Correlation and Copula

Correlation

People (at least myself) have loosely interpreted Correlation as the strength of predictability between two random variables. I.E. A correlation coeffecient of 0 indicates the value of Y is independent of the value of X. Turns out that's not really the case. In the following example:

X	Y
1	1
-1	1
0	0

The correlation coeffecient is 0, but the value of Y is perfectly predicatable when the value of X is known. Correlation is only an indication of the strength of a linear relationship betweem the two variables.

The same kind of simple yet common mistake as the misconception of volatility.

Copula

Dr. David Li's original paper on using Copulas to model default correlations.