The base sde
object
represents the most general model.
Tip
The sde
class is not an abstract class. You can instantiate sde
objects directly to extend
the set of core models.
Creating an sde
object using sde
requires the following inputs:
A drift-rate function F
. This function returns an
NVars
-by-1
drift-rate vector
when run with the following inputs:
A real-valued scalar observation time t.
An NVars
-by-1
state
vector Xt.
A diffusion-rate function G
. This function returns
an NVars
-by-NBrowns
diffusion-rate
matrix when run with the inputs t and
Xt.
Evaluating object parameters by passing (t, Xt) 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.
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 (t,Xt) interface:
F = @(t,X) 0.1 * X; G = @(t,X) 0.3 * X;
Pass the functions to sde
to create 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 class
A brief description of the object
A summary of the dimensionality of the model
The object's displayed parameters are as follows:
StartTime
: The initial observation
time (real-valued scalar)
StartState
: The initial state vector
(NVars
-by-1
column
vector)
Correlation
: The correlation structure
between Brownian process
Drift
: The drift-rate function F(t,Xt)
Diffusion
: The diffusion-rate
function G(t,Xt)
Simulation
: The simulation method
or function.
Of these displayed parameters, only Drift
and Diffusion
are
required inputs.
The only exception to the (t, Xt)
evaluation interface is Correlation
. Specifically,
when you enter Correlation
as a function, the SDE
engine assumes that it is a deterministic function of time, C(t).
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.
bates
| bm
| cev
| cir
| diffusion
| drift
| gbm
| heston
| hwv
| interpolate
| merton
| sde
| sdeddo
| sdeld
| sdemrd
| simByEuler
| simByQuadExp
| simBySolution
| simBySolution
| simulate
| ts2func