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Simulate Cox-Ingersoll-Ross sample paths with transition density

`[Paths,Times] = simByTransition(MDL,NPeriods)`

`[Paths,Times] = simByTransition(___,Name,Value)`

`[`

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`

)

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.

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