Construct stochastic differential equation from linear drift-rate models
SDE = sdeld(A, B, Alpha, Sigma)
SDE = sdeld(A, B, Alpha, Sigma, 'Name1', Value1, 'Name2',
This constructor creates and displays SDE objects whose drift
rate is expressed in linear drift-rate form and that derive from the
from drift and diffusion objects class).
SDELD objects to simulate sample paths
NVARS state variables expressed in linear drift-rate
form. They provide a parametric alternative to the mean-reverting
drift form (see
These state variables are driven by
motion sources of risk over
observation periods, approximating continuous-time stochastic processes
with linear drift-rate functions.
This method allows you to simulate any vector-valued SDE of the form:
Xt is an
state vector of process variables.
A is an
B is an
D is an
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
volatility rate matrix.
dWt is an
Brownian motion vector.
Specify required input parameters as one of the following types:
A MATLAB® array. Specifying an array indicates a static (non-time-varying) 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:
Although the constructor does not enforce restrictions on the
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:
|Scalar starting time of the first observation, applied to all
state variables. If you do not specify a value for |
If you do not specify
a value for
|Correlation between Gaussian random variates drawn to generate
the Brownian motion vector (Wiener processes). Specify |
As a deterministic function
If you do not specify a value for
|A user-defined simulation function or SDE simulation method.
If you do not specify a value for |
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 Xt,
and return an array of appropriate dimension. Even if you originally
specified an input as an array,
sdeld treats it
as a static function of time and state, by that means guaranteeing
that all parameters are accessible by the same interface.
Ait-Sahalia, Y., "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Spring 1996, Vol. 9, No. 2, pp. 385–426.
Ait-Sahalia, 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: Springer-Verlag, 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: Continuous-Time Models, New York: Springer-Verlag, 2004.