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

Emmanuel Gobet (), Isaque Pimentel () and Xavier Warin ()
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Emmanuel Gobet: Institut Polytechnique de Paris
Isaque Pimentel: Institut Polytechnique de Paris
Xavier Warin: Electricité de France (EDF)

Finance and Stochastics, 2020, vol. 24, issue 3, No 3, 633-675

Abstract: 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.

Keywords: Hedging; Asymmetric risk; Fully nonlinear parabolic PDE; Regression Monte Carlo; 60H30; 35K55; 91G60; 91G80 (search for similar items in EconPapers)
JEL-codes: C60 G13 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00780-020-00428-1

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