Objective Assumptions for the Monte Carlo Simulation when Historical Data with a Desired Interval Have Limited Size

This chapter indicates that building a time-series model can be a simple solution for making objective assumptions for the Monte Carlo simulation when historical data size with a desired interval is too small (there are very limited observations available to hand) to convincingly fit a theoretical probability distribution. This problem arises especially in the cash-flow focused financial models usually involved in corporate decision processes. Those models use relatively long forecasting horizons with an annual interval for a cash-flow projection which requires probability distributions of risk factors depicting them in an annual manner. The paper focuses on three of many available approaches for reproducing a probability distribution of a risk factor over a longer time horizon. The traditional geometric Brownian motion with normally distributed changes of risk factors is compared with simulation-based approaches where changes are randomly sampled from either a best-fitting or an empirical probability distribution. The paper addresses currency exchange rates and commodity prices as the examples of market risk factors affecting the entrepreneurial activity of enterprises.