Financial Modelling, Diffusion Processes, Stock Price Behaviour, Stochastic Methods, Rough Path Theory

Financial Modelling, Diffusion Processes, Stock Price Behaviour, Stochastic Methods, Rough Path Theory

Statistics

Aabid Anas, Anastasia Papavasiliou, Pablo Ramses Alonso Martín

2024

This study explores the validity of using the diffusion assumption to model stock prices across various timescales. The diffusion model, based on Geometric Brownian Motion, is commonly applied in financial markets but may not adequately capture price dynamics at finer timescales. By simulating paths and examining rough path signatures, we aim to determine the optimal timescale at which the diffusion approximation effectively models stock price movements.

diffusion models, geometric Brownian motion, stochastic processes, financial modelling, stock price analysis, multiscale modelling, rough path signatures, Ornstein-Uhlenbeck, Brownian motion, timescales, volatility