charNTS {TempStable} | R Documentation |
Theoretical characteristic function (CF) of the normal tempered stable distribution. See Rachev et al. (2011) for details.
charNTS(
t,
alpha = NULL,
beta = NULL,
delta = NULL,
lambda = NULL,
mu = NULL,
theta = NULL
)
t |
A vector of real numbers where the CF is evaluated. |
alpha |
Stability parameter. A real number between 0 and 1. |
beta |
Skewness parameter. Any real number. |
delta |
Scale parameter. A real number > 0. |
lambda |
Tempering parameter. A real number > 0. |
mu |
A location parameter, any real number. |
theta |
A vector of all other arguments. |
theta
denotes the parameter vector (alpha, beta, delta, lambda,
mu)
. Either provide the parameters individually OR provide theta
.
\varphi_{NTS}(t;\theta)=E\left[\mathrm{e}^{\mathrm{i}tZ}\right]= \exp
\left(\mathrm{i}t\mu+\delta\Gamma(-\alpha)\left((\lambda-\mathrm{i}t
\beta+t^2/2)^{\alpha}-\lambda^{\alpha}\right)\right)
The CF of the normal tempered stable distribution.
Massing, T. (2022), 'Parametric Estimation of Tempered Stable Laws'
Rachev, Svetlozar T. & Kim, Young Shin & Bianchi, Michele L. & Fabozzi, Frank J. (2011) 'Financial models with Lévy processes and volatility clustering' doi:10.1002/9781118268070
x <- seq(-10,10,0.25)
y <- charNTS(x,0.5,1,1,1,0)