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137 "Remarquez qu'on a un peu trich\351 dans la figure ci-dessus: on a
 simplement distingu\351 (par des petits ronds rouges), les point o
\371 la valeur" }}{PARA 0 "" 0 "" {TEXT -1 135 "de l'option est \351ga
le au payoff : seuls les ronds rouges du bas repr\351sentent des point
s o\371 il convient d'exercer l'option; ceux du haut" }}{PARA 0 "" 0 "
" {TEXT -1 63 "correspondent simplement au cas o\371 l'option ne vaut \+
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\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"\"%!\"\"" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG$\"\"&!\"#" }}{PARA 11 "" 1 "" 
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{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"RG$\"+G%or+\"!\"*" }}{PARA 11 "" 
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" {MPLTEXT 1 0 178 "Sdiv:=proc(i,j1,j2) option remember;\n  # 0<=j1<=i
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2<=i-i_star repr\351sente le nombre de \"up\" intervenus pour i>i_star
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "if    i<i_star then S0*up^j1*d
own^(i-j1)\nelif  i=i_star then S0*up^j1*down^(i-j1)-div             \+
\nelse  Sdiv(i_star,j1,0)*up^j2*down^(i-i_star-j2) fi end;" }}{PARA 
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Sdiv(i,j1,0)]),\n                     line([i,Sdiv(i,j1,0)],[i+1,Sdiv(
i,j1,0)*up]),\n                     arbreSdiv(i+1,j1+1,0),\n          \+
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f i<i_star-1 then  point([i,Sdiv(i,j1,0)]),\n                      lin
e([i,Sdiv(i,j1,0)],[i+1,Sdiv(i+1,j1+1,0)]),\n                      arb
reSdiv(i+1,j1+1,0),                                                   \+
              line([i,Sdiv(i,j1)],[i+1,Sdiv(i+1,j1,0)]),\n            \+
          arbreSdiv(i+1,j1,0)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 269 "e
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([i,Sdiv(i,j1,j2)],[i+1,Sdiv(i+1,j1,j2+1)]),\n                    arbr
eSdiv(i+1,j1,j2+1),                                                   \+
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0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 39 "Calldiv:=proc(i,j1,j2) option remember;" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 110 "if i=n then max(Sdiv(n,j1,j2)-K,0) \nelif i>
=i_star then (p*Calldiv(i+1,j1,j2+1)+(1-p)*Calldiv(i+1,j1,j2))*actu" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "else (p*Calldiv(i+1,j1+1,0)+(1-p)*
Calldiv(i+1,j1,0))*actu   # ici on a donc i<i_star  \nfi: end;" }}
{PARA 12 "" 1 "" {XPPMATH 20 "6#>%(CalldivG:6%%\"iG%#j1G%#j2G6\"6#%)re
memberGF*@'/9$%\"nG-%$maxG6$,&-%%SdivG6%F09%9&\"\"\"%\"KG!\"\"\"\"!1%'
i_starGF/*&,&*&%\"pGF:-F$6%,&F/F:F:F:F8,&F9F:F:F:F:F:*&,&F:F:FCF<F:-F$
6%FFF8F9F:F:F:%%actuGF:*&,&*&FCF:-F$6%FF,&F8F:F:F:F=F:F:*&FIF:-F$6%FFF
8F=F:F:F:FLF:F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "filletCdiv:=proc(i,j1,j2) op
tion remember;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 356 "# if   i=i_star-
1 then          #on supprime le decrochement repr\351sent\351 artifici
ellement       \n#            line([i,Sdiv(i,j1,0),Calldiv(i,j1,0)],[i
+1,Sdiv(i,j1,0)*up,Calldiv(i+1,j1+1,0)]),\n#            filletCdiv(i+1
,j1+1,0),\n#            line([i,Sdiv(i,j1,0),Calldiv(i,j1,0)],[i+1,Sdi
v(i,j1,0)*down,Calldiv(i+1,j1,0)]),\n#            filletCdiv(i+1,j1,0)
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 358 "# elif i<i_star-1 then  \nif i
<=i_star-1 then \n    line([i,Sdiv(i,j1,0),Calldiv(i,j1,0)],[i+1,Sdiv(
i+1,j1+1,0),Calldiv(i+1,j1+1,0)]),\n    filletCdiv(i+1,j1+1,0),       \+
                                                                      \+
                      line([i,Sdiv(i,j1),Calldiv(i,j1)],[i+1,Sdiv(i+1,
j1,0),Calldiv(i+1,j1,0)]),\n    filletCdiv(i+1,j1,0)" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 322 "elif i<n    then      #ici on a donc i>i_star  \+
\n    line([i,Sdiv(i,j1,j2),Calldiv(i,j1,j2)],[i+1,Sdiv(i+1,j1,j2+1),C
alldiv(i+1,j1,j2+1)]),\n    filletCdiv(i+1,j1,j2+1),                  \+
                                                     line([i,Sdiv(i,j1
,j2),Calldiv(i,j1,j2)],[i+1,Sdiv(i+1,j1,j2),Calldiv(i+1,j1,j2)]),  " }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "    filletCdiv(i+1,j1,j2)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "fi" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 4 "end;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%+filletCdivG:6%%\"iG%#j
1G%#j2G6\"6#%)rememberGF*@&19$,&%'i_starG\"\"\"!\"\"F26&-%%lineG6$7%F/
-%%SdivG6%F/9%\"\"!-%(CalldivGF;7%,&F/F2F2F2-F:6%FA,&F<F2F2F2F=-F?FC-F
$FC-F66$7%F/-F:6$F/F<-F?FK7%FA-F:6%FAF<F=-F?FO-F$FO2F/%\"nG6&-F66$7%F/
-F:6%F/F<9&-F?FY7%FA-F:6%FAF<,&FZF2F2F2-F?Fhn-F$Fhn-F66$FW7%FA-F:6%FAF
<FZ-F?F`o-F$F`oF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "plot
s[display](filletCdiv(0,0,0),axes=boxed,orientation=[-27,57]);" }}
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#7$F[el7%FD$\"+iY4&*))F-$\"+:pL@5F[`l-F$6#7$FfelFf_lF\\`lFd`lF\\alFdal
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$6#7$Fafl7%FX$\"+7ofmsF-F(-F$6#7$Fgfl7%F\\o$\"+j!)f_%)F-F(-F$6#7$F]gl7
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\"#dF(F0" 3 485 485 485 1 0 1 0 2 1 0 2 2 1.000000 57.000000 
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1 }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "Calldiv(0,0,0);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+mWK?T!\")" }}}{EXCHG {PARA 0 "> " 
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