gammaKernelBSS {BSS} | R Documentation |
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.
gammaKernelBSS(
N,
n,
T,
kappa = 3,
alpha,
lambda,
sigma = rep(1, N + n * T + 1)
)
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 |
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 |
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)