Jump process
This article needs attention from an expert in Statistics. The specific problem is: the article lacks a definition, illustrative examples, but is of importance (Poisson process, Lévy process).. (December 2013) |
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
- Levy process
- Poisson process
- Counting process
- Interacting particle system
- Kolmogorov equations
- Kolmogorov equations (Markov jump process)
References
- ↑ 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.
- ↑ 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.
This probability-related article is a stub. You can help Infogalactic by expanding it. |
This economics-related article is a stub. You can help Infogalactic by expanding it. |