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Create HWV model
HWV = hwv(Speed, Level, Sigma)
HWV = hwv(Speed, Level, Sigma, 'Name1', Value1, 'Name2', Value2, ...)
This constructor creates and displays HWV objects, which derive from the SDEMRD (SDE with drift rate expressed in meanreverting form) class. Use HWV 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 HWV stochastic processes with Gaussian diffusions.
This method allows you to simulate vectorvalued HWV processes of the form:
(187) 
where:
X_{t} is an NVARSby1 state vector of process variables.
S is an NVARSbyNVARS of mean reversion speeds (the rate of mean reversion).
L is an NVARSby1 vector of mean reversion levels (longrun mean or level).
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 the function S.
If you specify Speed as an array, it must be an NVARSbyNVARS matrix
of meanreversion speeds (the rate at which the state vector reverts
to its longrun average Level). If you specify Speed as
a function, it calculates the speed of mean reversion. This function
must generate an NVARSbyNVARS matrix
of reversion rates when called with two inputs:

Level  Level represents the function 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 called with two inputs:

Sigma  Sigma represents the parameter V.
If you specify Sigma as an array, it must be an NVARSbyNBROWNS matrix
of instantaneous volatility rates. In this case, each row of Sigma corresponds
to a particular state variable. Each column 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
it as a function, Sigma must return an NVARSbyNBROWNS matrix
of volatility rates when invoked with two inputs:

Specify optional input arguments as variablelength lists of matching parameter name/value pairs: 'Name1', Value1, 'Name2', Value2, ... and so on. The following rules apply when specifying parametername pairs:
Specify the parameter name as a character string, followed by its corresponding parameter 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, hwv applies the same initial value to all state variables on all trials. If StartState is a column vector, hwv applies a unique initial value to each state variable on all trials. If StartState is a matrix, hwv 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). 
HWV  Object of class hwv with the following displayed
parameters:

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.