extract.ew.density {RND}

Extract Edgeworth Based Density

Description

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

Usage

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))

Arguments

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

Details

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.

Value

sigma

volatility of the underlying lognormal

skew

normalized skewness

kurt

normalized kurtosis

converge.result

Did the result converge?

hessian

Hessian matrix

Author(s)

Kam Hamidieh

References

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

Examples

#
#  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