as i understand it, moments in a PDF are as follows...1. mean2. variance3. skewness4. kurtosis but what are the fifth, sixth (and other higher order) moments? i promise i'll buy dynamic hedging at the end of the month...

I have never heard generally accepted names for higher moments.Once you get beyond kurtosis, moments are not generally useful. This is for the same reason that high-order polynomials are usually not good for curve fitting. If you want to approximate some complex distribution, you will have better luck most of the time by piecewise use of simple functions than a global polynomial of degree more than four.Skewness and Kurtosis measure easily-described characteristics of nearly normal distributions (asymmetry and tail weight respectively). The fifth moment measures, I guess, the asymmetry of tail weight. That's seldom useful. It might make more sense to see if you have a mixture, or data errors, or need a transformation.

Higher order moments!?They are refer to more complex options and irrelevant for plain vannila (regular options). If you find a true interest in American trigger options and compound ones, fifth and six order moments "may" be useful. Anyway, sometimes it difficult to follows Nasim's own thinking, so be prepare to bend forward with a magnifying glas and try find what was Nasim's deep thinking of seven, eight and nine order moments. David

From the mathematical point of view, one can define moments of each order n bigger then 1, by just taking the expectation of X^n. The n-th moment is defined by:E(X^n)The second order moment is thus not the variance, but the expectation of X^2!The variance is just a kind of centered second order moment, Var(X)=E[(X-E(X))^2],which gives the expected deviation of the random variable X from the expected mean. The same is true for the moment of order 3 and 4. Just apply the definition and you will that they are not the same as Skweness and Kurtosis.It can also be, that moments of higher order don't exist, meaning that they are infinity, or -infinity. A standard example is the Cauchy distibution, for which already the first order moment (the expectation) doesn't exist!You are right when you say that higher order are usually not of relevance for describing time series, but sometime you need conditions on the higher order to obtain some good convergence property!Best Regards,Enrico

In statistics, moments are typically centered and scaled so that a standard normal distribution has zero for all odd moments and one for all even moments.

Thank you for your comment. You are right. I used the mathematical definition to explain the general idea of the moments and to answer the question about the existence of higher order moments. Usually a general normal distribution is scaled and centered to obtain a standard normal distribution. n any case the kurtosis of a standard normal distribution is equal to 3 and thus one has to pay attention with the right definitions.Best Regards,Enrico