charNTS {TempStable}

Characteristic function of the normal tempered stable (NTS) distribution

Description

Theoretical characteristic function (CF) of the normal tempered stable distribution. See Rachev et al. (2011) for details.

Usage

charNTS(
  t,
  alpha = NULL,
  beta = NULL,
  delta = NULL,
  lambda = NULL,
  mu = NULL,
  theta = NULL
)

Arguments

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.

Details

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)

Value

The CF of the normal tempered stable distribution.

References

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

Examples

x <- seq(-10,10,0.25)
y <- charNTS(x,0.5,1,1,1,0)