Pricing and hedging for a sticky diffusion

Alexis Anagnostakis

doi:10.1017/jpr.2025.2

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arXiv · 2311.17011

Pricing and hedging for a sticky diffusion

Alexis Anagnostakis

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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.

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Alexis Anagnostakis. 2023-11-28. Pricing and hedging for a sticky diffusion. https://doi.org/10.1017/jpr.2025.2

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