Random Variables and Distributions

Random variables represent uncertain outcomes in financial markets, such as asset returns, interest rates, or default events. These variables quantify possible future values and serve as the basis for modeling risk and pricing derivatives.

Distributions describe the probabilities of those outcomes. A probability distribution assigns likelihoods to different values a random variable can take.

For example, the normal distribution is commonly used to model returns due to its symmetry and well-understood properties.

The binomial distribution is used for modeling binary outcomes, such as up or down movements in discrete time steps.

The lognormal distribution is often applied to asset prices, since it ensures that values remain strictly positive and reflects compounding behavior over time.