extract.ew.density: Extract Edgeworth Based Density
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

ew.extraction extracts the parameters for the density approximated by the Edgeworth expansion method.

1
2
3

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

`initial.values`	initial values for the optimization
`r`	risk free rate
`y`	dividend yield
`te`	time to expiration
`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
`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

If initial.values are not specified then the function will attempt to pick them automatically. cl in form of a list can be used to pass parameters to the optim function.

`sigma`	volatility of the underlying lognormal
`skew`	normalized skewness
`kurt`	normalized kurtosis
`converge.result`	Did the result converge?
`hessian`	Hessian matrix

Kam Hamidieh

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

R. Jarrow and A. Rudd (1982) Approximate valuation for arbitrary stochastic processes. Journal of Finanical Economics, 10, 347-369

C.J. Corrado and T. Su (1996) S&P 500 index option tests of Jarrow and Rudd's approximate option valuation formula. Journal of Futures Markets, 6, 611-629

#
#  ln.skew & ln.kurt are the normalized skewness and kurtosis of a true lognormal.
#

r       = 0.05
y       = 0.03
s0      = 1000
sigma   = 0.25
te      = 100/365
strikes = seq(from=600, to = 1400, by = 1)
v       = sqrt(exp(sigma^2 * te) - 1)
ln.skew = 3 * v + v^3
ln.kurt = 16 * v^2 + 15 * v^4 + 6 * v^6 + v^8

#
# Now "perturb" the lognormal
#

new.skew = ln.skew * 1.50
new.kurt = ln.kurt * 1.50

#
# new.skew & new.kurt should not be extracted.
# Note that weights are automatically set to 1.
#

market.calls      =  price.ew.option(r = r, te = te, s0 = s0, k=strikes, sigma=sigma, 
                     y=y, skew = new.skew, kurt = new.kurt)$call
ew.extracted.obj  =  extract.ew.density(r = r, y = y, te = te, s0 = s0, 
                     market.calls = market.calls, call.strikes = strikes, 
                     lambda = 1, hessian.flag = FALSE)
ew.extracted.obj