his paper outlines a few of the new methods in the Risk modelling space, it doesn't provide exhaustive description of Risk modelling techniques but rather tries to summarise some examples and put into layman's terms.

A Different View

A lot has been written about the changing Risk landscape due to regulations such as BASEL I, II, III (and now IV), Dodd-Frank, IFRS9, CCAR and FRTB. These have meant the introduction of hundreds of new models into the risk management functions across the industry.

Analytical models are used extensively in Risk Management across credit, liquidity, market, and operational risk and are typically created using a variety of statistical mathematical techniques. These range from balanced scorecard to complex scenario based Monte Carlo simulations.

Individual simulations can create many billions of results and are used to gauge the probability of the relevant risk that's being measured. These include: Forecasting likely losses, client probability of default, risk not being able to sell a financial product into a market when needed (liquidity risk)

Many financial institutions have seen challenges in creating models that can a) keep pace with the regulation and, more importantly b) can accurately capture the type of risk in a robust, explainable and repeatable way. Many models have failed to capture the Risk which has led to banks and other firms carrying massive exposure and, as has been said many times, was a major factor in the financial crisis.

In addition, many risk models calculate risk factors that feed into capital requirements that are a key factor in a financial company's profitability. Firms are constantly looking for more accurate ways of measuring risk in order to reduce their capital requirements to improve their balance sheet and return on equity.

Some Examples Are:

Credit Risk IRB-Rating

Credit Rating production is being revolutionised by the use of Machine Learning techniques such as Random forests. This method can create predictive models with high stability, accuracy and easy exploration, which makes them very good to explain to regulators.

The typical Random forest method divides up the problem into smaller units by selecting different sub sets of the input data and building a decision tree for each. The input data is then labelled with the objective of the exercise e.g. categorising the risk of default. Once complete, a Random forest algorithm (a collection of learning techniques, whereby a group of weak models is combined to form a powerful model) is applied to produce the required result i.e. a credit rating.

To create the credit rating, each tree assigns a classification i.e. it "votes" for that particular rating. The forest picks the classification with the highest amount of votes (over all the other trees in the forest).

This method is very attractive as it reduces the chance of errors and can be explained, as the decision tree and forest structures are preserved and easily followed by an external party (e.g. internal audit or a regulator).

Agent Based Modelling

Many Financial institutions are looking at Agent Based Modelling for forecasting key risk events. An example Risk area that falls into this category is: Stress testing, whereby a portfolio performance is "shocked" during a period of financial crisis.

This type of Risk simulation is typically performed by creating a number of scenarios based on theoretical market conditions (in the investment banking world this would involve creating market data such as credit/yield curves with values for each tenor point based on what they would be in a theoretical market).

These scenarios are then used with Monte-Carlo based simulation to create many (could be 1000s or more) simulated paths of expected values for each trade in a portfolio. Each path may have many of values, using continuous time stochastic methods to simulate Brownian motion for the paths. These results are then collated into probability distributions whereby the most likely result is used to assess the relevant risks.

This "top-down" approach. (I.e. trying use an overarching algorithmic approach to predict the outcome) has a number of challenges

• a)     Very computationally expensive i.e. in order to create an accurate result one needs to create enough paths with enough of the financial products to produce a statistically significant distribution. For large portfolios this could billions of calculation' of values of a trades (valuing derivatives, especially exotics can be computationally expensive)
• b)    The accuracy of measure of Risk is dependent on the probability distribution of the results accurately capturing the behaviour of the portfolio i.e. if simulation doesn't mirror what happens in real life, the simulation fails to be useful.

Agent based modelling (as described in Turrell - 2016) takes a different approach by modelling each participant (e.g. a financial company, person, legal entity) as an agent, which is a virtual copy of that agent with a set of rules that mimic the behaviours in the market.

If we wanted to model a how a company we have financial exposure to would behave given a particular set of conditions, we would create a set of rules that each describes how each agent would behave. Each agent would then be given a set of data that simulates a hypothetical market and their behaviour would be observed to see how they a) react and b) interact.

The interaction is very important as this can capture 2nd and 3rd order behaviours such as contagion risk (i.e. shock in a particular economy or region spreads out and affects others) and emergent patterns and trends that couldn't be easily picked up with traditional methods.

This is a "bottom-up" approach. I.e. we are using the behaviour of the lowest level entity (in our case individual companies or people) rather than one overarching stochastic algorithm to create the result of the simulation.

Some companies have also combined Machine Learning methods (e.g. as described in Rand, W. (2006)) to make the allow agents to continuously update their internal model. This means models can improve their own accuracy without continuous major re-engineering of the model over time.

Note:Worth noting there are a number of other Machine Learning and Artificial Intelligence approaches being applied to Risk other than the ones mentioned here

Compute at Scale

These methods can significantly improve the way Risk is modelled, but as, I have said earlier has only been a practical due to the fact large scale compute farms, virtualisation of IT servers have are being commoditised coupled with increasing use of Big Data software technology like Hadoop and Spark.

Agent Based Models are intrinsically massively parallel computational systems and require large scale infrastructure to model the behaviours of millions of agents (in a complex system). Monte-Carlo based simulations typically use large grid base technologies to perform billions of calculations in parallel. Both these approaches typically need large amounts of IT compute infrastructure (i.e. powerful servers) in order to complete their simulations in any reasonable time.

With the widespread usage of Big Data systems like Hadoop and the increasing adoption of elastic compute cloud based services mean both these types of approaches to simulations are not only possible but easily affordable for many types of use-cases.

Cloud compute services are available that use "Elastic compute" (systems that can automatically adapt to an increasing workload) to spin up extra virtual machines to process the many calculations required and then shutdown afterwards. This has a massive saving on hardware that otherwise would have had to be purchased outright and maintained at great expense.

In addition, optimised processing data structures (e.g. graphs) can be incorporated into the simulation software that enables execution of the only parts that are needed of the whole simulation based on only what has changed. This can not only create further speed enhancements (and thereby saving on compute cost) but can also provide processing lineage (i.e. show what was processed, including each step, what data was used, and all the dependencies) which will give confidence to the regulators and drive further adoption across the industry

In summary

The whole space of Risk Analytics and modelling is undergoing a fundamental revolution that will enable Financial institutions to not only model their current Risk in a much more accurate way, but start to model their business in much finer granularity and increasing breath have not been possible before.