price.gb.option {RND}

Generalized Beta Option Pricing

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)