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Pricing and hedging for a sticky diffusion

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  • Alexis Anagnostakis

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. "Pricing and hedging for a sticky diffusion," Papers 2311.17011, arXiv.org, revised Oct 2024.
    • Handle: RePEc:arx:papers:2311.17011
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    References listed on IDEAS

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    1. Paolo Guasoni, 2006. "No Arbitrage Under Transaction Costs, With Fractional Brownian Motion And Beyond," Mathematical Finance, Wiley Blackwell, vol. 16(3), pages 569-582, July.
    2. John Y. Zhu, 2013. "Optimal Contracts with Shirking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 812-839.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    4. Rossello, Damiano, 2012. "Arbitrage in skew Brownian motion models," Insurance: Mathematics and Economics, Elsevier, vol. 50(1), pages 50-56.
    5. Amir, Madjid, 1991. "Sticky Brownian motion as the strong limit of a sequence of random walks," Stochastic Processes and their Applications, Elsevier, vol. 39(2), pages 221-237, December.
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