PRICING and HEDGING of VIX OPTIONS for BARNDORFF-NIELSEN and SHEPHARD MODELS

Research output: Contribution to journalArticle

Abstract

The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein-Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.

Original languageEnglish
Article number1950043
JournalInternational Journal of Theoretical and Applied Finance
DOIs
Publication statusAccepted/In press - 2019 Jan 1

Fingerprint

Volatility index
Call option
Option prices
Assets
Fast Fourier transform
Derivatives
Numerical experiment
Stochastic volatility model
Numerical methods

Keywords

  • Barndorff-Nielsen and Shephard models
  • fast Fourier transform
  • local risk-minimization
  • stochastic volatility models
  • VIX
  • VIX options

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

Cite this

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title = "PRICING and HEDGING of VIX OPTIONS for BARNDORFF-NIELSEN and SHEPHARD MODELS",
abstract = "The VIX call options for the Barndorff-Nielsen and Shephard models will be discussed. Derivatives written on the VIX, which is the most popular volatility measurement, have been traded actively very much. In this paper, we give representations of the VIX call option price for the Barndorff-Nielsen and Shephard models: non-Gaussian Ornstein-Uhlenbeck type stochastic volatility models. Moreover, we provide representations of the locally risk-minimizing strategy constructed by a combination of the underlying riskless and risky assets. Remark that the representations obtained in this paper are efficient to develop a numerical method using the fast Fourier transform. Thus, numerical experiments will be implemented in the last section of this paper.",
keywords = "Barndorff-Nielsen and Shephard models, fast Fourier transform, local risk-minimization, stochastic volatility models, VIX, VIX options",
author = "Takuji Arai",
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language = "English",
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