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  • Modern capital markets are typical by the presence of kurtosis and skewness of returns. The stochastic environment can also result into significant changes in kurtosis. To model the stochastic environment, we focus in this paper on two types of modern Lévy processes - simple case of Lévy process and a Lévy processes interpreted as a time changed process. In particular, the first case is the Variance Gamma model, the second is the Variance Gamma model driven by a Cox-Ingersoll-Ross time. In this paper we also study replication of digital option, without knowing details of the underlying distribution.
  • Modern capital markets are typical by the presence of kurtosis and skewness of returns. The stochastic environment can also result into significant changes in kurtosis. To model the stochastic environment, we focus in this paper on two types of modern Lévy processes - simple case of Lévy process and a Lévy processes interpreted as a time changed process. In particular, the first case is the Variance Gamma model, the second is the Variance Gamma model driven by a Cox-Ingersoll-Ross time. In this paper we also study replication of digital option, without knowing details of the underlying distribution. (en)
  • Moderní kapitálové trhy jsou typické přítomností špičatosti a šikmosti výnosů. Stochastické prostředí rovněž může vyústit v jejich výraznou fluktuaci. Za účelem modelování stochastického prostředí je v tomto článku pozornost soustředěna na dva typy moderních Lévyho procesů - jednoduchý Lévyho proces a proces, který je chápan jako vývoj v rámci komplexně pojatého stochastického času. Konkrétně se jedná o Variance Gama model (tj. geometrický Brownův pohyb v gama čase) a Variance Gama model řízený CIR procesem. Hlavní pozornost je v článku soustředěna na replikaci digitálních opcí při neúplných informacích o podkladovém procesu. (cs)
Title
  • Lévy processes and time changed Lévy processes - the efficiency of digital option replication
  • Lévy processes and time changed Lévy processes - the efficiency of digital option replication (en)
  • Lévyho procesy a Lévyho procesy ve změně času - efektivnost digitální opční replikace (cs)
skos:prefLabel
  • Lévy processes and time changed Lévy processes - the efficiency of digital option replication
  • Lévy processes and time changed Lévy processes - the efficiency of digital option replication (en)
  • Lévyho procesy a Lévyho procesy ve změně času - efektivnost digitální opční replikace (cs)
skos:notation
  • RIV/61989100:27510/05:00011848!RIV06-GA0-27510___
http://linked.open.../vavai/riv/strany
  • 223-230
http://linked.open...avai/riv/aktivita
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  • P(GP402/05/P085)
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  • 528060
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  • RIV/61989100:27510/05:00011848
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  • Stochastic environment; Lévy models; time-changed processes; digital option replication (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...ontrolniKodProRIV
  • [2B4776920168]
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  • Brno, Česká republika
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  • Brno
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  • Evropské finanční systémy
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  • Tichý, Tomáš
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number of pages
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  • Masarykova univerzita
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  • 80-210-3753-9
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  • 27510
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