price.ew.option: Price Options with Edgeworth Approximated Density

In RND: Risk Neutral Density Extraction Package

Description

price.ew.option computes the option prices based on Edgeworth approximated densities.

Usage

price.ew.option(r, te, s0, k, sigma, y, skew, kurt)

Arguments

r	risk free rate
te	time to expiration
s0	current asset value
k	strike
sigma	volatility
y	dividend rate
skew	normalized skewness
kurt	normalized kurtosis

Details

Note that this function may produce negative prices if skew and kurt are not well estimated from the data.

Value

call	Edgeworth based call
put	Edgeworth based put

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

#
# Here, the prices must match EXACTLY the BSM prices:
#

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

ew.option.prices  =  price.ew.option(r = r, te = te, s0 = s0, k=k, sigma=sigma, 
                                     y=y, skew = ln.skew, kurt = ln.kurt)
bsm.option.prices =  price.bsm.option(r = r, te = te, s0 = s0, k=k, sigma=sigma, y=y)

ew.option.prices
bsm.option.prices

###
### Now ew prices should be different as we increase the skewness and kurtosis:
###

new.skew = ln.skew * 1.10
new.kurt = ln.kurt * 1.10

new.ew.option.prices  =  price.ew.option(r = r, te = te, s0 = s0, k=k, sigma=sigma, 
                                         y=y, skew = new.skew, kurt = new.kurt)
new.ew.option.prices
bsm.option.prices

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