Poisson Process Integration

A Poisson process is a mathematical model used to describe the occurrence of independent events over a fixed interval of time. In finance, it is integrated into pricing models to simulate the arrival of random, discrete events like market shocks or news-driven price spikes.

By defining an intensity parameter, which represents the average frequency of these events, analysts can mathematically account for the probability of a jump occurring at any moment. This is essential for pricing derivative instruments where the risk of a sudden crash is a significant factor in the premium.

Integrating this process allows for a more nuanced understanding of risk exposure in crypto markets, where volatility is often driven by unpredictable, high-impact news. It provides a structured way to quantify the likelihood of rare but damaging market movements.