Using Monte Carlo Simulation in Your Financial Model

Once a model of a system has been constructed, you can simulate the system to predict how it will evolve through time. By definition, however, the performance of most financial systems is stochastic (i.e., inherently variable), since many inputs (e.g., unit values for investments, interest rates) are generally described stochastically. That is, we can't say exactly how an investment will perform in the future; we can only describe it's possible future behavior statistically (e.g., using a mean growth rate and a volatility).

In addition to this inherent variability, we might also be uncertain about some of the input parameters controlling the model. For example, if we had limited cost data regarding a particular component of a project we were simulating, the parameters describing the costs for that component would be uncertain, and we could enter these as probability distributions in order to capture this uncertainty.

Variability and uncertainty are represented in GoldSim using Monte Carlo simulation. Monte Carlo simulation consists of calculating a large number of “realizations” (potential futures). Each realization simulates the same system with the same initial conditions, but with different sampled stochastic values, both at the beginning of the simulation and as the system evolves through time. This results in a large number of separate and independent results, each of which is considered equally likely. These realizations can then be combined to provide statistical information on possible outcomes.

The number of realizations that are required in order to accurately capture the behavior of a system is a complex issue that can be influenced by the computational requirements of running a realization, and the frequency of the behaviors you wish to capture.

A rule of thumb for determining the number of realizations is that the number of realizations should be large enough that at least 10 simulations will have an occurrence of the most infrequent behavior you want to capture. For example, if you wanted to observe two consequences, one which occurred once in every 10 realizations, and another that occurred once in every 500 realizations, an adequate number of realizations for the simulation would be 5000.