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:
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—Bob Dylan [Robert Allen Zimmerman] (b. 1941)
“The invention of photography provided a radically new picture-making process—a process based not on synthesis but on selection. The difference was a basic one. Paintings were made—constructed from a storehouse of traditional schemes and skills and attitudes—but photographs, as the man on the street put, were taken.”
—Jean Szarkowski (b. 1925)