Derivatives under market impact: Disentangling cost and information

Behzad Alimoradian, Karim Barigou and Anne Eyraud-Loisel
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Behzad Alimoradian: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Karim Barigou: UCL - Université Catholique de Louvain = Catholic University of Louvain
Anne Eyraud-Loisel: LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon

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Abstract: In this paper, we examine the implications of a large trader's activity and its market impact when pricing and hedging a large derivatives position. We highlight the issue of market manipulation in this context, providing examples to illustrate how the trader can manipulate the payoff. To understand how a large trader's knowledge influences their actions, we introduce a problem reduction by considering the perspective of an insider trader, who is aware of the large trader's trading policy but does not incur transaction costs. Through this framework, we establish the existence of information-neutral probability measures, under which the discounted asset is a martingale process for the insider trader. We then develop a derivatives hedging policy for the large trader that accounts for both transaction costs and the permanent impact of their hedging activities, while mitigating market manipulation. The paper concludes with numerical results that showcase the optimal delta-hedging strategy for an out-of-the-money call option, comparing it to the Black-Scholes model.

Keywords: Option pricing; market impact; illiquid markets; transactions costs; stochastic optimal control (search for similar items in EconPapers)
Date: 2025-01-18
Note: View the original document on HAL open archive server: https://hal.science/hal-03668432v2
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