GeneralizedHyperbolic (version 0.8-7)

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. $\mu ,\delta ,\overline{\alpha },\overline{\beta },\lambda$

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. $\overline{\alpha },\delta$

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, $\overline{\alpha }$ must be greater than the absolute value of $\overline{\beta }$.

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