A jump process is a type of stochastic process that has discrete movements, called jumps, rather than small continuous movements.
In physics, jump processes result in diffusion. On a microscopic level, they are described by jump diffusion models.
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 small, continuous, random movements. John Carrington Cox, Stephen Ross and Nassim Nicholas Taleb proposed that prices actually follow a 'jump process'. The Cox-Ross-Rubinstein binomial options pricing model formalizes this approach. This is a more intuitive view of financial markets, with allowance for larger moves in asset prices caused by sudden world events.
Robert C. Merton extended this approach to a hybrid model known as jump diffusion, which states that the prices have large jumps followed by small continuous movements.
Famous quotes containing the words jump and/or process:
“One is twice as willing to jump in after a person who has fallen into the water when there are people present who do not dare to do so.”
—Friedrich Nietzsche (1844–1900)
“Science is a dynamic undertaking directed to lowering the degree of the empiricism involved in solving problems; or, if you prefer, science is a process of fabricating a web of interconnected concepts and conceptual schemes arising from experiments and observations and fruitful of further experiments and observations.”
—James Conant (1893–1978)