Overview

The base sde object

represents the most general model.

Creating an sde object using sde requires the following inputs:

Evaluating object parameters by passing (t, X_t) to a common, published interface allows most parameters to be referenced by a common input argument list that reinforces common method programming. You can use this simple function evaluation approach to model or construct powerful analytics, as in the following example.

Specify Base Stochastic Differential Equation (SDE) Model

Create an sde object using sde to represent a univariate geometric Brownian Motion model of the form:

Create drift and diffusion functions that are accessible by the common ($\mathit{t},{\mathit{X}}_{\mathit{t}}^{}$) interface.

F = @(t,X) 0.1 * X;
G = @(t,X) 0.3 * X;

Pass the drift and diffusion functions to sde to creare an sde object.

obj = sde(F, G)    % dX = F(t,X)dt + G(t,X)dW

obj = 
   Class SDE: Stochastic Differential Equation
   -------------------------------------------
     Dimensions: State = 1, Brownian = 1
   -------------------------------------------
      StartTime: 0
     StartState: 1
    Correlation: 1
          Drift: drift rate function F(t,X(t)) 
      Diffusion: diffusion rate function G(t,X(t)) 
     Simulation: simulation method/function simByEuler

The sde object displays like a MATLAB® structure, with the following information:

The object's displayed parameters are as follows:

Of these displayed parameters, only Drift and Diffusion are required inputs.

The only exception to the ($\mathit{t},{\mathit{X}}_{\mathit{t}}^{}$) evaluation interface is Correlation. Specifically, when you enter Correlation as a function, the SDE engine assumes that it is a deterministic function of time, $\mathit{C}\left(\mathit{t}\right)$. This restriction on Correlation as a deterministic function of time allows Cholesky factors to be computed and stored before the formal simulation. This inconsistency dramatically improves run-time performance for dynamic correlation structures. If Correlation is stochastic, you can also include it within the simulation architecture as part of a more general random number generation function.