CoxIngersollRossProcess

CoxIngersollRossProcess[μ,σ,θ,x0]

represents a CoxIngersollRoss process with longterm mean μ, volatility σ, speed of adjustment θ, and initial condition x0.

Details

Examples

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Basic Examples  (3)

Simulate a CoxIngersollRoss process:

Mean and variance functions:

Covariance function:

Scope  (14)

Basic Uses  (9)

Simulate an ensemble of random paths for a CoxIngersollRoss 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 CoxIngersollRoss 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 CoxingersollRoss process is not weakly stationary:

Conditional cumulative distribution function:

A CoxingersollRoss process is a special ItoProcess:

As well as StratonovichProcess:

Neat Examples  (3)

Simulate a CoxIngersollRoss process in two dimensions:

Simulate a CoxIngersollRoss process in three dimensions:

Simulate 500 paths from a CoxIngersollRoss process:

Take a slice at 1 and visualize its distribution:

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

Introduced in 2012
 (9.0)