Jump process
Encyclopedia
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.
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
process that has discrete movements, called jumps, rather than small continuous movements.
In physics, jump processes result in diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
. On a microscopic level, they are described by jump diffusion models.
In finance
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
, 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
Diffusion process
In probability theory, a branch of mathematics, a diffusion process is a solution to a stochastic differential equation. It is a continuous-time Markov process with continuous sample paths....
, with small, continuous, random movements. John Carrington Cox, Stephen Ross
Stephen Ross
Stephen Ross may refer to:* Stephen Jay Ross , U.S. communications businessman* Stephen Ross, Baron Ross of Newport , former Liberal Member of Parliament* Stephen Ross , financial economist and textbook author...
and Nassim Nicholas Taleb
proposed that prices actually follow a 'jump process'. The Cox-Ross-Rubinstein binomial options pricing model
Binomial options pricing model
In finance, the binomial options pricing model provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. Essentially, the model uses a “discrete-time” model of the varying price over time of the underlying...
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
Robert C. Merton
Robert Carhart Merton is an American economist, Nobel laureate in Economics, and professor at the MIT Sloan School of Management.-Biography:...
extended this approach to a hybrid model known as jump diffusion
Jump-diffusion models
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in condensed matter physics and in option pricing.- In physics :In crystals, atomic diffusion typically consists of jumps between vacant lattice sites...
, which states that the prices have large jumps followed by small continuous movements.