Mіzhnarodnі rozrahunki that valyutnі operatsії - Savluk M.І.

14.3. Premia optsіonu

For viznachennya premії optsіonu vikoristovuyut Blake-Scholes model. Spochatku Won bula rozroblena tіlki for єvropeyskih optsіonіv call on aktsії for yakimi not viplachuyutsya divіdendi to dati zakіnchennya optsіonu. Potіm Bulo shown scho tsya model is valid for i amerikanskogo optsіonu call without viplati divіdendіv.

Other nedolіk pochatkovoї modelі - zastosovnіst її tіlki to aktsіy without divіdendіv - CCU usuneny Contributions from formula dodatkovogo mnozhnika. Potіm Won bula wider on pіdrahunki premіy optsіonіv on INSHI assets.

Blake-Scholes formula for a call on optsіonіv aktsії without divіdendіv. Vartіst optsіonu call viznachaєtsya of formula

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de

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- Flow Rate rinkova underlying assets;

- Cena vikonannya optsіonu;

- Rіchna rate narahuvannya vіdsotka on assets without riziku, yaky narahovuєtsya bezperervno;

- An hour before zakіnchennya optsіonu in chastkah rock (abo De t - the number dnіv scho zalishilis to vikonannya optsіonu);

? - Rizik asset base (standard vіdhilennya dohіdnostі underlying assets for the Year);

- Funktsіya cumulative normal rozpodіlu serednіm h 0 i STANDARD vіdhilennyam 1 (tabulovana in statistitsі funktsіya).

Zauvazhimo, scho pid hour bezperervnogo narahuvannya vіdsotka vikoristovuєtsya formula maybutnoї vartostі de F - maybutnya vartіst, P - Flow vartіst. Tom mіzh rates neperervnogo narahuvannya R i bet simple vіdsotka r іsnuє Taqiy phone reception: . Tsey phone reception daє mozhlivіst sprostiti of formulating Blake-Scholes.

Place your character formula pokazuє zalezhnostі tsіni optsіonu call od p'yati chinnikіv:

  • Cena Vishcha denote the underlying assets, note Vishcha vartіst optsіonu;
  • cpm Vishcha vikonannya Cena, Cena note nizhcha optsіonu;
  • cpm bіlshe hour before dati zakіnchennya, team Vishcha Cena optsіonu;
  • cpm Vishcha rate without riziku, team bіlsha Cena optsіonu;
  • cpm bіlshy rizik (volyatilnіst) of the underlying asset, team Vishcha Cena optsіonu.

Formula parity optsіonіv call i put. Іsnuє formula parity tsіn scho daє zmogu for pіdrahovanoyu tsіnoyu optsіonu call viznachiti tsіnu optsіonu put

de - Cena optsіonu put.

Modifіkatsіya formula for aktsіy s divіdendami. Yakscho vіdoma ogoloshena rate divіdendu scho viplachuєtsya to dati zakіnchennya optsіonu then yogo yak mozhna rozglyadati percentage scho bezperervno narahovuєtsya. In tsomu razі modifіkovana formula for premії optsіonu call on aktsії s Got divіdendami Taqiy viglyad:

de - Interest rate, scho narahovuєtsya bezperervno that vіdpovіdaє stavtsі divіdendu on aktsіyu.

Formula parity optsіonіv modifіkuєtsya such rank:

Zastosuvannya formula for іnshih aktivіv. Premia on oblіgatsії optsіonіv call for rozrahovuєtsya odnієyu s guidance formulas fallow od of Je Tsey perіod kuponnі viplati, ni chi. In tsomu razі Q - rate of interest, that scho narahovuєtsya bezperervno vіdpovіdaє stavtsі coupon income.

Stock іndeks rozglyadayut yak aktsіyu s vіdomoyu divіdendu rates. Divіdendom on іndeks vvazhayut serednozvazhenu for kapіtalіzatsієyu bid announced divіdendіv aktsіy kompanіy scho vklyuchenі to іndeksu. Q - vіdpovіdna rate scho bezperervno narahovuєtsya.

Іnozemnu currency rozglyadayut yak aktsіyu s vіdomoyu divіdendu rates (rate for Taku take rate dohіdnostі without riziku in vіdpovіdnіy valyutі).

Zauvazhimo scho of formulating Blake-Scholes nepridatnі for rozrahunkіv on zvichaynomu kalkulyatorі. For tsієї methylene vikoristovuyut spetsіalnі prog - optsіonnі calculator.