extract.shimko.density: Extract Risk Neutral Density based on Shimko's Method
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

shimko.extraction extracts the implied risk neutral density based on modeling the volatility as a quadratic function of the strikes.

1	extract.shimko.density(market.calls, call.strikes, r, y, te, s0, lower, upper)

`market.calls`	market calls (most expensive to cheapest)
`call.strikes`	strikes for the calls (smallest to largest)
`r`	risk free rate
`y`	dividend yield
`te`	time to expiration
`s0`	current asset value
`lower`	lower bound for the search of implied volatility
`upper`	upper bound for the search of implied volatility

The correct values for range of search must be specified.

`implied.curve.obj`	variable that holds a0, a1, and a2 which are the constant terms of the quadratic polynomial
`shimko.density`	density evaluated at the strikes
`implied.volatilities`	implied volatilities at each `call.strike`

Kam Hamidieh

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

#
#  Test the function shimko.extraction.  If BSM holds then a1 = a2 = 0. 
#

r       =  0.05
y       =  0.02
te      =  60/365
s0      =  1000
k       =  seq(from = 800, to = 1200, by = 5)
sigma   =  0.25

bsm.calls = price.bsm.option(r = r, te = te, s0 = s0, k = k, 
                             sigma = sigma, y = y)$call
extract.shimko.density(market.calls = bsm.calls, call.strikes = k, r = r, y = y, te = te, 
                  s0 = s0, lower = -10, upper = 10)

#
# Note: a0 is about equal to sigma, and a1 and a2 are close to zero.
#