Pricing and hedging for a sticky diffusion

Alexis Anagnostakis ()
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Alexis Anagnostakis: AIRSEA - Mathematics and computing applied to oceanic and atmospheric flows - Centre Inria de l'Université Grenoble Alpes - Inria - Institut National de Recherche en Informatique et en Automatique - UGA - Université Grenoble Alpes - LJK - Laboratoire Jean Kuntzmann - Inria - Institut National de Recherche en Informatique et en Automatique - CNRS - Centre National de la Recherche Scientifique - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes - Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology - UGA - Université Grenoble Alpes

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Abstract: We introduce a financial market model featuring a risky asset whose price follows a sticky geometric Brownian motion and a riskless asset that grows with a constant interest rate $r\in \mathbb R$. We prove that this model satisfies No Arbitrage (NA) and No Free Lunch with Vanishing Risk (NFLVR) only when $r=0 $. Under this condition, we derive the corresponding arbitrage-free pricing equation, assess replicability and representation of the replication strategy. We then show that all locally bounded replicable payoffs for the standard Black--Scholes model are also replicable for the sticky model. Last, we evaluate via numerical experiments the impact of hedging in discrete time and of misrepresenting price stickiness.

Keywords: no-arbitrage condition; derivatives pricing; arbitrage-free valuation; hedging time-granularity; model mismatch; sticky geometric Brownian motion (search for similar items in EconPapers)
Date: 2024
Note: View the original document on HAL open archive server: https://inria.hal.science/hal-04756051v1
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Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-04756051

DOI: 10.48550/arXiv.2311.17011

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