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

Emmanuel Gobet (emmanuel.gobet@polytechnique.edu), Isaque Pimentel (pimentel.isaque@gmail.com) and Xavier Warin (xavier.warin@edf.fr)
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Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - 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 - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique, EDF - EDF
Xavier Warin: EDF - EDF

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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.

Keywords: hedging; asymmetric risk; fully nonlinear parabolic PDE; regression Monte Carlo (search for similar items in EconPapers)
Date: 2020-06-12
Note: View the original document on HAL open archive server: https://hal.science/hal-01761234v1
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Published in Finance and Stochastics, 2020, 24 (3), pp.633-675. ⟨10.1007/s00780-020-00428-1⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01761234

DOI: 10.1007/s00780-020-00428-1

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