# Do stock prices follow a Brownian motion?

## Do stock prices follow a Brownian motion?

However, stock markets, the foreign exchange markets, commodity markets and bond markets are all assumed to follow Brownian motion, where assets are changing continually over very small intervals of time and the position, namely the change of state on the assets, is being al- tered by random amounts.

Why the Brownian motion is not suitable to be used to model stock prices?

However, Brownian motion process has the independent increments property. This means that the present price must not affect the future price. In fact, the present stock price may influence the price at some time in the future. Hence, Brownian motion process is not suitable to explain the stock price.

Who proposed that stock price movement was similar to Brownian motion?

The Brownian motion models for financial markets are based on the work of Robert C. Merton and Paul A. Samuelson, as extensions to the one-period market models of Harold Markowitz and William F.

### How do you explain Brownian motion?

Particles in both liquids and gases (collectively called fluids) move randomly. This is called Brownian motion. They do this because they are bombarded by the other moving particles in the fluid. Larger particles can be moved by light, fast-moving molecules.

How do you calculate Brownian motion?

For example, if B(t) denotes Brownian motion, then X(t) = B(t) + ct is called Brownian motion with drift c. This model is appropriate for Brownian motion of a particle under the influence of a constant force field such as gravity.

How is Brownian motion related to random walk?

While simple random walk is a discrete-space (integers) and discrete-time model, Brownian Motion is a continuous-space and continuous-time model, which can be well motivated by simple random walk.

#### Why is Brownian motion significant?

Albert Einstein’s paper on Brownian motion provides significant evidence that molecules and atoms exist. In the kinetic theory of gases, the particles of the Brownian motion model are responsible for describing temperature, volume, and pressure.

What are examples of Brownian motion?

Brownian Motion Examples The motion of pollen grains on still water. Movement of dust motes in a room (although largely affected by air currents) Diffusion of pollutants in the air. Diffusion of calcium through bones.

Why should Brownian motion increase the longer?

Q: Why should Brownian motion increase the longer you observe a hanging drop or wet mount preparation? o A: Brownian motion is due to cells colliding with the water molecules.