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Option Pricing and Hedging with Liquidity Costs and Market Impact

Abstract : We study the influence of taking liquidity costs and market impact into account when hedging a contingent claim. In the continuous time setting and under the assumption of perfect replication, we derive a fully non-linear pricing partial differential equation, and characterize its parabolic nature according to the value of a numerical parameter interpreted as a relaxation coefficient for market impact. We also investigate the case of stochastic volatility models with pseudo-optimal strategies.
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https://hal-centralesupelec.archives-ouvertes.fr/hal-02402364
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Submitted on : Tuesday, December 10, 2019 - 2:07:43 PM
Last modification on : Thursday, July 2, 2020 - 9:12:02 AM

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Frédéric Abergel, Gregoire Loeper. Option Pricing and Hedging with Liquidity Costs and Market Impact. International Workshop on Econophysics and Sociophysics - Recent Progress and Future Directions (Econophys), Jan 2017, Jawaharlal Nehru Univ, New Delhi, India. ⟨10.1007/978-3-319-47705-3_2⟩. ⟨hal-02402364⟩

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