Change Parameterizations of the Generalized Hyperbolic Distribution
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, alpha bar, beta bar, 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.
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 |
In the 5 parameterizations, the following must be positive:
1. alpha, delta
2. zeta, delta
3. xi, delta
4. alpha bar, 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, 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 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.
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
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