Imodeli ye -Black-Scholes iyithuluzi eliyisisekelo emkhakheni wezezimali, ikakhulukazi ekulinganisweni kwezinketho. Yasungulwa nguFisher Black noMyron Scholes ngo-1973, le modeli yezibalo yashintsha indlela amanani ezinketho abalwa ngayo. Ifomula ye-Black-Scholes ivumela ukunqunywa kwenani elifanele lenketho yaseYurophu, ngokusekelwe eziguquguquki ezifana nentengo yamanje yempahla eyisisekelo, intengo yokushaya, isikhathi sokuphelelwa yisikhathi, ukuguquguquka, kanye nesilinganiso esingenazo izingcuphe.
Isendlalelo kanye nokuthuthukiswa kwemodeli
Ukudalwa kwemodeli ye -Black-Scholes kwakungeyona into eyenzeka yodwa; kwakuwumphumela weminyaka yokusebenza kanye nokubambisana phakathi kwezazi zezibalo kanye nezomnotho. UFisher Black noMyron Scholes basebenzisana eSikoleni Sebhizinisi sase-University of Chicago, futhi umnikelo wabo awuzange nje uthole ukuqashelwa kwezemfundo kodwa futhi wabatholela uMklomelo KaNobel Kwezomnotho ngo-1997. Lokhu kuqashelwa kwamukelwa nguScholes kanye nozakwabo uRobert C. Merton, owandisa futhi wathuthukisa imodeli yokuqala, njengoba uBlack ashona ngo-1995.
Ukucatshangelwa okuyisisekelo
Imodeli ye -Black-Scholes isekelwe ekucabangeni okuthile okwenza kube lula ukuba khona kwemakethe yezezimali.
- Izimakethe zisebenza kahle, okusho ukuthi izintengo zempahla zibonisa lonke ulwazi olutholakalayo.
- Azikho izindleko zokuthengiselana noma izintela.
- Izinga lenzalo engenabungozi lihlala njalo futhi liyaziwa.
- Ukuguquguquka kwentengo yempahla eyisisekelo kuhlala njalo ngokuhamba kwesikhathi.
- Impahla eyisisekelo ayikhokhi izabelo phakathi nesikhathi senketho.
Lezi zicabango ziye zagxekwa futhi zalungiswa eminyakeni edlule, kodwa zakha isisekelo semodeli yakudala.
Ifomula ye-Black-Scholes
Ifomula edumile ye-Black-Scholes imi kanje:
[C=S[C=S 0 N(d 1) – X e^{-rt} N(d 2) ]Kule fomula, u-C uyintengo yenketho yokushaya ucingo , u-S 0 uyintengo yamanje yempahla eyisisekelo, u-X uyintengo yesiteleka, u-t yisikhathi sokuphelelwa yisikhathi, u-r uyisilinganiso senzalo esingenangozi, kanti u-N(d) umele umsebenzi wokusabalalisa oqongelelekayo wokusabalalisa okujwayelekile okujwayelekile. Amanani u-d 1 no -d2 abalwa kanje:
[d[d 1 = frac{ln(S 0 / X) + (r + (sigma^2 / 2))t}{sigma sqrt{t}} ][d[d 2 = d 1 – sigma sqrt{t} ]Lapha, u-σ umelela ukuguquguquka kwempahla eyisisekelo. Ifomula nayo inenguqulo yokubala intengo yenketho yokubeka , kodwa umqondo wezibalo ngemuva kwayo uyafana.
Izicelo kanye nemikhawulo
Imodeli ye -Black-Scholes isetshenziswa kabanzi emakethe yezinketho ukuze inikeze inani elihlukahlukene lezimpahla zezimali. Ukulula kwayo kanye namandla ayo okubikezela kuye kwaholela ekwamukelweni kwayo ngabadayisi, abatshalizimali , kanye nabahlaziyi bezezimali. Kodwa-ke, imikhawulo nayo iyabonakala, ikakhulukazi ezimakethe zangempela lapho ukucabanga kwemodeli kungahlali kuyiqiniso.
- Ukuqagela kokushintshashintsha njalo: Ukuguquguquka ezimakethe zangempela kungahluka ngokungazelelwe.
- Ukungabikho kwezindleko zokwenziwayo: Empeleni, lezi zindleko zingathinta kakhulu ukusebenza.
- Ubungozi bemakethe: Izinga lenzalo engenabungozi akuvamile ukuthi lihlale linjalo.
- Izabelo: Izimpahla eziyisisekelo zivame ukukhokha izinzuzo, ezithinta ukulinganisa.
Izilungiselelo nezandiso
Kusukela yashicilelwa okokuqala, abacwaningi abaningana kanye nochwepheshe bemakethe basebenzele ukuthuthukisa nokwandisa ifomula ye-Black-Scholes ukuze bathuthukise ukunemba kwayo. Ezinye zalezi zithuthukisi zifaka:
- Amamodeli ane-stochastic volatility: Babhekana nombono wokuthi ukuguquguquka akuhlali njalo.
- Amamodeli ane-jump: Bahlanganisa ukweqa okungazelelwe ezintengo zempahla.
- Amamodeli weBinomial: Bahlongoza indlela enobuhlakani futhi evumelana nezimo.
Lawa mamodeli andisa ukusebenza kwemodeli yakudala futhi avumela ukunemba okukhulu ekulinganisweni.
Ukuqaliswa okungokoqobo
Ukuze usebenzise imodeli ye -Black-Scholes ngokusebenzayo, udinga ukufinyelela idatha yemakethe enembile kanye nesofthiwe ekhethekile ekwazi ukuphatha izibalo eziyinkimbinkimbi. Amapulatifomu amaningi okuhweba kanye nesofthiwe yezezimali, njenge-Bloomberg Terminal, i-Reuters, noma i-Python, amathuluzi aphelele akuvumela ukuthi wenze lokhu kuhlola ngempumelelo nangesikhathi sangempela. Uma unesifiso sokuthola amathuluzi esofthiwe, ungavakashela amawebhusayithi e -Bloomberg Terminal kanye ne -Reuters.
Abatshalizimali kufanele futhi baqaphele ukuthi izimo zemakethe zingashintsha, futhi kusemandleni abo ukulungisa imodeli ngokwezidingo nezimo zabo ezithile.
Ukuhunyushwa kwemiphumela
Uma imodeli isisetshenzisiwe, ukuchazwa kwemiphumela kubalulekile ekwenzeni izinqumo ezinolwazi. Intengo yokukhetha ebalwe yimodeli ye-Black-Scholes kumele iqhathaniswe nentengo yemakethe. Ukungafani kungabonisa amathuba okuphikisana noma kudinge ukuhlolwa kabusha kwezibikezelo eziyisisekelo.
Ukuqonda ukuthi i-variable ngayinye ichazwa kanjani kanye nomthelela wesici ngasinye kunganquma inzuzo noma ukulahlekelwa ekutshalweni kwezimali.
Imodeli ye-Black-Scholes, ngokungangabazeki, iyingxenye ebalulekile yobunjiniyela bezezimali. Nakuba ingakhululekile ekugxekweni futhi ingaphelele, indima yayo ekulinganisweni kwezinketho kanye nomthelela wayo kuthiyori yezezimali nokusebenza ayinakuphikwa. Yamukela, lungisa, futhi uthuthukise ukuqonda kwakho ukuze uthole okuningi emakethe yezinketho.