Poisson Distribution

Application

The Poisson Distribution, within cryptocurrency markets, models the probability of a specific number of events—such as trade executions or order book updates—occurring within a fixed time interval, assuming these events occur independently and at a constant average rate. Its utility extends to options pricing, particularly for exotic derivatives where discrete jumps in underlying asset prices are prominent, offering a framework to assess the likelihood of large, infrequent movements impacting option values. Consequently, it’s applied in volatility modeling, specifically jump-diffusion models, to capture sudden shifts in market dynamics not accounted for by standard Brownian motion, and is crucial for risk management in decentralized finance (DeFi) protocols.