MONTE CARLO SIMULATION - Multi-Variable Stress Testing in Practice

I had the pleasure of listening in to one of the speakers at one of our Risk Management Forums, who enlightened the audience with a specific take on stress testing (Van Der Steen, J., Risk Advisor). The presentation was a rather specific take, on a specific western European country, on a specific credit portfolio. In his discussion on Multi-variable stress-tests, he discussed a number of situation analysis techniques that was in use by his team. One of them, which certainly grabbed my attention, was the Monte Carlo Stimulation (MCS) technique. Perhaps, for risk management experts in the field of finance, the technique might sound a fairly basic method but the fact that Monte Carlo method is a so-called ‘all rounder’, is what directed me towards enlightening myself and perhaps the readers of this blog.

In computational physics, the Monte Carlo method is grouped amongst a broad class of computational algorithms, which depend on repeated random sampling to obtain numerical results. The specialty of the method is that, it is most useful when other similar algorithms are impossible to use, in cases of physical and mathematical problems. With the simple reality of MCS assisting the decision-making process with a range of cases, it is sure to assist risk analysts with probabilities for a number of cases within the scenario analysed. In other words, the probability for any action to take place within the tested scenario can be computed with the help of MCS for even an indistinguishable stress scenario under consideration.

The modern MCS version was introduced by a group of scientists working at the Los Alamos National Laboratory, on the atom bomb. Incidentally, MCS’s name derived from Monte Carlo, the resort town famous for its casinos in Monaco. Since its invention during the 2^nd World War, MCS has been a well-used model in various industries and fields.    

MCS’s distinction is the use of 'probability distributions function' (PDF) that causes the effect of a range of results for all associated risks that could occur within the selected scenario. Palisade, the company behind a number of MCS applications, states that “MCS’s probability distributions are a much more realistic way of describing uncertainty in variables of a risk analysis” (Palisade, linked) 

Probability distribution

During the computation, MCS uses an iteration (a set of samples), with values sampled at random. This derives from the input probability distribution. The results of the outcome are recorded. This single process is being repeated through the simulation for over a thousand times. This gives us the probability distribution of all possible outcomes to the associated risks of the scenario. This is why MCS is an all-inclusive risk analysis technique because it clearly indicates not just all probabilities but also the likeliness of each probability occurring.

Dr. Tilo Nemuth in his publication (linked) clears out the use of MCS in risk management. If, Identification > Analysing > Evaluation > Monitoring was the systematic approach behind risk management, the MCS will fit within the 3^rd tier of the process. Once the scenario has been established, the first priority is to identify all risks associated to the scenario. MCS will kick-off thereon, evaluating all identified risks. Dr. Nemuth further explains that “for regular and practical cases the triangular distribution with the threshold values Minimum, Mean and maximum are useful. Other continuous distributions, for instance, rectangular distribution, beta distribution, normal distribution or uniform distribution, could be used in this context too” (Nemuth, T. 2008). He further explains MCS in practice in this brief article using a practical example, which is worth a read.

Many experts agree that MCS has an upper hand over single-point or deterministic analysis techniques. Not forgetting the outcomes of various probabilities and the graphical output of the MCS results, the other main 3 advantages are:

• The possibility of modeling interdependent connections between variables known as Correlation of Inputs
• The possibility of identifying the most impactful variable to the given analysis known as Sensitivity Analysis
• Last but not least, the most important advantage which guided me to writing this blog is Scenario Analysis. With the use of MCS analyzing a variety of combinations of values for a range of inputs has been an easy task. Analysts now have the ability to identify which input had which value together when the outcome resulted. 

An example of a graphical MCS result of various probabilities associated to a single scenario

Analysing multi-variable stress testing scenarios for a mortgage credit portfolio a risk analyst might consider the following drivers and use MCS as explained below.

Ø  Considering “loss of income” as the main risk driver:

•       Higher probability of unemployment

•       Increasing expenditure and decreasing income

Ø   Additional stress factors

•       Increasing interest rates

•       Decreasing real estate prices

Ø   Monte-Carlo simulation

•      Set of mortgage borrowers at random with a probability of loss of income (the main risk driver)

•      Multiple testing

Also worth watching is the following video (source: MomentsInTrading)

A number of easy to understand videos are available on PalisadeCorp's youtube channel

Latin Hypercube Sampling is an extended version of MCS, which according to Palisade, (linked) “samples more accurately from the entire range of distribution functions”. Perhaps, another attempt to dig deeper! And, another attempt to enlighten myself in the near future!!

By Ron David

Director - Conference Research, Production & Management

Global Leading Conferences