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CoxIngersollRoss meanreverting square root diffusion models
CIR = cir(Speed, Level, Sigma)
CIR = cir(Speed, Level, Sigma, 'Name1', Value1, 'Name2', Value2, ...)
This constructor creates and displays CIR objects, which derive from the SDEMRD (SDE with drift rate expressed in meanreverting form) class. Use CIR objects to simulate sample paths of NVARS state variables expressed in meanreverting driftrate form. These state variables are driven by NBROWNS Brownian motion sources of risk over NPERIODS consecutive observation periods, approximating continuoustime CIR stochastic processes with square root diffusions.
This method allows you to simulate any vectorvalued SDE of the form:
(183) 
where:
X_{t} is an NVARSby1 state vector of process variables.
S is an NVARSbyNVARS matrix of mean reversion speeds (the rate of mean reversion).
L is an NVARSby1 vector of mean reversion levels (longrun mean or level).
D is an NVARSbyNVARS diagonal matrix, where each element along the main diagonal is the square root of the corresponding element of the state vector.
V is an NVARSbyNBROWNS instantaneous volatility rate matrix.
dW_{t} is an NBROWNSby1 Brownian motion vector.
Specify required input parameters as one of the following types:
A MATLAB^{®} array. Specifying an array indicates a static (nontimevarying) parametric specification. This array fully captures all implementation details, which are clearly associated with a parametric form.
A MATLAB function. Specifying a function provides indirect support for virtually any static, dynamic, linear, or nonlinear model. This parameter is supported via an interface, because all implementation details are hidden and fully encapsulated by the function.
The required input parameters are:
Speed  Speed represents S. If you specify Speed as an array, it must be an NVARSbyNVARS matrix of meanreversion speeds (the rate or speed at which the state vector reverts to its longrun average Level). If you specify Speed as a function, it must generate an NVARSbyNVARS matrix of reversion rates when invoked with two inputs:

Level  Level represents L. If you specify Level as an array, it must be an NVARSby1 column vector of reversion levels. If you specify Level as a function, it must generate an NVARSby1 column vector of reversion levels when invoked with two inputs:

Sigma  Sigma represents the parameter V. If you specify Sigma as an array, it must be an NVARSbyNBROWNS 2dimensional matrix of instantaneous volatility rates. In this case, each row of Sigma corresponds to a particular state variable. Each column of Sigma corresponds to a particular Brownian source of uncertainty, and associates the magnitude of the exposure of state variables with sources of uncertainty. If you specify Sigma as a function, it must generate an NVARSbyNBROWNS matrix of volatility rates when invoked with two inputs:

Specify optional inputs as matching parameter name/value pairs as follows:
Specify the parameter name as a character string, followed by its corresponding value.
You can specify parameter name/value pairs in any order.
Parameter names are case insensitive.
You can specify unambiguous partial string matches.
Valid parameter names are:
StartTime  Scalar starting time of the first observation, applied to all state variables. If you do not specify a value for StartTime, the default is 0. 
StartState  Scalar, NVARSby1 column vector, or NVARSbyNTRIALS matrix
of initial values of the state variables. If StartState is a scalar, cir applies the same initial value to all state variables on all trials. If StartState is a column vector, cir applies a unique initial value to each state variable on all trials. If StartState is a matrix, cir applies a unique initial value to each state variable on each trial. If you do not specify a value for StartState, all variables start at 1. 
Correlation  Correlation between Gaussian random variates drawn to generate
the Brownian motion vector (Wiener processes). Specify Correlation as
an NBROWNSbyNBROWNS positive
semidefinite matrix, or as a deterministic function C(t) that
accepts the current time t and returns an NBROWNSbyNBROWNS positive
semidefinite correlation matrix. A Correlation matrix represents a static condition. As a deterministic function of time, Correlation allows you to specify a dynamic correlation structure. If you do not specify a value for Correlation, the default is an NBROWNSbyNBROWNS identity matrix representing independent Gaussian processes. 
Simulation  A userdefined simulation function or SDE simulation method. If you do not specify a value for Simulation, the default method is simulation by Euler approximation (simByEuler). 
CIR  Object of class CIR with the following displayed parameters:

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