# Simulation of stock prices

Modeling the volatility of an asset (e.g., index, bond, stock, commodities) allows to simulate the value of that asset. Based on the simulated value range derived or composite financial products (i.e., funds, portfolios, certificates or derivatives) can be evaluated. Such simulations, in combination with a Monte-Carlo simulation, can be easily done with Excel spreadsheets.

A simulation of an asset price can be seen as a random walk. The price goes randomly up and down. The are several methods to realize such a random walk.

## Brownian motion

A simple way is the Brownian motion. During a small period of time, the asset price is changing with an expected value plus a random normal distributed variation around that expectation. It is important that the asset price is modeled based on small periods, such as days. Follow the instructions in the video:

## Bootstrap sampling

A distribution-free method to simulate asset prices is to use observed values already. If historical returns of that asset are given, then choose for each simulation period a random historical return. Follow the instructions in the video:

## Binomial model

If you assume an asset price increases or decreases with one discrete value, then use the binomial model. The idea behind the basic model you can find here:

The random simulation of an asset price with the binomial model you can find here:

## Two-dimensional random walk

Consider a drunkhard’s walk. In other words it is a two-dimensional random walk / two-dimensional Brownian motion. Going one step up if the random number is small than 0.5 and down if it is higher than 0.5. For left and right it is the same. See the video for an implementation in Excel: