Local risk-minimization for Barndorff-Nielsen and Shephard models

Takuji Arai, Yuto Imai, Ryoichi Suzuki

    Research output: Contribution to journalArticle

    2 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

    Fingerprint

    Minimal Martingale Measure
    Malliavin Calculus
    Stochastic Volatility Model
    Differentiability
    Numerical Experiment
    Model
    Strategy
    Local risk-minimization
    Market
    Call option
    Minimal martingale measure
    Numerical experiment
    Stochastic volatility model
    Put option
    Malliavin calculus

    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

    Cite this

    Local risk-minimization for Barndorff-Nielsen and Shephard models. / Arai, Takuji; Imai, Yuto; Suzuki, Ryoichi.

    In: Finance and Stochastics, Vol. 21, No. 2, 01.04.2017, p. 551-592.

    Research output: Contribution to journalArticle

    Arai, Takuji ; Imai, Yuto ; Suzuki, Ryoichi. / Local risk-minimization for Barndorff-Nielsen and Shephard models. In: Finance and Stochastics. 2017 ; Vol. 21, No. 2. pp. 551-592.
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