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:
“Thus twice before, and jump at this dead hour,
With martial stalk hath he gone by our watch.”
—William Shakespeare (1564–1616)
“At the heart of the educational process lies the child. No advances in policy, no acquisition of new equipment have their desired effect unless they are in harmony with the child, unless they are fundamentally acceptable to him.”
—Central Advisory Council for Education. Children and Their Primary Schools (Plowden Report)