Predicting the movement of stock prices is an alluring challenge with the promise of riches. Unfortunately, predicting future stock prices consistently and reliably is generally considered impossible. However, we can use models to make useful predictions, manage risk, and profit probalistical...

Monthly simple and logarithmic returns of IBM stock with fitted normal distributions. We observe more returns at the extremities of the distributions than the normal distribution would predict. We call these 'fat tails' or 'excess kurtosis'. This image has been taken from 'Analysi...

Brownian motion describes the motion of a particle in a fluid or gas. Such a particle bounces a...

Monte-Carlo simulation is a statistical technique inspired by the casinos of Monaco. Much like gamblers resigning their fates to probability, we hand over the results of statistical analysis to chance. By running enough trials, we can make conclusions with statistical significance.

Consider...

Monte-Carlo simulation of terminal values is a relatively simple simulation, and one can probably be completed analytically. The true power of Monte-Carlo simulation is unlocked when analysing scenarios that are more difficult to solve analytically, if not impossible. For example, if we wanted to...