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Finance and Stochastics

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12-06-2020

Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations

Authors: Emmanuel Gobet, Isaque Pimentel, Xavier Warin

Published in: Finance and Stochastics | Issue 3/2020

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Abstract

Discrete-time hedging produces a residual P&L, namely the tracking error. The major problem is to get valuation/hedging policies minimising this error. We evaluate the risk between trading dates through a function penalising profits and losses asymmetrically. After deriving the asymptotics from a discrete-time risk measurement for a large number of trading dates, we derive the optimal strategies minimising the asymptotic risk in a continuous-time setting. We characterise optimality through a class of fully nonlinear partial differential equations (PDEs). Numerical experiments show that the optimal strategies associated with the discrete and the asymptotic approaches coincide asymptotically.

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Title: Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations
Authors: Emmanuel Gobet
Isaque Pimentel
Xavier Warin
Publication date: 12-06-2020
Publisher: Springer Berlin Heidelberg
Published in: Finance and Stochastics / Issue 3/2020
Print ISSN: 0949-2984
Electronic ISSN: 1432-1122
DOI: https://doi.org/10.1007/s00780-020-00428-1

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