Option Pricing and Hedging with Liquidity Costs and Market Impact

Frédéric Abergel (1) , Gregoire Loeper (2)

1 MICS - Mathématiques et Informatique pour la Complexité et les Systèmes
2 Monash University [Clayton]

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.

Domains: Mathematics [math]; Statistics [math.ST]

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⟩