Simulation Modeling

We are all familiar with scale models, which represent the salient features of the scheme being studied. Typical examples would be the day-to-day operations of a financial institution, an office or factory, or the performance of a share portfolio. Of necessity, the model will be a simplification. Typically the model is employed to predict the effect that changing inputs to the system can have on the outputs. While the model should mimic the real system, its complexity should not be a barrier to its interpretation. It is sensible to commence with a very simple basic model and to progressively increase its difficulty. At each stage, the model should be checked for its validity: are the outputs as expected? The simulation approach is adopted in contrast to a formal analytic approach that would give a purely theoretical solution. While the analytic approach may be more reliable and numerically more complex, it does lack flexibility, but with relative ease, additional factors may be “bolted on” to the model to be simulated.

Simulation is also referred to as the Monte Carlo simulation, stressing its obvious links to the gambling casinos in the Monégasque resort, and in particular the roulette wheel, a very accessible (hopefully) random number generator.

At the outset it must be appreciated that this approach has its foundations in probability and statistics. When building a model, you identify the key variables (both input and output) that are central to the problem being studied. Any variable that can be measured and that can take on different values, such as the value of an equity portfolio over a given number of years, is commonly referred to as a random variable. Having built what is essentially a mathematical model, the simulation stage may commence. This should clarify how the variables are interrelated. For example, the expected return on an equity portfolio in 12 months time is clearly not known with certainty, although we will know the historic returns that have been achieved. The simulation may be performed with specialist software or the facilities within popular brands of spreadsheets. Models can be developed for a variety of scenarios. A deterministic model has fixed values as both inputs and outputs (the outcome is predictable given specific initial conditions); while for a stochastic model, at least one of the input or output variables follows a probability distribution. A further level of complexity is introduced by considering the temporal relationship between the variables. Most simulation models encompass the stochastic and time-dependent properties of the system. The probability structure that is normally created is called the distribution function; it shows the frequency with which the random variable actually takes specific values within a certain range. It is this function, via its cumulative equivalent, that lies at the root of the simulation.

The simulation phase is the repeated operation of the constructed model. The model may be rapidly adjusted to address a series of scenarios, which would be prohibitively expensive in terms of time and/or resources in the real system being modeled. The results will indicate how the actual system is likely to perform. While in reality a system cannot be tested to destruction, extreme situations may be investigated via the model. In particular, results representative of long periods of time may be investigated.

...