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
)The CF of the normal tempered stable distribution.
A vector of real numbers where the CF is evaluated.
Stability parameter. A real number between 0 and 1.
Skewness parameter. Any real number.
Scale parameter. A real number > 0.
Tempering parameter. A real number > 0.
A location parameter, any real number.
A vector of all other arguments.
theta denotes the parameter vector (alpha, beta, delta, lambda,
mu). Either provide the parameters individually OR provide theta.
$$\varphi_{NTS}(t;\theta)=E\left[\mathrm{e}^{\mathrm{i}tZ}\right]= \exp
\left(\mathrm{i}t\mu+\delta\Gamma(-\alpha)\left((\lambda-\mathrm{i}t
\beta+t^2/2)^{\alpha}-\lambda^{\alpha}\right)\right)
$$
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' tools:::Rd_expr_doi("10.1002/9781118268070")
x <- seq(-10,10,0.25)
y <- charNTS(x,0.5,1,1,1,0)
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