Tail Dependance - coefficients

The examiners could ask you to derive them - but haven't to date.
Past exam history indicates that the examiners are more interested in testing your ability to apply knowledge to a practical problem, rather than show academic prowess by manipulating formulae.
You can find questions in Part 3 of the Q&A bank. Assignment X3 also covers this topic area.

 

Further to David's point, the IFoA's advice to candidates (see Study Guide p15) states:

It should be noted that the focus of the examination will be on testing candidates’ understanding of the material and their ability to apply the techniques described in the Core Reading in practical situations and scenarios.

Formulae for any required probability distributions (including means and variances, generator functions and expressions of copulas), if not already given in the Formulae & Tables book, will be provided in the question.

Other formulae that form part of a definition are examinable and should be known. The remainder of formulae contained in the required reading are examinable but will be provided in the question if they are needed.


This suggests deriving such formulae is unlikely to be tested, but showing an understanding of what tail dependence is, how it can be determined mathematically (ie the definition is probably examinable as mentioned above), and the relationship to other formulae (such as the parameters of copulas) etc may be.

 

The Sept 2014 exam is a good example of the application of the IFoA advice. The examiners expected students to know the definitions of Pearson and Kendall and then apply these (no derivation or proof required).

Hopefully, there are sufficient worked examples of correlation measures in Sweeting, the Course Notes (Ch 11) and even in ActEd Tutorials.

It is a good idea if retaking to focus on areas where you think you may have done less well. If sitting ST9 for the first time you may be better off focussing on the big picture (understanding and applying key concepts) rather than on the detailed mathematics.

Best of luck...