extract.shimko.density {RND}

Extract Risk Neutral Density based on Shimko's Method

Description

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

Usage

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

Arguments

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

Details

The correct values for range of search must be specified.

Value

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

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

#
#  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.
#