jump process

{{Short description|Stochastic process with discrete movements}}

{{Expert needed|statistics|reason=the article lacks a definition, illustrative examples, but is of importance (Poisson process, Lévy process)|date=December 2013}}

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{{Cite journal | last1 = Cox | first1 = J. C. | author-link1 = John Carrington Cox| last2 = Ross | first2 = S. A. | author-link2 = Stephen Ross (economist)| doi = 10.1016/0304-405X(76)90023-4 | title = The valuation of options for alternative stochastic processes | journal = Journal of Financial Economics| volume = 3 | issue = 1–2 | pages = 145–166 | year = 1976 | citeseerx = 10.1.1.540.5486 }}{{rp|145–166}} 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.{{Cite journal | last1 = Merton | first1 = R. C. | author-link1 = Robert C. Merton| doi = 10.1016/0304-405X(76)90022-2 | title = Option pricing when underlying stock returns are discontinuous | journal = Journal of Financial Economics| volume = 3 | issue = 1–2 | pages = 125–144 | year = 1976 | hdl = 1721.1/1899| citeseerx = 10.1.1.588.7328 }}