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JumpDiusion Stock Return Models in Finance Stochastic Process Density with UniformJump Amplitude Floyd B

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

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JumpDiusion Stock Return Models in Finance Stochastic Process Density with UniformJump Amplitude Floyd B






Presentation on theme: "JumpDiusion Stock Return Models in Finance Stochastic Process Density with UniformJump Amplitude Floyd B"— Presentation transcript:

                   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 "* (    D4$9C )D#C8         D) ( E   &1 )(   %&9 ( 2Corollary2.1."&     '      %&/      &%&/    (  -                *   %&% )- (    #   (    &F %&/ -          )(         (                 *      &,&%&/     (     %&4 )D  =  *         )( D         -  &,&%&$                   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   &Acknowledgement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