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Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations

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  • Emmanuel Gobet

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Isaque Pimentel

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, EDF - EDF)

  • Xavier Warin

    (EDF - EDF)

Abstract

Discrete time hedging produces a residual risk, namely, the tracking error. The major problem is to get valuation/hedging policies minimizing this error. We evaluate the risk between trading dates through a function penalizing asymmetrically profits and losses. After deriving the asymptotics within a discrete time risk measurement for a large number of trading dates, we derive the optimal strategies minimizing the asymptotic risk in the continuous time setting. We characterize the optimality through a class of fully nonlinear Partial Differential Equations (PDE). Numerical experiments show that the optimal strategies associated with discrete and asymptotic approach coincides asymptotically.

Suggested Citation

  • Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using asymmetric risk function: asymptotic optimality through fully nonlinear Partial Differential Equations," Post-Print hal-01761234, HAL.
    • Handle: RePEc:hal:journl:hal-01761234
    DOI: 10.1007/s00780-020-00428-1
    Note: View the original document on HAL open archive server: https://hal.science/hal-01761234
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    References listed on IDEAS

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