gammaKernelBSS {BSS}

Simulation of gamma kernel Brownian semistationary processes

Description

gammaKernelBSS uses the Hybrid scheme to simulate a Brownian semistationary process from the gamma kernel. It simulates a path where the volatility process is independent of the driving Brownian motion of the BSS process.

Usage

gammaKernelBSS(
  N,
  n,
  T,
  kappa = 3,
  alpha,
  lambda,
  sigma = rep(1, N + n * T + 1)
)

Arguments

N

positive integer determining the number of terms in the Riemman sum element of the hybrid scheme calculation. Should be of order at least n.

n

positive integer indicating the number of observations per unit of time. It represents the fineness or frequency of observations.

T

the time interval to simulate the BSS process over.

kappa

positive integer giving the number of terms to use in the 'lower' sum of the hybrid scheme. Default set to 3.

alpha

the smoothness parameter of the BSS process to simulate.

lambda

the exponent parameter of the BSS process to simulate.

sigma

the volatility process used in the BSS simulation. This should be a vector of length N + n*T + 1 representing the sample path of sigma from -N to nT. By default this is set to by a vector of 1s so that the Gaussian core is simulated.

Value

The function returns a list of three objects, core gives the Gaussian core of the process between 0 and T, at intervals of 1/n. bss gives the BSS sample path on the between 0 and T, at intervals of 1/n, and vol gives the volatilty process over the same time period.

N <- 10000 n <- 100 T <- 1.0 theta <- 0.5 beta <- 0.125

kappa <- 3 alpha <- -0.2 lambda <- 1.0

vol <- exponentiatedOrnsteinUhlenbeck(N, n, T, theta, beta) bss_simulation <- gammaKernelBSS(N, n, T, kappa, alpha, lambda, sigma = vol)