TY - JOUR
T1 - PRICING and HEDGING of VIX OPTIONS for BARNDORFF-NIELSEN and SHEPHARD MODELS
AU - Arai, Takuji
N1 - Funding Information:
The author gratefully acknowledges the financial support of the MEXT Grant in Aid for Scientific Research (C) Nos. 15K04936 and 18K03422, and would like to thank a managing editor and two anonymous referees for their valuable comments and suggestions.
Publisher Copyright:
© 2019 World Scientific Publishing Company.
PY - 2019/12/1
Y1 - 2019/12/1
N2 - 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.
AB - 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.
KW - Barndorff-Nielsen and Shephard models
KW - VIX
KW - VIX options
KW - fast Fourier transform
KW - local risk-minimization
KW - stochastic volatility models
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U2 - 10.1142/S0219024919500432
DO - 10.1142/S0219024919500432
M3 - Article
AN - SCOPUS:85076211657
SN - 0219-0249
VL - 22
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 8
M1 - 1950043
ER -