Function File: SDE = sde (DriftRate, DiffusionRate)
Function File: SDE = sde (DriftRate, DiffusionRate, OptionName, OptionValue, …)

Creates an object to represent a stochastic differential equation (SDE).

dX_t = DriftRate(t, X_t)dt + DiffusionRate(t, X_t)dW_t.
  • (X_t) is an NVARS-dimensional process;
  • (W_t) is an NBROWNS-dimensional Wiener process.
  • Variable: DriftRate A drift object or function that returns an NVARS-by-1 vector.
  • Variable: DiffusionRate A diffusion object or function that returns an NVARS-by-NBROWNS matrix.

A list of options recognized by sde are given below:

  • StartTime - Time of the first observation. If unspecified, the default is 0.
  • StartState - Scalar, NVARS-dimensional column vector, or NVARS-by-NTRIALS matrix of initial values of the state variables. If unspecified, X_0 is taken to be a vector of ones.
  • Correlation - NBROWNS-by-NBROWNS real symmetric positive definite matrix specifying correlations between Wiener processes. For nonconstant correlation, a function of time returning an NBROWNS-by-NBROWNS matrix can be specified. If unspecified, the identity matrix is used.
  • Simulation - Function handle pointing to simulation method. If unspecified, simByEuler is used.

See also: drift, diffusion.

Package: financial