02. Introduction to Geometric Brownian motion

Understanding Geometric Brownian Motion

Geometric Brownian Motion (GBM), a mathematical model, is significant in understanding stock prices and market capital growth.

Components of GBM:

• Drift Term (dt): Represents the predictable aspect, akin to the average growth rate.
• Diffusion Term (dW_t): Covers the random fluctuations, essential for capturing market volatility.

Characteristics:

• The change in value depends on the current value of x. Larger x leads to faster changes and more significant fluctuations.
• High market capital companies appear to grow more and fluctuate more, due to many components contributing to growth.

Business Analogy:

• Large companies grow in monetary terms through several independent business units, each acting like smaller companies. This multi-layered structure leads to greater overall growth and fluctuations than smaller firms.

Implications for Share Prices:

• GBM's attributes align with the behavior of stock prices, serving as a suitable model for predicting share value movements, assuming no significant structural changes.

Further exploration into GBM occurs in subsequent discussions, enriching understanding of this crucial financial model.