price.gb.option: Generalized Beta Option Pricing

In RND: Risk Neutral Density Extraction Package

Description

price.gb.option computes the price of options.

Usage

price.gb.option(r, te, s0, k, y, a, b, v, w)

Arguments

r	risk free interest rate
te	time to expiration
s0	current asset value
k	strike
y	dividend yield
a	power parameter > 0
b	scale paramter > 0
v	first beta paramter > 0
w	second beta parameter > 0

Details

This function is used to compute European option prices when the underlying has a generalized beta (GB) distribution. Let B be a beta random variable with parameters v and w. Then Z = b *(B/(1-B))^(1/a) is a generalized beta random variable with parameters with (a,b,v,w).

Value

prob.1	Probability that a GB random variable with parameters (a,b,v+1/a,w-1/a) will be above the strike
prob.2	Probability that a GB random variable with parameters (a,b,v,w) will be above the strike
call	call price
put	put price

Author(s)

Kam Hamidieh

References

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

Examples

#
# A basic GB option pricing....
#

r  = 0.03
te = 50/365
s0 = 1000.086
k  = seq(from = 800, to = 1200, by = 10)
y  = 0.01
a  = 10
b  = 1000
v  = 2.85
w  = 2.85

price.gb.option(r = r, te = te, s0 = s0, k = k, y = y, a = a, b = b, v = v, w = w)

RND documentation built on May 1, 2019, 10:52 p.m.