A fat tail is a property of some probability distributions (alternatively referred to as heavy-tailed distributions) exhibiting extremely large kurtosis particularly relative to the ubiquitous normal which itself is an example of an exceptionally thin tail distribution. The term fat tail is a reference to the tendency of many financial instrument price and return distributions to have more observations in the tails and to be thinner in the midrange than a normal distribution. Assets prone to price jumps tend to exhibit fat-tailed distributions.
Fat tail distributions have power law decay. Some reserve the term "fat tail" for distributions only where 0 < a < 2 (i.e. only in cases with infinite variance).