Construct 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:
$$d{X}_{t}=S(t)[L(t){X}_{t}]dt+D(t,{X}_{t}^{\frac{1}{2}})V(t)d{W}_{t}$$
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.
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 t
as
its only input argument. Otherwise, a parameter is assumed to be a
function of time t and state X(t) and
is invoked with both input arguments.
The required input parameters are:
Speed 
If
you specify

Level 
If
you specify

Sigma 
If
you specify

Although the constructor does not enforce restrictions on the signs of these input arguments, each argument is specified as a positive value.
Specify optional inputs as matching parameter name/value pairs as follows:
Specify the parameter name as a character vector, 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 character vector 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, 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 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

Creating CoxIngersollRoss (CIR) Square Root Diffusion Models
When you specify the required input parameters as arrays, they are associated with a specific parametric form. By contrast, when you specify either required input parameter as a function, you can customize virtually any specification.
Accessing the output parameters with no inputs simply returns the original input specification. Thus, when you invoke these parameters with no inputs, they behave like simple properties and allow you to test the data type (double vs. function, or equivalently, static vs. dynamic) of the original input specification. This is useful for validating and designing methods.
When you invoke these parameters with inputs, they behave like
functions, giving the impression of dynamic behavior. The parameters
accept the observation time t followed by a state
vector X_{t}, and return an
array of appropriate dimension. Even if you originally specified an
input as an array, cir
treats it as a static function
of time and state, by that means guaranteeing that all parameters
are accessible by the same interface.
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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.