Construct sdeddo
model from Drift and
Diffusion objects
SDE = sdeddo(DriftRate, DiffusionRate)
SDE = sdeddo(DriftRate, DiffusionRate, 'Name1', Value1,
'Name2', Value2, ...)
This constructor creates and displays sdeddo
objects,
specifically instantiated with objects of classdrift
and diffusion
. These restricted sdeddo
objects
contain the input drift
and diffusion
objects;
therefore, you can directly access their displayed parameters.
This abstraction also generalizes the notion of drift and diffusionrate
objects as functions that sdeddo
evaluates for
specific values of time t and state X_{t}.
Likesde
objects, sdeddo
objects
allow you to simulate sample paths of NVARS
state
variables driven by NBROWNS
Brownian motion sources
of risk over NPERIODS
consecutive observation periods,
approximating continuoustime stochastic processes.
This method enables you to simulate any vectorvalued SDE of the form:
$$d{X}_{t}=F(t,{X}_{t})dt+G(t,{X}_{t})d{W}_{t}$$  (186) 
X_{t} is an NVARS
by1
state
vector of process variables.
dW_{t} is an NBROWNS
by1
Brownian
motion vector.
F is an NVARS
by1
vectorvalued
driftrate function.
G is an NVARS
byNBROWNS
matrixvalued
diffusionrate function.
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 ). 
SDE  Object of class

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 and a state vector X_{t},
and return an array of appropriate dimension. Even if you originally
specified an input as an array, sdeddo
treats as
a static function of time and state, by that means guaranteeing that
all parameters are accessible by the same interface.
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.