Explaining Copulas to CEO!(Actuaries or Quants?)

Edwin · Jul 7, 2014

Hi friends, here is a teaser;-

Let's see if Actuaries can beat Quants at Communication.

CEO - What's is a Copula?

Quant; -

Q1;

Just tell them that stuff moves around sometimes for idiosyncratic reasons, and sometimes because everything moves together. The copula describes the part that moves together. Then hand them some pages with complicated looking equations and expressions with lots of greek letter and ask them if they have any questions. These guys always want to pretend they're smarter than they are, so they will pretend to look over the equations very carefully.

Also, make sure you pronounce"copula" so it sounds as lascivious as possible.
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Q2; (Aaron Brown, GARP Risk Manager of the year 2011)

I think the key property of copulae that will interest intelligent senior management is that you estimate the chance of two or more unlikely events happening at once from their individual chances of occuring rather than from patterns of common events. The example I like to give is suppose we wrote someone an insurance policy that pays $1 million if they get a hole in one at the golf course and are hit by lightning just as the ball drops into the cup.

It's never happened before (I assume) so we can't use direct historical data. There's no really good, reliable way of pricing the policy.

Copulae look at the total numbers of holes in one and the total number of people hit by lightning on golf courses, then makes some simple, reasonable assumption about overlap. There's guesswork involved, but you're looking at the right data.

Standard analysis will look at the correlation between golf scores and rainfall. This is silly, you're not looking at the events of interest. Although the analysis will appear more precise, it cannot possibly be right because it doesn't have the right data.
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Actuary; - ???

Simon James · Jul 8, 2014

An actuary who hasn't taken CA3 is likely to say:

If the vector of random variables, X, has joint cumulative distribution function F with continuous marginal cumulative distributions $ {F_1}, \ldots ,{F_N} $ then the copula of the distribution F is the distribution function $ C({F_1}({x_1}), \ldots ,{F_N}({x_N})) $

The best non-technical description I had from a student defining a copula was: "It's like a glue that joins up different probabilities .. and some glues are stickier than others."

Edwin · Jul 15, 2014

I would try but eventually stop when I remember the CEO probably spent their school days wallowing; "I hate Maths!" and skipping classes.

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