Levy Processes And Stochastic Calculus -

The behavior of any Lévy process is entirely determined by its

: The classic continuous Lévy process used in the Black-Scholes model.

: The statistical properties of an increment depend only on the length of the time interval, not when it occurred. Levy processes and stochastic calculus

: Changes in the process over non-overlapping time intervals do not influence each other.

: The probability of a large jump occurring in a vanishingly small time interval is zero. The behavior of any Lévy process is entirely

: Used to change probability measures, a vital step in risk-neutral pricing for options. Real-World Applications

, representing its variation (diffusion), jump measure, and location (drift). Key Examples representing its variation (diffusion)

: Generalizes the Poisson process by allowing jumps of random sizes.