GeneralizedHyperbolic (version 0.8-6)

ghypChangePars: 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)

Value

A numerical vector of length 5 representing param in the

to parameterization.

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.

Author

David Scott , Jennifer Tso, Richard Trendall

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 \(\bar\beta\).

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