Nonlinear Feedback Loops using @RISK: Adding Uncertainty to a Dynamic Model of Oil Prices

Nonlinear feedback loops describe many of the processes that make up the real world, with resulting rising and falling patterns with overshoot (feast or famine).

The oil sector is best modeled using systems of differential equations due to positive and negative feedbacks and the slow responses of the supply side (exploration, production) to price signals and shocks. Long-term trends are accompanied by cyclic price fluctuations that also influence demand. Interacting feedback loops make the system complex.

We use a tool that is specific to developing complex nonlinear systems using visual maps to create the structure for the oil price forecasting model. However, this tool (STELLA from ISSE Systems) does not provide a robust method of incorporating variable uncertainty into the model’s dynamics. STELLA will always output the same expected values for the forecasts for a given set of initial conditions.

But many of the driving variables in a model of the oil market are uncertain. For example: what are the expected proven reserves over time and how rapidly will supply respond to price signals (which includes well productivity, discovery rate, price elasticity of supply, etc.); how rapidly will demand respond to price signals (efficiency of transportation, power generation, price elasticity of demand, etc.); how rapidly will demand grow (the developing world, etc.); and other areas of uncertainty for key equation parameters.

Based on real expectations regarding the key elements of the model, distributions are developed that encompass a set of possible outcomes. Correlations between these data are also estimated. Using @RISK, these correlated distributions are then dynamically linked from Excel cells into the STELLA model in which multiple runs forecast a range of potential paths. We can then see a map of the many potential future oil price paths with the map’s density signaling more or less probable outcomes.