price.shimko.option {RND}

Price Option based on Shimko's Method

Description

price.shimko.option prices a European option based on the extracted Shimko volatility function.

Usage

price.shimko.option(r, te, s0, k, y, a0, a1, a2)

Arguments

r

risk free rate

te

time to expiration

s0

current asset value

k

strike

y

dividend yield

a0

constant term in the quadratic polyynomial

a1

coefficient term of k in the quadratic polynomial

a2

coefficient term of k squared in the quadratic polynomial

Details

This function may produce negative option values when nonsensical values are used for a0, a1, and a2.

Value

call

call price

put

put price

Author(s)

Kam Hamidieh

References

D. Shimko (1993) Bounds of probability. Risk, 6, 33-47

E. Jondeau and S. Poon and M. Rockinger (2007): Financial Modeling Under Non-Gaussian Distributions Springer-Verlag, London

Examples

r       =  0.05
y       =  0.02
te      =  60/365
s0      =  1000
k       =  950
sigma   =  0.25
a0      =  0.30
a1      =  -0.00387
a2      =  0.00000445

#
#  Note how Shimko price is the same when a0 = sigma, a1=a2=0 but substantially 
#  more when a0, a1, a2 are changed so the implied volatilies are very high!
#

price.bsm.option(r = r, te = te, s0 = s0, k = k, sigma = sigma, y = y)$call
price.shimko.option(r = r, te = te, s0 = s0, k = k, y = y, 
                    a0 = sigma, a1 = 0, a2 = 0)$call
price.shimko.option(r = r, te = te, s0 = s0, k = k, y = y, 
                    a0 = a0, a1 = a1, a2 = a2)$call