Simulating Geometric Brownian Motion and Jump-Diffusion Price Paths
Summary
This article describes an object-oriented framework for generating synthetic asset-price paths using Geometric Brownian Motion (GBM) and a jump-diffusion process. A shared model interface accepts a starting price, time step, and externally supplied random shocks, allowing model components to fit into a larger correlated-data generator. The GBM implementation evolves prices through constant drift and volatility, while the jump-diffusion extension adds randomly timed jumps with variable magnitudes.
The article proposes plotting multiple realizations side by side to compare the models, and supplies illustrative parameter settings and a reproducible random seed. It explains that GBM omits features such as volatility clustering and abrupt price moves, while jumps can represent sudden news effects. These are stylized stochastic models for synthetic data, not forecasts of actual market prices. The excerpt does not provide calibration evidence or a quantitative comparison of model fit, and its stated assumptions and parameters should not be mistaken for empirically validated estimates.
Key ideas
- A shared abstract interface allows different price models to generate paths from supplied random shocks.
- GBM models prices with constant drift and volatility and produces lognormally evolving paths.
- Jump-diffusion augments the continuous process with random jump arrivals and sizes.
- Multiple simulated paths can illustrate how the two model classes behave under chosen parameters.
- Neither model captures every empirical feature of real asset returns, and the examples are not calibration evidence.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.