I am using an implied volatility surface model to price equity and index options. I am trying to incorporate similar parameters that would have similar effect as skew and kurtosis on the volatility curve. I am not reverse engineering anything from market prices because i am going to be trading in an illiquid market. How would i quantify or model these parameters. Are there any functions out there of volatility or Vega , that will help me to capture and quantify similar moments like skew or kurtosis on the vol curve. Basically, when i put my params similar to skew or kurt at zero it should give equal sensitives to equidistant upside and downside options from at the money. Any help will be much appreciated.Best RegardsSteve

I understand you want to start with the moments of the risk neutral distribution and then map that into a vol surface?You could do the edgeworth method of rubinstein, if you have a feel for what the higher moments should be. Otherwise, you may could use SABR by first calibrating it to liquid market options that are similar to what you want to trade. Then you fiddle with the parameters rho or volvol to get the "right" shape of the vol smile. I find this more intuitive than directly specifying the kurtosis of the RND.

The solution to your problem or a good way to look at it is in the following paperPeter Lee, Limin Wang and Abdelkerim Karim, “Index volatility surface via momentmatchingtechniques”, Risk, December 2003.

In the previous paper, you don't realy need the index volatility construction. So just the two firs pages of this document are important to you and they will even give you a close form solution to the call option depending to the skewness and kurtosis.The technique is exactly the edgeworth method

Hey there JW,Do you have an alectronic copy of the paper which I could have please?Baz