$%B% #) # &"# $ " # 6 ) D !&6 6 "* ( D 4$9C ) D # C8 D) ( E &1 )( %&9 ( 2Corollary2.1." & ' %&/ & %&/ ( - * %&% )- ( # ( &F %&/ - )( ( * &,& %&/ ( %&4 )D = * )( D - &,& %&$ D ) . #0 . 0 #0 D ) .0 * D#$ % 5 ! ) * ! &5 ) ) * )) D ! ( & ( 6 "#$$%% # =# 5 #) ! & % %% )% %# )D & * &G * ) E %$#4!( / 8! ) ! E & ! ! * ) *!( ! E &1 ) E ( E &6 .8) 0) ( ,(( * * * &1)(( , .$0 )(bin) ( ( ) , , -=% %#&+ ( )(( ( * (2Theorem3.1. * ( " " + " * ' ! (jdsim) (jdsim)=H ! "# ' * ( * )(jd)(bin)(jd) ) - * & 4 - ) * )( %& ) * * & -, - ,- .C0)* .8) 0)( 4&# & " * .$0 .90& ( ( ** #9I5 & ( , 5 %)( & ) & 0.1 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.1 0 50 100 150 200 250 300 350 GSF JumpDiffusion Theory Fit, f(jdth)Frequency, f(jdth)LogReturns, xi+0.5 0.1 0.08 0.06 0.04 0.02 0 0.02 0.04 0.06 0.08 0.1 0 50 100 150 200 250 300 350 GSF JumpDiffusion Simulation Fit, f(jdsim)Frequency, f(jdsim)LogReturns, xi+0.5 5 %21 ) 6 " #$$%B% #( 5 &#) # & )( & 6 ) ( ) !)#$$%% # 6 "& * * .80& * ( ,( ( ,( , &6 ) 6 " & ! ) .90 &Acknowledgement2J! F 5 K 7 I ;7B$$BC4%4#&.#05&' ! 7& )L M K : )N. $ )* &/#)94C9 $)#$C4&.%05&'&1 O&O&J )LM K 6 O 27 K K )N$ //0% 1 1) &88 9899#)% O % #&.405&'&1 O&O&J )L + O B; 5 :BG )N$ 1 23) BH )F(P!) &## ) )7% %&.805&'&1 O&O&J )LM K K O ; !( :F O )N$ // % 1 1) 	) /7 % %) &. 05&'&1 O&O&J )L M - ( O B; 2 + )N$ // 1 1 ) &## ) C7% %) * &.905&'&1 O&O&J )LK 7 K M - :F ; ):Q O * )N$ 04 ) 5 6 #3 ) 	)+% %) &.C05&'&1 O&O&J )LI 5 27 7 I Q 6 ; )N )+ % %&./0G&K&7 )1 - )' ' !( )K )7+)#$$ & .$0J&1&)&+&! ! )J&&H '&&5 )6 7 18% 1 )K Q * )K )QR)#$$%&.# 0P?5 )L1 S) ) K)N97:8 8;; ;5 % %&