New Causation Paper

Julia set

The website phys.org reported last week on a paper that addresses a enigmatic issue around downward causation.   The enigma is where a higher organized state of an organism or organization can cause changes at the lower levels that make up the upper level.   However, the argument that the higher level is temporary since it exists due the behavior of the lower levels, which appears contradictory.  This problem relates to complexity models, where there is evident self-similarity as you zoom in on the details.

This is almost a which came first, the chicken or the egg?

When creating your ERM models,  you can use either a top-down or a bottom-up design.  The best models address both of directions of design.

Bottom-up design is where you assess all of the known risks and controls.  Then you design your ERM program by prioritizing that list and create your models.

Top-down is where you determine what is needed for strategic planning and decision making.  For instance, you look to solve problems and set up controls at the corporate level.  In this situation you look at controlling management and financial risks.  Also, top-down design places a high priority on the modeling and the efficient use of the company’s capital.  Top-down usually leads to greater understanding and controls, but it is difficult to create buy-in from the divisions and subsidiaries.

Bottom-up design requires risk assessments at the lower levels and are more costly.  The summary of these assessments usually lead to some surprises to upper management, but ERM buy-in is natural.

Take a look at the Downward Causation article for more details on course-graining and natural systems.  Enjoy!

Causal vs. Non-causal Models

Stork Bringing Baby Casual

In certain northern European countries, parents used to tell their children that storks bring babies.  For many years, I did not understand the actual link of how the old tale arose.  However, I found out that in these countries that after a baby was born, the child’s nursery was frequently placed at the top of the house.  Also, the parents would increase the heat within the house to keep the new born warm throughout the night.  What happened is that the storks would discover these warmer roofs and would exploit this extra heat and would build their nests over the same rooms at the top of the house.  So, the birth of the baby actually brought the storks and not the other way.

Stork on Nest Causal

This amusing analogy can relate to causal vs non-causal models and well as an example with the idea of model dependency.

When constructing ERM models, if you know that situation A impacts situation B which again impacts situation C, you want your ERM model to reflect this causality.   Usually a causal system is one that depends on current or past input only. If the the model depends on future values as well, you have an non-causal (or a-causal) model. Also see https://en.wikipedia.org/wiki/Causality  for a further discussion around this topic.

However, when modeling various risks, initially, you may not be able to determine how different risks are properly interrelated. In these situations, you might use non-causal modeling to set up various statistical models to estimate a specific risk.  Or you may set up a loose correlation model.  In this situation, you know storks and delivery of babies are related so you would have a strong positive correlation.

Non-causal models with correlations were more frequently used before the financial crisis of 2008, primarily, because no one actually knew how to model credit. So, credit derivatives were modeled for several years, by setting up a VaR model and using copulas for the aggregation of risk. However, we saw that the relationship of the high quality bonds issues that were built off of the sub-prime mortgages and additional collateral was actually highly correlated in the extreme scenarios.

Now it is more common to create causal models where you design your scenarios and models to interrelate, which is the best approach.  At least you would model the delivery of babies implying the arrival of storks.

However, in some companies, the non-causal models are still used, especially when that company wants to model a large diversity of risks. Also, if a company has several risks that are modeled separately with differing systems and scenarios, these risks may be segregated into silos. In these situations aggregation of capital may still require non-causal methods to handle the silos.

Dependency continued

I agree with Carlos that reading what Paul Embrechts has been saying about dependence modeling over the last 20 years is extremely useful and enlightening.   A link to one of his papers with Filip Lindskog and Alexander McNeil is Modelling Dependence with Copulas and Applications to Risk Management. A great read and an excellence reference to consider when trying to set up your dependency models.

Random Dice
Dice Thought Experiment

Thought Experiment

In the next few paragraphs I’m going to describe a thought experiment that may give some insight on how to think of the use of copulas in dependency models or dependency in general.

Imagine that you have a set of dice that has multiple sides. Each die represents a single risk. Also, that die has as many faces as the possible number of outcomes of the risk it represents. Now say that you have a portfolio of risks and your set of dice corresponds to that portfolio.

Environment

If you throw your dice individually, then there will be little to no interaction between the separate risks and you could say that the results of the dice are independent from one another. If you throw them all at once, maybe from a dice cup, there will be a small interaction between the dice that touch. However, if you throw the dice hard enough you might be able to assume that each dice doesn’t affect the faces that turn up on the other dice, but they would be affected more by the environment where they land. If you throw them on a infinitely flat table, they would all be affected similarly. However, if the surface is irregular then where the dice land would be affected by the local “geography” of the surface.

Copula Dice
Dependent Dice

Interaction

Now assume that you some way tie the dice to each other. Or perhaps you place the dice in a clear mesh bag. Now if you toss the bag and enumerate the separate dice faces, you now have a situation where the mesh bag effects the entire process. The results of the enumeration of the dice would then depend on the individual die, the relationship forced upon them by the mesh bag and also the environment of where the bag lands.

Bias

Realize too that the area of each die’s face doesn’t have to be the same for each face, so the die may be biased and may land on larger faces and this can affect the enumeration as well.

So now you can see where multiple ways that dependency can arise. It could arise from each separate die, the interaction between the separate dice, the constraints of the tossing of the dice and the environment that the dice land.

Materiality Dependency

If you are modeling risk dependency, you may want to model no dependency, all types of dependency combined, or separate types of dependency.  It is all relative to the materiality of the risks and their interaction.

Continue reading “Dependency continued”