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

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)
``` |

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