Pricing and hedging for a sticky diffusion

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.