Simulate time series from the SVC stochastic volatility model.

Simulate time series from the SVC stochastic volatility model.

svc_sim(
  nobs,
  dt,
  X0,
  log_VP0,
  log_V0,
  alpha,
  log_gamma,
  mu,
  log_sigma,
  logit_rho,
  logit_tau,
  logit_omega,
  dBt
)

Arguments

nobs

Length of time series.

dt

Interobservation time.

X0

Vector of length nasset + 1 or matrix of size (nasset + 1) x nseries of asset log prices at time t = 0.

log_VP0

Scalar or vector of length nseries of volatility proxy values at time t = 0 on the log standard deviation scale.

log_V0

Vector of length nasset + 1 or matrix of size (nasset + 1) x nseries of volatilities at time t = 0 on the log standard deviation scale.

alpha

Vector of length (nasset + 1) or matrix of size (nasset + 1) x nseries of asset growth rate parameters.

log_gamma

Vector of length nasset + 2 or matrix of size (nasset + 2) x nseries log-volatility mean reversion parameters on the log scale. The first two correspond to the volatility proxy and the common-factor asset's volatility, respectively.

mu

Vector of length nasset + 2 or matrix of size (nasset + 2) x nseries of log-volatility mean parameters.

log_sigma

Vector of length nasset + 2 or matrix of size (nasset + 2) x nseries or log-volatility diffusion parameters on the log scale.

logit_rho

Vector of length nasset + 1 or matrix of size (nasset + 1) x nseries correlation parameters between asset and volatility innovations, on the logit scale. The first one is that of the common-factor asset proxy. See 'Details'.

logit_tau

Vector of length nasset + 1 or matrix of size (nasset + 1) x nseries correlation parameters between the latent volatilities and the volatility proxy.

logit_omega

Vector of length nasset or matrix of size nasset x nseries correlation parameters between the residual asset price of the common-factor proxy and the other residual asset prices.

dBt

An optional list of Brownian innovations:

VP

An nobs x nseries matrix.

V

An nobs x (nasset+1) x nseries array.

Z

An nobs x (nasset+1) x nseries array.

If missing these are all iid draws from an N(0, dt) distribution.

Value

A list containing arrays Xt and log_Vt of size nobs x (nasset + 1) x nseries, and the matrix log_VPt of size nobs x nseries containing the simulations of nseries SVC processes observed at times t = dt, 2dt, ..., nobs*dt.