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Construct stochastic differential equation from linear driftrate models
SDE = sdeld(A, B, Alpha, Sigma)
SDE = sdeld(A, B, Alpha, Sigma, 'Name1', Value1, 'Name2', Value2, ...)
This constructor creates and displays SDE objects whose drift rate is expressed in linear driftrate form and that derive from the SDEDDO (SDE from drift and diffusion objects class).
Use SDELD objects to simulate sample paths of NVARS state variables expressed in linear driftrate form. They provide a parametric alternative to the meanreverting drift form (see sdemrd).
These state variables are driven by NBROWNS Brownian motion sources of risk over NPERIODS consecutive observation periods, approximating continuoustime stochastic processes with linear driftrate functions.
This method allows you to simulate any vectorvalued SDE of the form:
(1810) 
where:
X_{t} is an NVARSby1 state vector of process variables.
A is an NVARSby1 vector.
B is an NVARSbyNVARS matrix.
D is an NVARSbyNVARS diagonal matrix, where each element along the main diagonal is the corresponding element of the state vector raised to the corresponding power of α.
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:
A  A represents the parameter A.
If you specify A as an array, it must be an NVARSby1
column vector of intercepts. If you specify A as
a function, it must generate an NVARSby1 column
vector of intercepts when invoked with two inputs:

B  B represents the parameter B.
If you specify B as an array, it must be an NVARSbyNVARS matrix
of state vector coefficients. If you specify B as
a function, it must generate an NVARSbyNVARS matrix
of state vector coefficients when invoked with two inputs:

Alpha  Alpha determines the format of the parameter D.
If you specify Alpha as an array, it represents
an NVARSby1 column vector of exponents. If you
specify it as a function, it must return an NVARSby1
column vector of exponents when invoked with two inputs:

Sigma  Sigma represents the parameter V.
If you specify Sigma as an array, it represents
is 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
it 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, sdeld applies the same initial value to all state variables on all trials. If StartState is a column vector, sdeld applies a unique initial value to each state variable on all trials. If StartState is a matrix, sdeld 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). 
SDE  Object of class sdeld with the following 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.