Lévy Processes

Lévy processes are mathematical models used in finance to describe the random movement of asset prices over time. Unlike standard models that assume price changes are smooth and continuous, Lévy processes allow for sudden jumps or discontinuities.

These jumps represent the reality of market crashes, news events, and liquidity shocks that occur in cryptocurrency and derivative markets. By capturing these sharp movements, traders can better estimate the probability of extreme events.

This framework is essential for pricing options because it accounts for the fat tails often observed in financial returns. It serves as a foundational tool for understanding how prices evolve in volatile, high-frequency trading environments.