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  • In this paper we focus on the replication of digital options under (in)complete model. Digital options are regularly applied in hedging and static decomposition of many path-dependent options. Efficient approaches to digital option replication are therefore inevitable. In this paper we examine the performance of static and dynamic replication. We consider the case of a market agent for whom the right model of the underlying asset price evolution is not available. The only applicable one is the Black and Scholes model. By contrast the observed price dynamics is supposed to follow four distinct models: (i) Black and Scholes model, (ii) Black and Scholes model with stochastic volatility driven by Hull and White model, (iii) Variance Gamma model modeled as time changed Brownian motion, and (iv) Variance gamma model set in a stochastic environment modeled as the rate of time change via CIR model. Both replication methods are applied and examined within each of these settings.
  • In this paper we focus on the replication of digital options under (in)complete model. Digital options are regularly applied in hedging and static decomposition of many path-dependent options. Efficient approaches to digital option replication are therefore inevitable. In this paper we examine the performance of static and dynamic replication. We consider the case of a market agent for whom the right model of the underlying asset price evolution is not available. The only applicable one is the Black and Scholes model. By contrast the observed price dynamics is supposed to follow four distinct models: (i) Black and Scholes model, (ii) Black and Scholes model with stochastic volatility driven by Hull and White model, (iii) Variance Gamma model modeled as time changed Brownian motion, and (iv) Variance gamma model set in a stochastic environment modeled as the rate of time change via CIR model. Both replication methods are applied and examined within each of these settings. (en)
  • V tomto článku se zaměřujeme na replikaci digitální opce při (ne)úplném modelu. Digitální opce jsou běžně aplikovány při hedgingu a statické dekompozici mnoha derivítů s výplatou závislou na na průběhu ceny podkladového aktiva v čase. Z toho vyplývá potřeba efektivních metod replikace digitálních opcí. V článku je uvažován případ tržního subjektu, který nemá k dispozici model skutečného vývoje ceny podkaldového aktiva a aplikuje proto model dle Blacka a Scholese (BS) oproti tomu skutečná dynamika je dána BS modelem se stochastickou volatilitou, Variance gamma modelem ve formě řízeného Brownova pohybu a Variance gamma modelu ve stochastickém prostředí (dodatečná změna času dána CIR procesem). V článku je studován vliv jednotlivých prostředí na chybu replikace. (cs)
Title
  • Model dependency of the digital option replication - replication under incomplete model
  • Modelová chyba replikace digitální opce - replikace při neúplném modelu (cs)
  • Model dependency of the digital option replication - replication under incomplete model (en)
skos:prefLabel
  • Model dependency of the digital option replication - replication under incomplete model
  • Modelová chyba replikace digitální opce - replikace při neúplném modelu (cs)
  • Model dependency of the digital option replication - replication under incomplete model (en)
skos:notation
  • RIV/61989100:27510/06:00013489!RIV07-GA0-27510___
http://linked.open.../vavai/riv/strany
  • 361-379
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GP402/05/P085)
http://linked.open...iv/cisloPeriodika
  • 7-8
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 486073
http://linked.open...ai/riv/idVysledku
  • RIV/61989100:27510/06:00013489
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • digital options; dynamic and static replication; replication error; stochastic volatility; Lévy models; Variance gamma process; gamma time; stochastic time (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • CZ - Česká republika
http://linked.open...ontrolniKodProRIV
  • [90D4DB9F3E26]
http://linked.open...i/riv/nazevZdroje
  • Finance a úvěr - Czech Journal of Economics and Finance
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 56
http://linked.open...iv/tvurceVysledku
  • Tichý, Tomáš
issn
  • 0015-1920
number of pages
http://localhost/t...ganizacniJednotka
  • 27510
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