represents a Cox–Ingersoll–Ross process with long‐term mean μ, volatility σ, speed of adjustment θ, and initial condition x0.
- CoxIngersollRossProcess is also known as the CIR process.
- CoxIngersollRossProcess is a continuous‐time and continuous‐state random process.
- The state of the Cox–Ingersoll–Ross process satisfies an Ito differential equation , where follows a standard WienerProcess.
- CoxIngersollRossProcess allows x0 to be any positive real number, σ to be any nonzero real number, and θ and μ to be any nonzero real numbers of the same sign.
- CoxIngersollRossProcess can be used with such functions as Mean, PDF, Probability, and RandomFunction.
Examplesopen allclose all
Basic Examples (3)
Basic Uses (9)
Simulate an ensemble of random paths for a Cox–Ingersoll–Ross process:
Simulate with arbitrary precision:
Compare paths for different values of the drift parameter:
Compare paths for different values of the volatility parameter:
Compare paths for different values of the speed adjustment parameter:
Simulate a Cox–Ingersoll–Ross process with different starting points:
Process Slice Properties (5)
First-order probability density function for the slice distribution:
Multivariate slice distributions:
Compute the expectation of an expression:
Calculate the probability of an event:
CentralMoment and its generating function:
FactorialMoment and its generating function:
Cumulant and its generating function:
Properties & Relations (3)
A Cox–ingersoll–Ross process is not weakly stationary:
Conditional cumulative distribution function:
A Cox–ingersoll–Ross process is a special ItoProcess:
As well as StratonovichProcess:
Neat Examples (3)
Wolfram Research (2012), CoxIngersollRossProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html.
Wolfram Language. 2012. "CoxIngersollRossProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html.
Wolfram Language. (2012). CoxIngersollRossProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html