What is coskewness and how can it be calculated? I would like to calculate coskewness of two random variables. However I couldn't find even basic information on this matter. Is there a standard definition? How to calculate it? If not what are my alternative options? Is it possible to have a normalized coskewness like correlation coefficient? 
Thanks 
 A: In this paper coskewness is defined as
$$
coskew_{i,m} = \frac{COV(r_i,(r_m-\mu_m)^2) }{E[(r_m-\mu_m)^3]}.
$$
You can calculate it by using the standard moment estimators - that's what I would do.
Thus, given a sample for market returns $(r_m^j)_{j=1}^N$ and asset returns $(r_i^j)_{j=1}^N$ you calculate the quantities for each sample pair and do the calculation. 
A: Is there a standard definition?
Yes, these quantities were defined in 

Kraus, A., Litzenberger, R.H., 1976. Skewness preference and the valuation of risk assets.
  Journal of Finance 31, 1085-1100.

How to calculate it?
Check page 6 of the following document
http://asianfa2012.mcu.edu.tw/fullpaper/10312.pdf
what are my alternative options?
Depends on what information you need.
Is it possible to have a normalized coskewness like correlation coefficient?
Yes, in page 6 of the aforementioned document the autors say

More recent studies use standardised measures of co-skewness and co-kurtosis (Harvey and Siddique, 2000; Monero and Rodríguez, 2009), which are better behaved, with less extreme observations and smaller variance ...

A: This link might help you get a clearer idea: http://www.quantatrisk.com/2013/01/20/coskewness-and-cokurtosis/
It includes the mathematical definition along with a Matlab implementation.
