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

Author

Listed:
  • Emmanuel Gobet

    (Institut Polytechnique de Paris)

  • Isaque Pimentel

    (Institut Polytechnique de Paris
    Electricité de France (EDF))

  • Xavier Warin

    (Electricité de France (EDF))

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.

Suggested Citation

  • Emmanuel Gobet & Isaque Pimentel & Xavier Warin, 2020. "Option valuation and hedging using an asymmetric risk function: asymptotic optimality through fully nonlinear partial differential equations," Finance and Stochastics, Springer, vol. 24(3), pages 633-675, July.
    • Handle: RePEc:spr:finsto:v:24:y:2020:i:3:d:10.1007_s00780-020-00428-1
    DOI: 10.1007/s00780-020-00428-1
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    References listed on IDEAS

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    More about this item

    Keywords

    Hedging; Asymmetric risk; Fully nonlinear parabolic PDE; Regression Monte Carlo;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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