dgb: Generalized Beta Density
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

dgb is the probability density function of generalized beta distribution.

1	dgb(x, a, b, v, w)

`x`	value at which the denisty is to be evaluated
`a`	power parameter > 0
`b`	scale paramter > 0
`v`	first beta paramter > 0
`w`	second beta parameter > 0

Let B be a beta random variable with parameters v and w, then Z = b(B/(1-B))^{1/a} is a generalized beta with parameters (a,b,v,w).

density value at x

Kam Hamidieh

R.M. Bookstaber and J.B. McDonald (1987) A general distribution for describing security price returns. Journal of Business, 60, 401-424

X. Liu and M.B. Shackleton and S.J. Taylor and X. Xu (2007) Closed-form transformations from risk-neutral to real-world distributions Journal of Business, 60, 401-424

E. Jondeau and S. Poon and M. Rockinger (2007): Financial Modeling Under Non-Gaussian Distributions Springer-Verlag, London

#
# Just simple plot of the density
#

x = seq(from = 500, to = 1500, length.out = 10000)
a = 10
b = 1000
v = 3
w = 3
dx = dgb(x = x, a = a, b = b, v = v, w = w)
plot(dx ~ x, type="l")