When we developed all the concepts of quantitative finance and financial risk management, we were first assaulted by the question: What are Monte Carlo’s methods? Well, the time has come to develop this concept and how it can help us in our financial learning. Are you ready? Get ready to learn!
What are Monte Carlo’s methods?
The Monte Carlo method is a non-deterministic or numerical statistical method, used to approximate complex and costly mathematical expressions to evaluate accurately. The method was named after the Casino de Montecarlo (Monaco) for being “the capital of gambling”, as roulette is a simple generator of random numbers.
The use of the Monte Carlo methods as a research tool comes from the work done in the development of the atomic bomb during the Second World War in the National Laboratory of Los Alamos in the USA. UU This work involved the simulation of hydrodynamic probabilistic problems concerning neutron diffusion in the fission material. This diffusion has an eminently random behaviour. Currently, it is a fundamental part of the raytracing algorithms for the generation of 3D images.
The Monte Carlo method provides approximate solutions to a wide variety of mathematical problems making it possible to carry out experiments with pseudorandom number sampling in a computer. The method is applicable to any type of problem, whether stochastic or deterministic. Unlike numerical methods that are based on evaluations at N points in an M-dimensional space to produce an approximate solution.
Why is this method so important now?
The current importance of the Monte Carlo method is based on the existence of problems that are difficult to solve by exclusively analytical or numerical methods, but that depends on random factors or can be associated with an artificial probabilistic model (resolution of integrals of many variables, minimization of functions, etc.).
Thanks to advances in computer design, Monte Carlo calculations that would have been inconceivable in the past, nowadays they are presented as affordable for solving certain problems. In these methods, the error ~ 1 / √N, where N is the number of tests and, therefore, to gain a decimal number in the precision implies to increase N in 100 times.
The basis is the generation of random numbers that we will use to calculate probabilities. In short, get a good generator of these numbers, as well as an adequate statistical set on which to work, are the first difficulties we will find when using this method.
Computer science as an ally of the Monte Carlo method
Technology is undoubtedly one of the great foundations of modern life, without which the infinite majority of processes of daily life could not be carried out. For this same reason, this method finds a fundamental pillar in the use of certain software that allows to systematize and computerize the task of risk assessment.
Some of the most useful programs and used in different projects for years, with the aim of establishing the degree of feasibility of planning when managing projects, are the following:
- Risk. It is an application used in Microsoft Excel that allows incorporating the analysis of the risk of a specific project in the schedule of the same.
- Crystal Ball. As with the previous one, it is also based on Excel and allows Monte Carlo analysis to be applied to project management. It is able to elucidate concrete predictive models and apply the best solution. One of its major uses is that it allows considering the correlation that exists between different variables.
- Gold Sim. It is an analysis program that is very applicable to the business and engineering sector.
Why is the Monte Carlo method useful for projects?
The idea behind the application of the Monte Carlo method is that there are aspects, such as term or cost, that can not be determined exactly since they are variable points. It is a variability with a double slope. On the one hand, the estimates that are carried out are in themselves variables, since an action does not always last the same or always cost the same; and on the other hand, the risk itself, since they have a probability of occurring differently in different situations, as well as an impact that varies from one situation to another.
What makes this analysis possible is to give a project a conceptual value, not in a determined way, but by establishing a “mean value” and a certain variability. It allows to determine up to what point the determined valuations of a project are realistic and show confidence with respect to the objectives pursued with a certain action.
Monte Carlo allows the analysts in charge of carrying out risk prevention to indicate in what percentage of the random simulations that have been carried out aspects such as the term and the cost with less than the objectives that are pursued with the project itself.
In this way, if this percentage is lower than the degree of confidence that a certain company or group considers minimally acceptable, this would be a case in which planning is not feasible and should be modified.
What do you think about Monte Carlo’s methods? Do not you think they are really useful for the current scenario? If you want to learn more about them we recommend you start your studies with our Master in Financial Risk Management. Take a look at our training offer and contact us if you have any questions! We are here to help you decide your future!
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