fit.implied.volatility.curve: Fit Implied Quadratic Volatility Curve
In RND: Risk Neutral Density Extraction Package

Description Usage Arguments Details Value Author(s) References Examples

fit.implied.volatility.curve estimates the coefficients of the quadratic equation for the implied volatilities.

1	fit.implied.volatility.curve(x, k)

`x`	a set of implied volatilities
`k`	range of strikes

This function estimates volatility σ as a quadratic function of strike k with the coefficents a_0, a_1, a_2: σ(k) = a_0 + a_1 k + a_2 k^2

`a0`	constant term in the quadratic ploynomial
`a1`	coefficient term of k in the quadratic ploynomial
`a2`	coefficient term of k squared in the quadratic polynomial
`summary.obj`	statistical summary of the fit

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

#
# Suppose we see the following implied volatilities and strikes:
#

implied.sigma = c(0.11, 0.08, 0.065, 0.06, 0.05)  
strikes       = c(340, 360, 380, 400, 410)
tmp           = fit.implied.volatility.curve(x = implied.sigma, k = strikes)
tmp

strike.range = 340:410
plot(implied.sigma ~ strikes)
lines(strike.range, tmp$a0 + tmp$a1 * strike.range + tmp$a2 * strike.range^2)