Binomial Distribution

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The binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes, such as success or failure, with the same probability each time.

The binomial distribution applies when there is a set number of trials, each trial is independent, there are only two outcomes and the probability of success stays constant. Examples include the number of heads in ten coin tosses or the number of defaults in a group of similar loans.

For example, if a lender makes 10 loans, each with an independent 10% chance of default, the probability that none default is about 34.9%, and the probability that two or more default is about 26.4%.

The binomial distribution is used in finance in several ways. The binomial option pricing model represents an asset's price as moving up or down in each period, building a tree of possible prices to value options. It is also used in credit risk, quality control and testing whether outcomes differ from chance.

In reality, financial events are often not independent. Loan defaults tend to cluster during recessions, which means simple binomial models can underestimate the risk of many defaults happening together.

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