Poisson Process
Also called: jump process, counting process, Poisson arrivals
A Poisson process counts events that arrive randomly at a constant average rate, with waiting times that are exponentially distributed and memoryless. In finance it models things that happen suddenly rather than continuously: defaults, market jumps, order arrivals. Pairing it with a diffusion gives jump-diffusion, which explains the fat tails and short-dated smile that pure Brownian motion cannot.
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