Function File: DiffusionRate = diffusion (Alpha, Sigma)

Creates an object to represent the diffusion rate of a stochastic differential equation (SDE).

DiffusionRate(t, X_t) = diag(X_t.^Alpha(t)) * V(t)
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: Alpha An NVARS-by-1 vector or a function. As a function, Alpha returns an NVARS-by-1 vector and has either exactly one input (time: Alpha(t)) or exactly two inputs (time and space: Alpha(t, X_t)).
  • Variable: Sigma An NVARS-by-NBROWNS matrix or a function. As a function, Sigma returns an NVARS-by-NBROWNS matrix and has either exactly one input (time: Sigma(t)) or exactly two inputs (time and space: Sigma(t, X_t)).

See also: drift.

Package: financial