TY - JOUR
T1 - Local risk-minimization for Barndorff-Nielsen and Shephard models
AU - Arai, Takuji
AU - Imai, Yuto
AU - Suzuki, Ryoichi
N1 - Funding Information:
Takuji Arai gratefully acknowledges the financial support of Ishii Memorial Securities Research Promotion Foundation and Scientific Research (C) No. 15K04936 from the Ministry of Education, Culture, Sports, Science and Technology of Japan.
Publisher Copyright:
© 2017, Springer-Verlag Berlin Heidelberg.
PY - 2017/4/1
Y1 - 2017/4/1
N2 - We obtain explicit representations of locally risk-minimizing strategies for call and put options in Barndorff-Nielsen and Shephard models, which are Ornstein–Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Lévy processes, Arai and Suzuki (Int. J. Financ. Eng. 2:1550015, 2015) obtained a formula for locally risk-minimizing strategies for Lévy markets under many additional conditions. Supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in (Arai and Suzuki in Int. J. Financ. Eng. 2:1550015, 2015). Among others, we investigate the Malliavin differentiability of the density of the minimal martingale measure. Moreover, we introduce some numerical experiments for locally risk-minimizing strategies.
AB - We obtain explicit representations of locally risk-minimizing strategies for call and put options in Barndorff-Nielsen and Shephard models, which are Ornstein–Uhlenbeck-type stochastic volatility models. Using Malliavin calculus for Lévy processes, Arai and Suzuki (Int. J. Financ. Eng. 2:1550015, 2015) obtained a formula for locally risk-minimizing strategies for Lévy markets under many additional conditions. Supposing mild conditions, we make sure that the Barndorff-Nielsen and Shephard models satisfy all the conditions imposed in (Arai and Suzuki in Int. J. Financ. Eng. 2:1550015, 2015). Among others, we investigate the Malliavin differentiability of the density of the minimal martingale measure. Moreover, we introduce some numerical experiments for locally risk-minimizing strategies.
KW - Barndorff-Nielsen and Shephard models
KW - Local risk-minimization
KW - Lévy processes
KW - Malliavin calculus
KW - Stochastic volatility models
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U2 - 10.1007/s00780-017-0324-8
DO - 10.1007/s00780-017-0324-8
M3 - Article
AN - SCOPUS:85015002022
SN - 0949-2984
VL - 21
SP - 551
EP - 592
JO - Finance and Stochastics
JF - Finance and Stochastics
IS - 2
ER -