Local risk-minimization for Barndorff-Nielsen and Shephard models

Takuji Arai, Yuto Imai, Ryoichi Suzuki

Research output: Contribution to journalArticle

3 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)551-592
Number of pages42
JournalFinance and Stochastics
Volume21
Issue number2
DOIs
Publication statusPublished - 2017 Apr 1

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Keywords

  • Barndorff-Nielsen and Shephard models
  • Local risk-minimization
  • Lévy processes
  • Malliavin calculus
  • Stochastic volatility models

ASJC Scopus subject areas

  • Statistics and Probability
  • Finance
  • Statistics, Probability and Uncertainty

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