Jump process

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

A general mathematical framework relating discrete-time processes to continuous time ones is the continuous-time random walk.

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 and Stephen Ross[1]:145-166 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.[2]

See also


  1. Cox, J. C.; Ross, S. A. (1976). "The valuation of options for alternative stochastic processes". Journal of Financial Economics. 3: 145. doi:10.1016/0304-405X(76)90023-4. 
  2. Merton, R. C. (1976). "Option pricing when underlying stock returns are discontinuous". Journal of Financial Economics. 3: 125–144. doi:10.1016/0304-405X(76)90022-2. hdl:1721.1/1899.