ew.objective: Edgeworth Exapnsion Objective Function
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

ew.objective is the objective function to be minimized in ew.extraction.

1 2	ew.objective(theta, r, y, te, s0, market.calls, call.strikes, call.weights = 1, lambda = 1)

`theta`	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

This function evaluates the weighted squared differences between the market option values and values predicted by Edgworth based expansion of the risk neutral density.

Objective function evalued at a specific set of values

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

r       = 0.05
y       = 0.03
s0      = 1000
sigma   = 0.25
te      = 100/365
k       = seq(from=800, to = 1200, by = 50)
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

#
# The objective function should be close to zero.  
# Also the weights are automatically set to 1.
#

market.calls.bsm = price.bsm.option(r = r, te = te, s0 = s0, k=k, 
                   sigma=sigma, y=y)$call
ew.objective(theta = c(sigma, ln.skew, ln.kurt), r = r, y = y, te = te, s0=s0, 
             market.calls = market.calls.bsm, call.strikes = k, lambda = 1)