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Pricing and hedging for a sticky diffusion

Part of: Mathematical finance Markov processes

Published online by Cambridge University Press:  28 April 2025

Alexis Anagnostakis Open the ORCID record for Alexis Anagnostakis [Opens in a new window]
Alexis Anagnostakis*
Affiliation:
Université Grenoble-Alpes, CNRS, LJK
*
*Postal address: Laboratoire Jean Kuntzmann, 150 Pl. du Torrent, 38400 Saint-Martin-d’Hères, France. Email: [email protected]
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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 and no free lunch with vanishing risk only when $r=0$. Under this condition, we derive the corresponding arbitrage-free pricing equation, assess the replicability, and give a 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

Sticky geometric Brownian motionno-arbitrage conditionderivatives pricingarbitrage-free valuationhedging time-granularitymodel mismatch

MSC classification

Primary: 91G20: Derivative securities
Secondary: 91G30: Interest rates (stochastic models) 60J60: Diffusion processes
Type
Original Article
Information
Journal of Applied Probability , First View , pp. 1 - 25
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Applied Probability Trust

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