[R-SIG-Finance] SPD and RND estimation

Brian G. Peterson brian at braverock.com
Sun Jul 15 15:44:36 CEST 2007

Sankalp Upadhyay wrote:
> Hi,
> I am trying to do an estimation of State Price Density (SPD) and Risk
> Neutral Density (RND) from a set of option prices - preferably in a
> non-parametric way.
> Is there some package in R that can help? fOptions does not seem to be have
> this.
> Alternatively, would you know a standard method or a very good research
> paper/article/reference on this topic? The utility being that a good
> paper/article can be changed to R code easily.

The function 'ksmooth' provides a nonparametric kernel regression 
smoothing algorithm which should be sufficient for the estimation of the 
density function. Kernel smoothing regression is the method utilized in 
the original Ait-Sahalia and Lo paper you reference.

The last paper referenced below uses several other distribution fitting 
mechanisms, and may be informative.

A quick citation survey indicates that the original paper is referenced 
several times, but no one seems to take up a direct implementation of 
the techniques described in the 1995 paper.

R contains a multitude of distribution fitting methods, so if the kernel 
smoothing method is not sufficient, I'd read the last paper referenced 
here first, and then look for R methods of doing those fittings.

As always, please consider sharing your resulting R code and functions 
with the community.


   - Brian

Ait-Sahalia, Yacine and Lo, Andrew W., "Nonparametric Estimation of 
State-Price Densities Implicit in Financial Asset Prices" (November 
1995). NBER Working Paper No. W5351.
Available at SSRN: http://ssrn.com/abstract=225414

Ait-Sahalia, Yacine and Lo, Andrew W., "Non-Parametric Risk Management 
and Implied Risk Aversion" (January 4, 1998). CRSP Working Paper No. 468.
Available at SSRN: http://ssrn.com/abstract=94133

Chang, P H Kevin and Melick, William R
"Workshop on estimating and interpreting probability density functions"
14 June 1999

Campa, Jose M. et. al.
"Implied Exchange Rate Distributions: Evidence from OTC Option Markets"
Working Paper, April 1997

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