# simByTransition

Simulate Cox-Ingersoll-Ross sample paths with transition density

## Description

`[`

simulates `Paths`

,`Times`

] = simByTransition(`MDL`

,`NPeriods`

)`NTrials`

sample paths of `NVars`

independent state variables driven by the Cox-Ingersoll-Ross (CIR) process sources
of risk over `NPeriods`

consecutive observation periods.
`simByTransition`

approximates a continuous-time CIR model
using an approximation of the transition density function.

`[`

specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax.`Paths`

,`Times`

] = simByTransition(___,`Name,Value`

)

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

Use the `simByTransition`

function to simulate any vector-valued CIR
process of the form

$$d{X}_{t}=S(t)[L(t)-{X}_{t}]dt+D(t,{X}_{t}^{\frac{1}{2}})V(t)d{W}_{t}$$

where

*X*is an_{t}`NVars`

-by-`1`

state vector of process variables.*S*is an`NVars`

-by-`NVars`

matrix of mean reversion speeds (the rate of mean reversion).*L*is an`NVars`

-by-`1`

vector of mean reversion levels (long-run mean or level).*D*is an`NVars`

-by-`NVars`

diagonal matrix, where each element along the main diagonal is the square root of the corresponding element of the state vector.*V*is an`NVars`

-by-`NBrowns`

instantaneous volatility rate matrix.*dW*is an_{t}`NBrowns`

-by-`1`

Brownian motion vector.

## References

[1] Glasserman, P. *Monte Carlo Methods in Financial
Engineering.* New York: Springer-Verlag, 2004.

**Introduced in R2018b**