Paper: arXiv 2311.17011
Authors: 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.
Complexity vs Empirical Score
- Math Complexity: 8.0/10
- Empirical Rigor: 3.0/10
- Quadrant: Lab Rats — theoretically deep, empirically untested
Why this score: The paper presents a rigorous mathematical analysis of sticky diffusions in financial modeling, proving crucial no-arbitrage conditions (NFLVR) and replication properties. While strong on stochastic calculus and theoretical derivative pricing, it relies mostly on basic numerical experiments rather than extensive empirical backtesting with real market data.
Research Flowchart
flowchart TD
A[Research Goal: Pricing & Hedging in a Sticky Geometric Brownian Motion Model] --> B[Model Setup: Risky asset with sGBM & Riskless asset with rate r]
B --> C[Theoretical Analysis: Prove NA & NFLVR holds iff r = 0]
C --> D[Derive Arbitrage-Free Pricing Equation & Delta Hedging Strategy]
D --> E[Replicability Proof: All BS replicable payoffs are replicable in Sticky Model]
E --> F[Numerical Experiments: Discrete-time hedging & stickiness misrepresentation]
F --> G[Key Outcomes: Option pricing framework & impact of ignoring price stickiness]