Jump process

Jump process

A jump process is a type of stochastic process that has large discrete movements (jumps), rather than small continuous movements.

This concept is frequently used 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 and Stephen Ross proposed that prices actually follow a 'jump process'. The Cox-Ross-Rubinstein binomial 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 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.

ee also

*Poisson Process


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