extract.gb.density: Generalized Beta Extraction

In RND: Risk Neutral Density Extraction Package

Description

extract.gb.density extracts the generalized beta density from market options.

Usage

extract.gb.density(initial.values = c(NA, NA, NA, NA), r, te, y, s0, market.calls, 
  call.strikes, call.weights = 1, market.puts, put.strikes, put.weights = 1, 
  lambda = 1, hessian.flag = F, cl = list(maxit = 10000))

Arguments

initial.values	initial values for the optimization
r	risk free rate
te	time to expiration
y	dividend yield
s0	current asset value
market.calls	market calls (most expensive to cheapest)
call.strikes	strikes for the calls (smallest to largest)
call.weights	weights to be used for calls
market.puts	market calls (cheapest to most expensive)
put.strikes	strikes for the puts (smallest to largest)
put.weights	weights to be used for puts
lambda	Penalty parameter to enforce the martingale condition
hessian.flag	if F, no hessian is produced
cl	list of parameter values to be passed to the optimization function

Details

This function extracts the generalized beta density implied by the options.

Value

a	extracted power parameter
b	extracted scale paramter
v	extracted first beta paramter
w	extracted second beta parameter
converge.result	Did the result converge?
hessian	Hessian matrix

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

#
# create some GB based calls and puts
#

r  = 0.03
te = 50/365
k  = seq(from = 800, to = 1200, by = 10)
a  = 10
b  = 1000
v  = 2.85
w  = 2.85
y  = 0.01
s0 = exp((y-r)*te) * b * beta(v + 1/a, w - 1/a)/beta(v,w) 
s0

call.strikes = seq(from = 800, to = 1200, by = 10)
market.calls = price.gb.option(r = r, te = te, y = y, s0 = s0, 
                               k = call.strikes, a = a, b = s0, v = v, w = w)$call

put.strikes  = seq(from = 805, to = 1200, by = 10)
market.puts  = price.gb.option(r = r, te = te, y = y, s0 = s0, 
                               k = put.strikes, a = a, b = s0, v = v, w = w)$put


#
# Extraction...should match the a,b,v,w above. You will also get warning messages.
# Weigths are automatically set to 1.
#

extract.gb.density(r=r, te=te, y = y, s0=s0, market.calls = market.calls, 
              call.strikes = call.strikes, market.puts = market.puts, 
              put.strikes = put.strikes, lambda = 1, hessian.flag = FALSE)

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