Key Concepts on Probability

Nigel Da Costa Lewis

Probability, randomness and risk are concepts intertwined in the popular view of the financial markets. We face risk when there is a chance of loss. A chance of loss is assumed to occur with a specific probability, and an event could be deemed random if we cannot control the outcome. Since our task is primarily empirical, we will need to use data to attempt to figure out risk, probabilities and the nature of randomness. To do this we will need to develop suitable models that describe and explain the characteristics of the data. These models need not be complex, but they will need to cater for uncertainty, which is inherent in financial data. This uncertainty can be captured in many cases by using probability. Underlying all statistical methods are the concepts of a random experiment (or experiment of chance) and random variable.

THE BASICS OF RANDOM VARIABLES

Take, for example, the price of Brent crude oil futures – it varies from one day to the next because there are factors affecting the price on any particularly day which are unknown or cannot be measured. In the language of statistics, the crude oil futures price is a random variable, trading activity an “experiment”, the