Monte Carlo Simulation in Excel

 

L`trmhuitlm` tm Om`tf Ikrdm Yloudktlm` l` Fxifd

Ubm usfs Om`tf Ikrdm Yloudktlm`=

Ok`y imopk`lfs usf Om`tf Ikrdm sloudktlm` ks k` lopmrtk`t pkrt ma tbflr hfilslm`-okcl`e prmifss. Bfrf krf smof fxkopdfs.  

Ef`frkd Omtmrs, ^rmitmr k`h Ekojdf, ^alzfr, Jrlstmd-Oyfrs Yquljj, k`h Fdl Dlddy usf sloudktlm` tm fstloktf jmtb tbf kvfrkef rftur` k`h tbf rlsc akitmr ma `fw  prmhuits. Kt EO, tbls l`amroktlm` ls usfh jy tbf IFM tm hftfrol`f wblib  prmhuits imof tm okrcft.

 

EO usfs sloudktlm` amr kitlvltlfs suib ks amrfikstl`e `ft l`imof amr tbf imrpmrktlm`, prfhlitl`e struiturkd k`h puribksl`e imsts, k`h hftfrol`l`e lts susifptljldlty tm hlaafrf`t cl`hs ma rlsc (suib ks l`tfrfst rktf ibk`efs ib k`efs k`h fxibk`ef rktf aduituktlm`s).

 

Dlddy usfs sloudktlm` tm hftfrol`f tbf mptlokd pdk`t ikpkilty ikpkilt y amr fkib hrue.

 

^rmitmr k`h Ekojdf usfs sloudktlm` tm omhfd k`h mptlokddy bfhef amrfle` fxibk`ef rlsc.

 

Yfkrs usfs sloudktlm` tm hftfrol`f bmw ok`y u`lts ma fkib prmhuit dl`f sbmudh jf mrhfrfh armo suppdlfrs ‘ amr amr fxkopdf, tbf `uojfr ma pklrs ma Hmicfrs trmusfrs tbkt sbmudh jf mrhfrfh tbls yfkr.

 

Mld k`h hrue imopk`lfs usf sloudktlm` tm vkduf "rfkd mptlm`s," suib ks tbf vkduf ma k` mptlm` tm fxpk`h, im`trkit, mr pmstpm`f k prmgfit.

 

Al`k`ilkd pdk``frs usf Om`tf Ikrdm sloudktlm` tm hftfrol`f mptlokd l`vfstof`t strktfelfs amr tbflr idlf`ts“ rftlrfof`t. 

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Ubkt bkppf`s wbf` ymu typf ZK@H() l` k ifdd=

Ubf` ymu typf tbf amroudk ?ZK@H() l` k ifdd, ymu eft k `uojfr tbkt ls fqukddy dlcfdy tm kssuof k`y vkduf jftwff` > k`h ;. Xbus, krmu`h :6 pfrif`t ma tbf tlof, ymu sbmudh eft k `uojfr dfss tbk` mr fqukd tm >.:63 krmu`h ;> pfrif`t ma tbf tlof ymu sbmudh eft k `uojfr tbkt ls kt dfkst >., k`h sm m`. Xm hfom`strktf bmw tbf ZK@H au`itlm` wmrcs, tkcf k dmmc kt tbf tkjdf, sbmw` l` Aleurf. Xbf ZK@H au`itlm` kdwkys kutmoktlikddy rfikdiudktfs tbf `uojfrs lt ef`frktfs wbf` k wmrcsbfft ls mpf`fh mr wbf` `fw l`amroktlm` ls f`tfrfh l`tm tbf wmrcsbfft.

 

 

Alrst, impy armo ifdd I9 tm I87I:5 tbf amroudk ?ZK@H(). Xbf` ymu `kof tbf rk`ef I97I:5 Hktk. Xbf`, l` imduo` A, ymu ik` trkic tbf kvfrkef ma tbf 8>> rk`hmo `uojfrs (ifdd A:) k`h usf tbf IMV@XLA au`itlm` tm hftfrol`f tbf arkitlm`s tbkt krf jftwff` > k`h >.:6, >.:6 k`h >.6>, >.6> k`h >.56, k`h >.56 k`h ;. Ubf` ymu prfss tbf A< cfy, tbf rk`hmo `uojfrs krf rfikdiudktfh. @mtlif tbkt tbf kvfrkef ma tbf `uojfrs ls kdwkys kpprmxloktfdy >.6, k`h tbkt krmu`h :6  pfrif`t ma tbf rfsudts krf l` l`tfrvkds ma >.:6. Xbfsf rfsudts krf im`slstf`t wltb tbf hfal`ltlm` ma k rk`hmo `uojfr. Kdsm `mtf tbkt tbf vkdufs ef`frktfh jy ZK@H l` hlaafrf`t ifdds krf l`hfpf`hf`t. Amr fxkopdf, la tbf rk`hmo `uojfr ef`frktfh l` ifdd I9 ls k dkref `uojfr (amr fxkopdf, >.>> wldd miiur ;> pfrif`t ma tbf tlof, k`h sm m`.

Xm hfom`strktf tbf sloudktlm` ma hfok`h, dmmc kt tbf aldf sbmw` jfdmw7

Xbf cfy tm mur sloudktlm` ls tm usf k rk`hmo `uojfr tm l`ltlktf k dmmcup armo tbf tkjdf rk`ef A:7E6 (`kofh dmmcup). Zk`hmo `uojfrs erfktfr tbk` mr fqukd tm > k`h dfss tbk` >.;> wldd ylfdh k hfok`h ma ;>,>>>3 rk`hmo `uojfrs erfktfr tbk` mr fqukd tm >.;> k`h dfss tbk` >.86 wldd ylfdh k hfok`h ma :>,>>>3 rk`hmo `uojfrs erfktfr tbk` mr fqukd tm >.86 k`h dfss tbk` >.56 wldd ylfdh k hfok`h ma 8>,>>>3 k`h rk`hmo `uojfrs erfktfr tbk` mr fqukd tm >.56 wldd ylfdh k hfok`h ma 1>,>>>. \mu

 

ef`frktf 8>> rk`hmo `uojfrs jy impyl`e armo I9 tm I87I:1 tbf amroudk ZK@H(). \mu tbf` ef`frktf 8>> trlkds, mr ltfrktlm`s, ma ikdf`hkr hfok`h  jy impyl`e armo J9 tm J87J:1 tbf amroudk QDMMCV^(I9,dmmcup,:). Xbls amroudk f`surfs tbkt k`y rk`hmo `uojfr dfss tbk` >.;> ef`frktfs k hfok`h ma ;>,>>>, k`y rk`hmo `uojfr jftwff` >.;> k`h >.86 ef`frktfs k hfok`h ma :>,>>>, k`h sm m`. L` tbf ifdd rk`ef A27A;;, usf tbf IMV@XLA au`itlm` tm hftfrol`f tbf arkitlm` ma mur 8>> ltfrktlm`s ylfdhl`e fkib hfok`h. Ubf` wf prfss A< tm rfikdiudktf tbf rk`hmo `uojfrs, tbf sloudktfh prmjkjldltlfs krf idmsf tm mur kssuofh hfok`h prmjkjldltlfs. Bmw ik` ymu sloudktf vkdufs ma k `mrokd rk`hmo vkrlkjdf=

La ymu typf l` k`y ifdd tbf amroudk @MZOL@Q(rk`h(),ou,sleok), ymu wldd ef`frktf k sloudktfh vkduf ma k `mrokd rk`hmo vkrlkjdf bkvl`e k ofk` ou k`h stk`hkrh hfvlktlm` sleok.

Dft“s suppmsf wf wk`t tm sloudktf 8>> trlkds, mr ltfrktlm`s, amr k `mrokd rk`hmo vkrlkjdf wltb k ofk` ma 8>,>>> k`h k stk`hkrh hfvlktlm` ma ;>,>>>. (\mu ik` typf tbfsf vkdufs l` ifdds F; k`h F:, k`h `kof tbfsf ifdds ofk` k`h sleok, rfspfitlvfdy.) Impyl`e tbf amroudk ?ZK@H() armo I8 tm I67I8>9 ef`frktfs 8>> hlaafrf`t rk`hmo `uojfrs. Impyl`e armo J8 tm J67J8>9 tbf amroudk @MZOL@Q(I8,ofk`,sleok)  ef`frktfs 8>> hlaafrf`t trlkd vkdufs armo k `mrokd rk`hmo vkrlkjdf wltb k ofk` ma 8>,>>> k`h k stk`hkrh hfvlktlm` ma ;>,>>>. Ubf` wf prfss tbf A< cfy tm rfikdiudktf tbf rk`hmo `uojfrs, tbf ofk` rfokl`s idmsf tm 8>,>>> k`h tbf stk`hkrh hfvlktlm` idmsf tm ;>,>>>.

Fssf`tlkddy, amr k rk`hmo `uojfr  x, tbf amroudk  @MZOL@Q (p,ou,  sleok) ef`frktfs tbf ptb pfrif`tldf ma k `mrokd rk`hmo vkrlkjdf wltb k ofk` ou k`h k stk`hkrh hfvlktlm` sleok. Amr fxkopdf, tbf rk`hmo `uojfr >.55

 

l` ifdd I8 ef`frktfs l` ifdd J8 kpprmxloktfdy tbf 55tb pfrif`tldf ma k `mrokd rk`hmo vkrlkjdf wltb k ofk` ma 8>,>>> k`h k stk`hkrh hfvlktlm` ma ;>,>>>. ^rmjdfos

;.  K EOI hfkdfr jfdlfvfs tbkt hfok`h amr :>>6 F`vmys wldd jf `mrokddy hlstrljutfh wltb k ofk` ma :>> k`h stk`hkrh hfvlktlm` ma 9>. Bls imst ma rfiflvl`e k` F`vmy ls $:6,>>>, k`h bf sfdds k` F`vmy amr $8>,>>>. Bkda ma kdd tbf F`vmys `mt smdh kt audd prlif ik` jf smdh amr $9>,>>>. Bf ls im`slhfrl`e mrhfrl`e :>>, ::>, :8>, :1>, :2>, mr 9>> F`vmys. Bmw ok`y sbmudh bf mrhfr= :.  K sokdd supfrokrcft ls tryl`e tm hftfrol`f bmw ok`y implfs ma ^fmpdf okekzl`f tbfy sbmudh mrhfr fkib wffc. Xbfy jfdlfvf tbflr hfok`h amr  ^fmpdf ls emvfr`fh  jy tbf amddmwl`e hlsirftf rk`hmo vkrlkjdf7

9.  Xbf supfrokrcft pkys $;.>> amr fkib impy ma ^fmpdf k`h sfdds lt amr $;..6>. Bmw ok`y implfs ma ^fmpdf sbmudh tbf stmrf mrhfr= Bmw ik` k erfftl`e ikrh imopk`y hftfrol`f bmw ok`y ikrh tm prmhuif=

L` tbls sfitlm`, ymu wldd sff bmw Om`tf Ikrdm sloudktlm` ik` jf usfh ks k hfilslm`-okcl`e tmmd.

 

Yuppmsf tbkt tbf hfok`h amr k Qkdf`tl`f“s Hky ikrh ls emvfr`fh jy tbf amddmwl`e hlsirftf rk`hmo vkrlkjdf7

Xbf erfftl`e ikrh sfdds amr $8.>>, k`h tbf vkrlkjdf imst ma prmhuil`e fkib ikrh ls $;.6>. Dfatmvfr ikrhs oust jf hlspmsfh ma kt k imst ma $>.:> pfr ikrh. Bmw ok`y ikrhs sbmudh jf prl`tfh= Jkslikddy, wf sloudktf fkib pmssljdf prmhuitlm` quk`tlty (;>,>>>, :>,>>>, 8>,>>>, mr 1>,>>>) ok`y tlofs fxkopdf, ;>>> prmalt ltfrktlm`s). Xbf` wfltfrktlm`s. hftfrol`f wblib mrhfr quk`tlty ylfdhs tbf(amr okxlouo kvfrkef m vfr tbf mvfr ;>>> \mu kssle` tbf rk`ef `kofs l` ifdds J;7J;; tm ifdds I;7I;;. Mur skdfs prlif k`h imst pkrkoftfrs krf f`tfrfh l` ifdds I87I1.

\mu ik` f`tfr k trlkd prmhuitlm` quk`tlty (8>,>>> l` tbls fxkopdf) l` ifdd I;.  @fxt, irfktf k rk`hmo `uojfr l` ifdd I: wltb tbf amroudk ?ZK@H(). Ks  prfvlmusdy hfsirljfh, ymu sloudktf hfok`h amr tbf ikrh l` ifdd I9 wltb tbf amroudk QDMMCV^(rk`h,dmmcup,:). (L` tbf QDMMCV^ amroudk, rk`h  ls   ls tbf ifdd `kof kssle`fh tm ifdd I9, `mt tbf ZK@H au`itlm`.) Xbf `uojfr ma u`lts smdh ls tbf sokddfr ma mur prmhuitlm` quk`tlty k`h hfok`h. L` ifdd I2, ymu imoputf mur rfvf`uf wltb tbf amroudk OL@(prmhuifh,hfok`h)*u`lt]prlif. L` ifdd I wltb tbf amroudk u`lt]hlsp]imst*LA(prmhuifh0hfok`h,prmhuifh  ’ hfok`h,>) hfok`h,>). Al`kddy, l` ifdd I;;, wf imoputf mur prmalt ks rfvf`uf ’  tmtkd]vkr]imst-tmtkd]hlspmsl`e]imst   tmtkd]vkr]imst-tmtkd]hlspmsl`e]imst . Uf wmudh dlcf k` faalilf`t wky tm prfss A< ok`y tlofs (amr fxkopdf, ;>>>) amr fkib prmhuitlm` quk`tlty k`h tkddy mur fxpfitfh prmalt amr fkib quk`tlty. Xbls sltuktlm` ls m`f l` wblib k twm-wky hktk tkjdf imofs tm mur rfsiuf. Xbf hktk tkjdf usfh l` tbls fxkopdf ls sbmw` l` Aleurf.

L` tbf ifdd rk`ef K;17K8;, f`tfr tbf `uojfrs ; ’:1 (imrrfspm`hl`e tm mur :1 trlkds). M`f fksy wky tm irfktf tbfsf vkdufs ls tm stkrt jy f`tfrl`e ; l` ifdd K;1. Yfdfit tbf ifdd, k`h tbf` m` tbf Bmof tkj l` tbf Fhltl`e ermup, idlic Aldd, k`h sfdfit Yfrlfs tm hlspdky tbf Yfrlfs hlkdme jmx. L` tbf Yfrlfs hlkdme jmx, sbmw` l` Aleurf, f`tfr k Ytfp Qkduf ma ; k`h k Ytmp Qkduf ma ;>>>. L` tbf Yfrlfs L` krfk, sfdfit tbf Imduo`s mptlm`, k`h tbf` idlic MC . Xbf `uojfrs ;’:1 wldd jf f`tfrfh l` imduo` K stkrtl`e l` ifdd K;1. 

 

 @fxt wf f`tfr mur pmssljdf prmhuitlm` quk`tltlfs q uk`tltlfs (;>,>>>, :>,>>>, 8>,>>>, 1>,>>>) l` ifdds J;67F;6. Uf wk`t tm ikdiudktf prmalt amr fkib trlkd `uojfr (; tbrmueb ;>>>) k`h fkib prmhuitlm` quk`tlty. Uf rfafr tm tbf amroudk amr prmalt (ikdiudktfh l` ifdd I;;) l` tbf uppfr-dfat ifdd ma mur hktk tkjdf (K;6) jy f`tfrl`e ?I;;. Uf krf `mw rfkhy tm trlic Fxifd l`tm sloudktl`e ;>>> ltfrktlm`s ma hfok`h amr fkib prmhuitlm` quk`tlty. Yfdfit tbf tkjdf rk`ef (K;67F8;), k`h tbf` l` tbf Hktk Xmmds ermup m` tbf Hktk tkj, idlic Ubkt La K`kdysls, k`h tbf` sfdfit Hktk Xkjdf. Xm sft up k twm-wky hktk tkjdf, ibmmsf mur prmhuitlm` quk`tlty (ifdd I;) ks tbf Zmw L`put Ifdd k`h sfdfit k`y jdk`c ifdd (wf ibmsf ifdd L;8) ks tbf Imduo` L`put Ifdd. Katfr idlicl`e MC, Fxifd sloudktfs ;>>> hfok`h vkdufs amr fkib mrhfr quk`tlty. Xm u`hfrstk`h wby tbls wmrcs, im`slhfr tbf vkdufs pdkifh jy tbf hktk tkjdf l` tbf ifdd rk`ef I;17I8;. Amr fkib ma tbfsf ifdds, Fxifd wldd usf k vkduf ma :>,>>> l` ifdd I;. L` I;1, tbf imduo` l`put ifdd vkduf ma ; ls pdkifh l` k jdk`c ifdd k`h tbf rk`hmo `uojfr l` ifdd I: rfikdiudktfs. Xbf imrrfspm`hl`e prmalt ls tbf` rfimrhfh l` ifdd I;1. Xbf` tbf imduo` ifdd l`put vkduf ma : ls pdkifh l` k jdk`c ifdd, k`h tbf rk`hmo `uojfr l` I: kekl` rfikdiudktfs. Xbf imrrfspm`hl`e prmalt ls f`tfrfh l` ifdd I;5. Jy impyl`e armo ifdd J;9 tm I;97F;9 tbf amroudk  KQFZKEF(J;17J8;), wf imoputf kvfrkef sloudktfh prmalt amr fkib prmhuitlm` quk`tlty. Jy impyl`e armo ifdd J;8 tm I;87F;8 tbf amroudk YXHFQ(J;17J8;), wf imoputf tbf stk`hkrh hfvlktlm` ma mur sloudktfh prmalts amr fkib mrhfr quk`tlty. Fkib tlof wf prfss A>> ltfrktlm`s ma hfok`h krf sloudktfh amr fkib mrhfr quk`tlty. ^rmhuil`e 8>,>>> ikrhs kdwkys ylfdhs tbf dkrefst fxpfitfh prmalt. Xbfrfamrf, lt kppfkrs tbkt  prmhuil`e 8>,>>> ikrhs ls tbf prmpfr hfilslm`. Xbf Lopkit ma Zlsc m` Mur Hfilslm` La wf prmhuifh :>,>>> l`stfkh ma 8>,>>> ikrhs, mur fxpfitfh prmalt hrmps kpprmxloktfdy :: pfrif`t, jut mur rlsc (ks ofksurfh jy tbf stk`hkrh hfvlktlm` ma prmalt) hrmps kdomst 59 pfrif`t. Xbfrfamrf, la wf krf fxtrfofdy kvfrsf tm rlsc, prmhuil`e :>,>>> ikrhs olebt jf tbf rlebt

hfilslm`. L`ilhf`tkddy, prmhuil`e ;>,>>> ikrhs kdwkys bks k stk`hkrh hfvlktlm` ma > ikrhs jfikusf la wf prmhuif ;>,>>> ikrhs, wf wldd kdwkys sfdd kdd ma tbfo wltbmut k`y dfatmvfrs. @mtf7  L` tbls wmrcjmmc, tbf Ikdiudktlm` mptlm` ls sft tm Kutmoktli Fxifpt Amr Xkjdfs. (Vsf tbf Ikdiudktlm` imook`h l` tbf Ikdiudktlm` ermup m` tbf t bf Amroudks tkj.) Xbls sfttl`e f`surfs tbkt mur hktk tkjdf wldd `mt rfikdiudktf u`dfss wf prfss A rk`hmo `uojfrs ls usfh tm ef`frktf hfok`hs amr fkib mrhfr quk`tlty.

 

K `kturkd qufstlm` tm ksc l` tbls Im`alhf`if L`tfrvkd amr Ofk` ^rmalt sltuktlm` ls, l`tm wbkt l`tfrvkd krf wf ikdf`hkrs krf prmhuifh wltb tbf amroudk  H;9 ’  ;.>>). L` ifdd G;:, ymu imoputf tbf uppfr dlolt amr mur >). Xbfsf ikdiudktlm`s krf sbmw` l` Aleurf.

Uf krf ,>>> ikdf`hkrs krf mrhfrfh ls  jftwff` $61,125 k`h $1:,62