ghypChangePars {GeneralizedHyperbolic}

Change Parameterizations of the Generalized Hyperbolic Distribution

Description

This function interchanges between the following 5 parameterizations of the generalized hyperbolic distribution:

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

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

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

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

5. \mu, \delta, \pi, \zeta, \lambda

The first four are the parameterizations given in Prause (1999). The final parameterization has proven useful in fitting.

Usage

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

Arguments

from

The set of parameters to change from.

to

The set of parameters to change to.

param

"from" parameter vector consisting of 5 numerical elements.

noNames

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

Details

In the 5 parameterizations, the following must be positive:

1. \alpha, \delta

2. \zeta, \delta

3. \xi, \delta

4. \bar\alpha, \delta

5. \zeta, \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.

Value

A numerical vector of length 5 representing param in the to parameterization.

Author(s)

David Scott [e-mail], Jennifer Tso, Richard Trendall

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

param1 <- c(0, 3, 2, 1, 2)               # Parameterization 1
param2 <- ghypChangePars(1, 2, param1)   # Convert to parameterization 2
param2                                   # Parameterization 2
ghypChangePars(2, 1, param2)             # Back to parameterization 1