HyperbolicDist (version 0.6-5)

ghypChangePars: Change Parameterizations of the Generalized Hyperbolic Distribution

Description

This function interchanges between the following 4 parameterizations of the generalized hyperbolic distribution:

1. \(\lambda, \alpha, \beta, \delta, \mu\)

2. \(\lambda, \zeta, \rho, \delta, \mu\)

3. \(\lambda, \xi, \chi, \delta, \mu\)

4. \(\lambda, \bar\alpha, \bar\beta, \delta, \mu\)

These are the parameterizations given in Prause (1999)

Usage

ghypChangePars(from, to, Theta, noNames = FALSE)

Value

A numerical vector of length 5 representing Theta in the

to parameterization.

Arguments

from

The set of parameters to change from.

to

The set of parameters to change to.

Theta

"from" parameter vector consisting of 5 numerical elements.

noNames

Logical. When TRUE, suppresses the parameter names in the output.

Author

David Scott , Jennifer Tso, Richard Trendall

Details

In the 4 parameterizations, the following must be positive:

1. \(\alpha, \delta\)

2. \(\zeta, \delta\)

3. \(\xi, \delta\)

4. \(\bar\alpha, \delta\)

Furthermore, note that in the first parameterization \(\alpha\) must be greater than the absolute value of \(\beta\); in the third parameterization, \(\xi\) must be less than one, and the absolute value of \(\chi\) must be less than \(\xi\); and in the fourth parameterization, \(\bar\alpha\) must be greater than the absolute value of \(\bar\beta\).

References

Barndorff-Nielsen, O. and Blæsild, P. (1983). Hyperbolic distributions. In Encyclopedia of Statistical Sciences, eds., Johnson, N. L., Kotz, S. and Read, C. B., Vol. 3, pp. 700--707. New York: Wiley.

Prause, K. (1999) The generalized hyperbolic models: Estimation, financial derivatives and risk measurement. PhD Thesis, Mathematics Faculty, University of Freiburg.

See Also

dghyp

Examples

Theta1 <- c(2,2,1,3,0)                   # Parameterization 1
Theta2 <- ghypChangePars(1, 2, Theta1)   # Convert to parameterization 2
Theta2                                   # Parameterization 2
ghypChangePars(2, 1, as.numeric(Theta2)) # Convert back to parameterization 1