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:
$$d{X}_{t}=S(t)[L(t){X}_{t}]dt+D(t,{X}_{t}^{\frac{1}{2}})V(t)d{W}_{t}$$  (183) 
where:
X_{t} is an NVARS
by1
state vector of process variables.
S is an NVARS
byNVARS
matrix
of mean reversion speeds (the rate of mean reversion).
L is an NVARS
by1
vector of mean reversion levels (longrun mean or level).
D is an NVARS
byNVARS
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
byNBROWNS
instantaneous
volatility rate matrix.
dW_{t} is an NBROWNS
by1
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.
Note: You can specify combinations of array and function input parameters as needed. Moreover, a parameter is identified as a deterministic function
of time if the function accepts a scalar time 
The required input parameters are:
Speed 
If
you specify

Level 
If
you specify

Sigma 
If
you specify

Note: Although the constructor does not enforce restrictions on the signs of these input arguments, each argument is usually specified as a positive value. 
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, NVARS by1 column vector, or NVARS byNTRIALS matrix
of initial values of the state variables. If If If If you do not specify
a value for 
Correlation  Correlation between Gaussian random variates drawn to generate
the Brownian motion vector (Wiener processes). Specify Correlation as
an NBROWNS byNBROWNS positive
semidefinite matrix, or as a deterministic function C(t) that
accepts the current time t and returns an NBROWNS byNBROWNS positive
semidefinite correlation matrix. A As a deterministic function
of time, If you do not specify a value for 
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

AitSahalia, Y., "Testing ContinuousTime Models of the Spot Interest Rate," The Review of Financial Studies, Spring 1996, Vol. 9, No. 2, pp. 385–426.
AitSahalia, Y., "Transition Densities for Interest Rate and Other Nonlinear Diffusions," The Journal of Finance, Vol. 54, No. 4, August 1999.
Glasserman, P., Monte Carlo Methods in Financial Engineering, New York: SpringerVerlag, 2004.
Hull, J. C., Options, Futures, and Other Derivatives, 5th ed. Englewood Cliffs, NJ: Prentice Hall, 2002.
Johnson, N. L., S. Kotz, and N. Balakrishnan, Continuous Univariate Distributions, Vol. 2, 2nd ed. New York: John Wiley & Sons, 1995.
Shreve, S. E., Stochastic Calculus for Finance II: ContinuousTime Models, New York: SpringerVerlag, 2004.