powerKernelBSS {BSS}R Documentation

Simulation of power law kernel Brownian semistationary processes


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


powerKernelBSS(N, n, T, kappa, alpha, beta, sigma = rep(1, N + n * T + 1))



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


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


the time interval to simulate the BSS process over.


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


the smoothness parameter of the BSS process to simulate.


the exponent parameter of the BSS process to simulate.


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.


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_vol <- 0.125

kappa <- 3
alpha <- -0.2
beta_pwr <- -1.0

vol <- exponentiatedOrnsteinUhlenbeck(N, n, T, theta, beta_vol)
bss_simulation <- powerKernelBSS(N, n, T, kappa, alpha, beta_pwr, sigma = vol)

[Package BSS version 0.1.0 Index]