CoxIngersollRossProcess

CoxIngersollRossProcess[μ,σ,θ,x0]

represents a Cox–Ingersoll–Ross process with long‐term mean μ, volatility σ, speed of adjustment θ, and initial condition x0.

Details

Examples

open allclose all

Basic Examples  (3)

Simulate a Cox–Ingersoll–Ross process:

Mean and variance functions:

Covariance function:

Scope  (14)

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 parameter estimation:

Correlation function:

Absolute correlation function:

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:

Skewness and kurtosis:

Moment of order r:

Generating functions:

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)

Simulate a Cox–Ingersoll–Ross process in two dimensions:

Simulate a Cox–Ingersoll–Ross process in three dimensions:

Simulate 500 paths from a Cox–Ingersoll–Ross process:

Take a slice at 1 and visualize its distribution:

Plot paths and histogram distribution of the slice distribution at 1:

Wolfram Research (2012), CoxIngersollRossProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html.

Text

Wolfram Research (2012), CoxIngersollRossProcess, Wolfram Language function, https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html.

CMS

Wolfram Language. 2012. "CoxIngersollRossProcess." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html.

APA

Wolfram Language. (2012). CoxIngersollRossProcess. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html

BibTeX

@misc{reference.wolfram_2024_coxingersollrossprocess, author="Wolfram Research", title="{CoxIngersollRossProcess}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html}", note=[Accessed: 21-November-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_coxingersollrossprocess, organization={Wolfram Research}, title={CoxIngersollRossProcess}, year={2012}, url={https://reference.wolfram.com/language/ref/CoxIngersollRossProcess.html}, note=[Accessed: 21-November-2024 ]}