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Pricing and hedging for a sticky diffusion

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  • Alexis Anagnostakis

Abstract

We consider a financial market model featuring a risky asset with a sticky geometric Brownian motion price dynamic and a constant interest rate $r \in \mathbb R$. We prove that the model is arbitrage-free if and only if $r =0 $. In this case, we find the unique riskless replication strategy, derive the associated pricing equation. We also identify a class of replicable payoffs that coincides with the replicable payoffs in the standard Black-Scholes model. Last, we numerically evaluate discrete-time hedging and the hedging error incurred from misrepresenting price stickiness.

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  • Alexis Anagnostakis, 2023. "Pricing and hedging for a sticky diffusion," Papers 2311.17011, arXiv.org, revised Jan 2024.
    • Handle: RePEc:arx:papers:2311.17011
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    References listed on IDEAS

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    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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