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Tuesday, September 25, 2012

Cluster Events

The world of risk management is continually evolving but where is the next developmental phase for the practice of risk theory?

In my opinion, one area which offers great opportunity is the relatively undiscovered work around event predictability. Let's be real of course, there is no way to predict the future but it might be nice to understand the shape of that future.

In this blog, we review the use of the Extensible Markov Model for shaping event clusters.

Current Best Practice
Most institutions that have enabled a risk function aren't really that good at measuring the statistics around the probability of an event. However for those that do, the generalized method in play is to fit "loss counts" to a Poisson model.  I have discussed this in brief elsewhere in this blog [ LINK ].

A lot has also been written on the use of Poisson models for event frequency analysis and its use across the world of engineering is prolific to say the least.  You will find that the operation of traffic lights for controlling congestion and traffic density are often based around this curve. In operational risk we use it to describe the expectation of a loss event occurring and yet, it only gives us a generalized answer.

This is frustrating for many reasons but mostly due to the fact that operational risk analysts could do a better job of managing an event if they could see how it clusters.

Poisson processes alone and without extension will not show the pattern of clustering.

More can be found on Poisson here [ LINK ]

Moving to Markov
The next step of thinking is to look at a system that goes through transitions. That is the system actually evolves as part of a broader random process of events.

Markov theory allows this random process of transition to be described and it is "memoryless" which makes it a bit of a red herring for solving the issues around Poisson curve fitting.

Memoryless defined as: The next state depends only on the current state and not on the sequence of events that preceded it. This specific kind of "memorylessness" is called the Markov property.

More information can be found on Markov Theory at this location [ LINK ].

So if we are to understand the clustering in the random walk of a Markov Process, we are going to need to capture the memory of transitions overtime. We are also going to need to know when to let go of those memories or the anchoring of them so that the clustering process can truly transition through and into a regime shift in a natural manner.

Extensible Markov Models
One technique for extending the Markov Model is to divide the random stream of data received into unique pieces so that we can understand whether a centroid exists or not. Using a CLUSTREAM of micro clusters allows us to capture vectors that prove or disprove the existence of potential clusters in a final set of events through time.

All good but this model needs to add unique operations into its overall method to cope with the following requirements before it can work.

[1] Adding a data point to an existing cluster
[2] Creating a new cluster
[3] Deleting clusters
[4] Merging clusters
[5] Splitting clusters
[6] Fading the cluster structure
[7] Understanding the Nearest Neighbor for a cluster algorithm

And of course ... We finish up implementing the model which Michael Hahsler and Margaret Dunham have so well developed and written up in their paper [ LINK ].

Additionally, the study these two analysts have carried out has resulted in the development of an R-Project library which allows their models to be used straight up.
How Data Clusters | Hahsler & Dunham

Applications of the model
The potential applications for the use of Extensible Markov Models in finance and risk management are diverse to say the least. The ability to toy with the R-Project functions as developed in the rEMM package from Hahsler & Dunham also make the theory a lot more accessible and more usable when applied to real and practical applications.

Useful applications of Extensible Markov Theory could include some of the following:

[1] Showing the impacts from multi-cluster events which is a relatively unexplored phenomena of operational risk.

[2] Gaining a better insight into how transitional outcome occurs from the volatility of individual positions in a portfolio of securities.

I welcome the suggestion of other ideas ...

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