Quantified Risk Modelling: Monte Carlo
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.
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.