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Quantified Risk Modelling: Monte Carlo

Faculty of Engineering and Industrial Science

Higher Education Division

Unit of Study Assessment

RSK80007 Quantified Risk Modelling


Part A

Your task is to develop quantified Risk models of three Risks of interest to you. This is an academic exercise and its purpose is to make you familiar with the process of quantified Risk modelling and to show me you understand the theory and the practice.

Don’t spend inordinate amounts of time trying to justify any of the values that have to be estimated/ judged in order to complete the task (eg. does a death cost $3M or is it $3.2M? Is the Exposure 20 times a year or 10? It really makes no difference for these purposes).

  1. Write up each Risk as a case study that explains what has happened or what could happen in the chosen situation.
  2. Estimate/judge the values that could realistically be given to the various parameters relevant to modelling Risk and explain your reasoning to me. If you know the situation and its potential but are also aware that nothing untoward has ever happened use Quiglie and Revie’s theory (see text) to estimate the probability implied by this lack of data. I am not interested in you picking numbers out of the air and inserting them into a spreadsheet just for the sake of it - anyone can multiply or divide or add and this has no academic value in this Unit.

  1. Use the spreadsheet you developed in Assignment 2 to estimate the Risk line and subject this to any appropriate reality check. In other words, justify your result or even make a clear statement of the inadequacies of it and the need for further investigation. Estimate the Risk value.
  2. Propose a possible control measure change/improvement and estimate the associated implications for productivity, recurrent costs and/or capital requirements. I am well aware these may based on judgement unless you have a close knowledge of a particular case.
  3. Provide me with an explanation of the anticipated effect of this proposed control measure on each of the parameters that determine Risk and use this to justify a reduction in the estimated Risk value before this improved control measure is applied.
  4. Use this to estimate the effect of the improved control measure on one or both (as appropriate) of recurrent costs and payback period.

Qualities I value in assessing your work are:

• Understanding of the theory

  • Logic, clarity, completeness
  • Units or meaning correct and made clear
  • Explanation and justification/critique of values used.

There is no target word count here. A short explanatory text associated with the written case study wold be helpful for you and for me.

Just set up a sensible spreadsheet that respects the theory and provide whatever succinct statements of logic, judgement etc. are needed, possibly as a cell note.

Bear in mind I primarily want to see evidence of your understanding of the process.

(This is very useful stuff, so I hope you find the development of your spreadsheet and understanding of how it all works stimulating, not a chore).

[25 marks each case study, 75 marks total]

Part B

Investigate the Monte Carlo method of statistical analysis by visiting at least:

If you have a PC you’ll be able to download a free trial version of @Risk from Palisade. You’ll also find links to free Excel add-ins there. As you browse you may well find other options.

  1. In your own words (up to 500 words) describe the Monte Carlo method and the effect it would have on data input and the results from your Risk modelling spreadsheet.
  2. Explain in your own words (up to 500 words) the likely benefits and the possible detriments of using the Monte Carlo method in your Risk modelling spreadsheet.


Answer 1

The technique was first used by scientists working on the atom bomb; it was named for Monte Carlo, the Monaco resort town renowned for its casinos. Since its introduction in World War II, Monte Carlo simulation has been used to model a variety of physical and conceptual systems.

Monte Carlo method is a simulation method for predicting results. Further, the method utilizes mathematical algorithms and random sampling methods. The maximum usage of this method is to solve problems that are deterministic in nature and are related to optimization, numerical integration and probabilities

It can be seen that since the method uses random sampling method with simulation; the method can be used in any case where probabilities are involved. Hence, the method is used very frequently to ascertain risk or uncertainty. . 

A particular method used within Monte Carlo simulation may vary but overall, the Monte Carlo simulation involves similar steps, irrespective of a selected method. It involves:

  • Defining possible inputs and corresponding domain
  • Random generation of inputs through probability distribution
  • Performing computations on the inputs generated through random selection
  • Aggregation of results given by above computation

Hence, through Monte Carlo simulation, we can determine the probability or likelihood of a particular event or series of events. This is done through random generation of values for each event. By multiple simulations, such as 500 or 1000 or more cycles, we can arrive at common characteristics of the determined model. Hence, Monte Carlo simulations help to understand what events will occur and the likelihood of these events to occur.

Some of the benefits of Monte Carlo simulation can be described as follows:

  • As described above, the simulations help to determine events (or outcomes) as well as the probability of the outcomes.
  • The data is simulated multiple number of times and the output is in the assumed range. Hence, it is very easy to present the data graphically so as to make it clear to any reader about the possible outcomes and corresponding probability
  • Due to availability of large number of scenarios through simulation, it is very easy to perform sensitivity analysis to a particular factor or create scenarios such as, most likely, least likely, worst case etc.
  • Further, the various inputs used in a Monte Carlo simulation can be interlinked to indicate interdependence and corresponding change in an input given a change in another input.

Currently, many software and spread sheet based models are available to perform Monte Carlo simulations. Some of the most widely used include Risk by Palisade, RiskAMP which is compatible with Microsoft Excel, Oracle’s Crystal Ball, ModelRisk, QuantumXL, Risk Analyzer, DiscoverSim, Ersatz, etc.

Answer 2

As described above, the Monte Carlo simulation helps to determine what the likely outcomes are and how likely are they to occur. Hence, through the use of this simulation technique, a person can get multiple output scenarios along with probability. This helps in determining what is the most likely scenario, worst case scenario etc. Also, it helps to determine what are the highest risks associated with the event in terms of monetary loss or other types of losses.

Given all the benefits as described in previous part, the model is not free from cons. Like with any forecasting model, the Monte Carlo simulation model will also give results based on assumptions entered and defined input range. Hence, the forecasted results are only as good as the assumptions and inputs used for the model.

Hence, if the assumptions are fraught with error, the same will be reflected in the output as well. Further, the assumptions for a forecast are mostly based on historical results and output. Hence, the simulation is likely to replicate similar results. However, in real world, there is no guarantee that historical results will hold true for future also. 

Additionally, the user of the model may introduce bias in the model, either intentionally or unintentionally. This will skew the results. Hence, the user needs to use proper control mechanisms so that assumptions and input are of good quality and free from biases. 

Despite all the criticism, the model is highly used to ascertain risk and at least provides an indicator of the likely success or failure or degree of risk, even if the quantum of output may be skewed due to error in assumptions or input. At the end of the day, it is a mathematical stochastic model that works basis assumptions entered by a user and is prone to errors on account of these two. However, with proper care and use of proper methods, these can be avoided to a large extent to create a good quality forecasting model.


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