Risk Management
Modeling rare events such as defaults, market crashes, or operational risks
Master the statistical tool that revolutionizes risk assessment and rare event prediction in finance
The Poisson distribution is a discrete probability distribution that expresses the probability of events occurring in a fixed interval of time or space, given a known average rate of occurrence and independent of the time since the last event.
The probability mass function is given by:
Modeling rare events such as defaults, market crashes, or operational risks
Predicting the number of large price movements in a given time period
Analyzing the frequency of portfolio rebalancing events
Modeling the number of insurance claims in a specific time period
Consider a portfolio of 1000 loans with a historical average of 3 defaults per year:
Analysis of significant market movements (>2% daily change):
Used in modeling aggregate claims in insurance and compound financial events.
Applications in modeling heterogeneous financial markets and risk scenarios.
Modeling events with non-constant rates, such as seasonal market volatility.
Important: The Poisson distribution is an approximation. In financial applications, validate its assumptions for your specific use case.