# dshimko: Density Implied by Shimko Method In RND: Risk Neutral Density Extraction Package

## Description

`dshimko` is the probability density function implied by the Shimko method.

## Usage

 `1` ```dshimko(r, te, s0, k, y, a0, a1, a2) ```

## Arguments

 `r` risk free rate `te` time to expiration `s0` current asset value `k` strike at which volatility to be computed `y` dividend yield `a0` constant term in the quadratic polynomial `a1` coefficient term of k in the quadratic polynomial `a2` coefficient term of k squared in the quadratic polynomial

## Details

The implied volatility is modeled as: σ(k) = a_0 + a_1 k + a_2 k^2

## Value

density value at x

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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```# # a0, a1, a2 values come from Shimko's paper. # r = 0.05 y = 0.02 a0 = 0.892 a1 = -0.00387 a2 = 0.00000445 te = 60/365 s0 = 400 k = seq(from = 250, to = 500, by = 1) sigma = 0.15 # # Does it look like a proper density and intergate to one? # dx = dshimko(r = r, te = te, s0 = s0, k = k, y = y, a0 = a0, a1 = a1, a2 = a2) plot(dx ~ k, type="l") # # sum(dx) should be about 1 since dx is a density. # sum(dx) ```

RND documentation built on May 29, 2017, 2:19 p.m.