PRICING AND HEDGING OF VIX OPTIONS FOR BARNDORFF-NIELSEN AND SHEPHARD MODELS

Takuji Arai ()
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Takuji Arai: Department of Economics, Keio University, 2-15-45 Mita, Minato-ku, Tokyo 108-8345, Japan

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 08, 1-26

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: VIX; VIX options; stochastic volatility models; Barndorff-Nielsen and Shephard models; local risk-minimization; fast Fourier transform (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500432

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