ghypChangePars: Change Parameterizations of the Generalized Hyperbolic...
In sjp/GeneralizedHyperbolic: The generalized hyperbolic distribution

Description Usage Arguments Details Value Author(s) References See Also Examples

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

1. mu, delta, alpha, beta, lambda

2. mu, delta, zeta, rho, lambda

3. mu, delta, xi, chi, lambda

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

These are the parameterizations given in Prause (1999)

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

`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.

In the 4 parameterizations, the following must be positive:

1. alpha, delta

2. zeta, delta

3. xi, delta

4. alpha bar, 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, alpha bar must be greater than the absolute value of beta bar.

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

David Scott d.scott@auckland.ac.nz, Jennifer Tso, Richard Trendall

Barndorff-Nielsen, O. and Bl<c3><a6>sild, 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.

dghyp

param1 <- c(0, 3, 2, 1, 2)               # Parameterization 1
param2 <- ghypChangePars(1, 2, param1)   # Convert to parameterization 2
param2                                   # Parameterization 2
ghypChangePars(2, 1, as.numeric(param2)) # Convert back to parameterization 1