Local risk-minimization for Barndorff-Nielsen and Shephard models

Takuji Arai (), Yuto Imai () and Ryoichi Suzuki ()
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Takuji Arai: Keio University
Yuto Imai: Waseda University
Ryoichi Suzuki: Keio University

Finance and Stochastics, 2017, vol. 21, issue 2, No 8, 592 pages

Abstract: Abstract 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.

Keywords: Local risk-minimization; Barndorff-Nielsen and Shephard models; Stochastic volatility models; Malliavin calculus; Lévy processes; 91G20; 60H07; 91G60 (search for similar items in EconPapers)
JEL-codes: G11 G12 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (10)

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DOI: 10.1007/s00780-017-0324-8

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