RND (version 1.2)

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

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

Value

Details

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

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