Abstract

In the article is proposed the algorithm of modeling the dynamics of asset prices by Markov process with continuous time and countable set of states and numerical option pricing.

Highlights

  • Markov model of option pricing In the article is proposed the algorithm of modeling the dynamics of asset prices by Markov process

  • Numerical Models of Systems Specified by Markovian Processes

  • SUMMARYE. Valakevicius. Markov model of option pricing In the article is proposed the algorithm of modeling the dynamics of asset prices by Markov process with continuous time and countable set of states and numerical option pricing. Keywords: assets dynamics, mixture of exponential distributions, Markov model of asset prices, numerical option pricing

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Summary

Ivadas

Ikainojant išvestinius vertybinius popierius, pvz. akciju pirkimo ar pardavimo pasirinkimo sandorius, reikia tureti pakankamai gera bazinio aktyvo (akcijos) vertes dinamikos matematini modeli. Paprastai reikia žinoti finansinio aktyvo kainu skirstini pasirinkimo sandorio pabaigoje, t.y. galimas jo kainas ir atitinkamas ju tikimybes. Pvz., išvedant žymiaja Black ir Scholes pasirinkimo sandoriu ikainojimo formule [1], buvo tariama, kad akciju kainos kinta pagal geometrini Brauno judesio procesa. Akciju kainu gražu logaritmai pasiskirste pagal normaluji desni. Su šia prielaida akciju kainos išreiškiamos per Gauso skirstini ir lengvai skaiciuojamos, nes gaunamos analizines raiškos. Empiriniai tyrimai rodo, kad pastaraisiais metais tik dalies akciju gražos pasiskirste pagal lognormaluji desni. Tokiu modeliu pagrindinis trukumas yra tas, kad gaunamos sudetingos skirstiniu analizines raiškos ir gauti diferencialines lygtis, kurias išsprendus gaunamos pasirinkimo sandoriu kainos, dažniausiai nepavyksta. Šiame straipsnyje pateiktas pasirinkimo sandoriu ikainojimo algoritmas tariant, kad bazinio aktyvo kainos kinta pagal Markovo procesa su tolydžiuoju laiku ir baigtine busenu aibe

Normalumo tikrinimas
Finansinio aktyvo vertes dinamikos Markovo procesas
Europietiškojo pirkimo pasirinkimo sandorio ikainojimas
Skaitmeninis pavyzdys
Išvados
SUMMARY

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