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Jump process

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Stochastic process with discrete movements
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A jump process is a type of stochastic process that has discrete movements, called jumps, with random arrival times, rather than continuous movement, typically modelled as a simple or compound Poisson process.

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 continuous, random movements at all scales, no matter how small. John Carrington Cox and Stephen Ross proposed that prices actually follow a 'jump process'.

Robert C. Merton extended this approach to a hybrid model known as jump diffusion, which states that the prices have large jumps interspersed with small continuous movements.

See also

References

  1. Tankov, P. (2003). Financial modelling with jump processes (Vol. 2). CRC press.
  2. Cox, J. C.; Ross, S. A. (1976). "The valuation of options for alternative stochastic processes". Journal of Financial Economics. 3 (1–2): 145–166. CiteSeerX 10.1.1.540.5486. doi:10.1016/0304-405X(76)90023-4.
  3. Merton, R. C. (1976). "Option pricing when underlying stock returns are discontinuous". Journal of Financial Economics. 3 (1–2): 125–144. CiteSeerX 10.1.1.588.7328. doi:10.1016/0304-405X(76)90022-2. hdl:1721.1/1899.
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