Jump process

 ( Stochastic Processes ) 

A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.Tankov, P. (2003). Financial modelling with jump processes (Vol. 2). CRC press.

In finance, various stochastic models are used to model the price movements of financial instruments; for example the Black–Scholes model for pricing options assumes that the underlying instrument follows a traditional diffusion process, with continuous, random movements at all scales, no matter how small. John Carrington Cox and Stephen Ross proposed that prices actually follow a 'jump process'.

Robert C. Merton extended this approach to a hybrid model known as jump diffusion, which states that the prices have large jumps interspersed with small continuous movements.

• Poisson process, an example of a jump process
• Continuous-time Markov chain (CTMC), an example of a jump process and a generalization of the Poisson process
• Counting process, an example of a jump process and a generalization of the Poisson process in a different direction than that of CTMCs
• Interacting particle system, an example of a jump process
• Kolmogorov equations (continuous-time Markov chains)