Pricing and hedging for a sticky diffusion
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866916710997557248 |
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| author | Anagnostakis, Alexis |
| author_facet | Anagnostakis, Alexis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17011 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pricing and hedging for a sticky diffusion Anagnostakis, Alexis Mathematical Finance Probability 91G20, 91G30, 60J60 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. |
| title | Pricing and hedging for a sticky diffusion |
| topic | Mathematical Finance Probability 91G20, 91G30, 60J60 |
| url | https://arxiv.org/abs/2311.17011 |