ew.objective {RND} | R Documentation |
Edgeworth Exapnsion Objective Function
Description
ew.objective
is the objective function to be minimized in ew.extraction
.
Usage
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
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
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)