Numerical analysis on local risk-minimization for exponential lévy models

Takuji Arai, Yuto Imai, Ryoichi Suzuki

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    Abstract

    We illustrate how to compute local risk minimization (LRM) of call options for exponential Lévy models. Here, LRM is a popular hedging method through a quadratic criterion for contingent claims in incomplete markets. Arai & Suzuki (2015) have previously obtained a representation of LRM for call options; here we transform it into a form that allows use of the fast Fourier transform (FFT) method suggested by by Carr & Madan (1999). Considering Merton jump-diffusion models and variance gamma models as typical examples of exponential Lévy models, we provide the forms for the FFT explicitly; and compute the values of LRM numerically for given parameter sets. Furthermore, we illustrate numerical results for a variance gamma model with estimated parameters from the Nikkei 225 index.

    Original languageEnglish
    Article number1650008
    JournalInternational Journal of Theoretical and Applied Finance
    Volume19
    Issue number2
    DOIs
    Publication statusPublished - 2016 Mar 1

    Fingerprint

    Local risk-minimization
    Numerical analysis
    Call option
    Fast Fourier transform
    Variance gamma
    Hedging
    Jump-diffusion model
    Incomplete markets
    Contingent claims

    Keywords

    • exponential Lévy processes
    • fast Fourier transform
    • Local risk minimization
    • Merton jump-diffusion processes
    • variance gamma processes

    ASJC Scopus subject areas

    • Economics, Econometrics and Finance(all)
    • Finance

    Cite this

    Numerical analysis on local risk-minimization for exponential lévy models. / Arai, Takuji; Imai, Yuto; Suzuki, Ryoichi.

    In: International Journal of Theoretical and Applied Finance, Vol. 19, No. 2, 1650008, 01.03.2016.

    Research output: Contribution to journalArticle

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