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

## Description

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

## Usage

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

## Arguments

 `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

## Details

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

## Value

Objective function evalued at a specific set of values

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```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) ```

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