Study Group Report 2009: oil price cycle and sensitivity model
This is the final report on the problem of oil price cycle and sensitivity model, brought to ESGI68 by EPRasheed. Click on the link at the bottom to download the full report as a pdf document.

Report coordinator
Lorcán Mac Manus (Knowledge Transfer Network for Industrial Mathematics)

Executive summary
EPRasheed wishes to be able to model and predict oil prices out to a time-horizon of 2050, taking into account a number of known factors. These include the finite supply of oil, growing and shifting demand, the viability of alternative energy sources (at different pricing levels) and the interactions of oil producers and oil consumers, as they respond to current pricing levels. The study group concluded that while ‘prediction’ of price in any meaningful sense was not viable, a model for scenario analysis could be realised. The model did not incorporate all of the factors of interest, but did model important time lags in the response of market players’ future behaviour to current oil prices. Consideration of the optimisation of supply through new capacity in the telecoms industry led to a generalisation of the standard Cournot-Nash equilibrium. This indicates how an output-constrained competitive market might operate. It enables identification of different pricing regimes determined by the level of competition and the resource limitations of particular supplier firms. Two models were developed sufficiently to enable simulation of various conditions and events. The first modelled oil price as a mean reverting Brownian motion process. Strategies and scenarios were included in the model and realistic simulations were produced. The second approach used stability analysis of an appropriate time-delayed differential equation. This enabled the identification of unstable conditions and the realisation of price oscillations which depended on the demand scenarios.

Introduction
At the present time, oil consumption is accounted for by a range of application areas. Transportation in general is 50% of total, split between aviation (18%), cars (61%), trucks (21%). Other sectors include: Power Generation, 20%; Petrochemicals 10%; Heating 10%; Surfacing 5% and Lubricants 5%. In the future, it is expected that transportation will account for 75% of total, so becoming the primary source of oil consumption. The world’s current refining capacity is primarily geared towards refining light crude oil. This is a problem because most new crude coming on the market has a higher molecular weight and is therefore heavier and more viscous. Fractional distillation is the basic process of refinement. If there is more heavy oil, what that means is that there is less light oil (for transportation). Heavy oil must be further refined, resulting in extra cost and additional infrastructure requirements. Furthermore, crude oil from different countries has different molecular weight and different impurities, such as varying levels of sulphur. Sour crude is that which has more than 5% sulphur and oil with less than that percentage of sulphur is referred to as sweet crude. Most of the world’s refining capacity is geared towards sweet crude. This is a problem because more and more sour crude is coming on to the market and this is difficult to refine, as there is not the refining capacity. A new installation for refining crude has a lifespan of about 20-25 years. Oil production that can be accounted for is 82M barrels per annum. However, the known consumption is 85M. The shortfall of 3M is accounted for by considering a variety of mechanisms, such as refinery gain (typically a factor of 1.02); undeclared production; there is a stock tank holding an unknown inventory.

The nature of the problem
The problem is to develop a new model that attempts to model oil and gas prices over the next 30 or 40 years. Data are provided for the finding and lifting costs in different locations. Also provided are the historic and adjusted oil prices, back to 1861. The oil price cycle is sensitive to geopolitical, nonlinear factors as well as delayed time scales. The model should be able to capture these factors in some way. The model should consider this oil and gas price cycle sensitivity across different application areas, for example: transportation (road and air); power generation; heating; petrochemicals; surfacings (road, roof, cement) and lubricants. The model should also account for the discontinuities that occur when renewables/alternatives start becoming viable.

Brownian motion with mean reversion
Many commodity prices are modelled using a geometric Brownian motion model with mean price reversion. The mean price is assumed to be the marginal cost of production of the commodity; or in the case of a cartel product such as oil, it is a pricing level at which the cartel are happy to sell the product, in the long term. In our system we assume a fixed, long-term mean and a daily mean. The system is driven by three separate phenomena: Brownian motion; shock events; and strategies employed by market players (consumers and suppliers).

Shock events are simulated as step changes to the system. The influence of players in the market is characterised by assuming that both suppliers and consumers act today based on their perception of how oil price is varying over time. This perception is arrived at by observing the mean price over a short time period (e.g. the previous 6 months)

Two shock event scenarios were simulated. In Event 1, a single, large shock event occurred starting at the start of Year 5 and ended 6 months later. In event 2, a series of shocks occurred. Figure 1 shows how oil price behaves in the shock received in Event 1 and Figure 2 shows how the oil price behaves when it receives the shock series of Event 2.

Figure 1: The blue curve shows the reaction of simulated oil price to a single large shock event. The red curve shows the underlying mean value to which the Brownian process is trying to revert. Note the oscillations caused by the actions of the market players to perceived changes in oil price.

Figure 2: The blue curve shows the reaction of simulated oil price to a series of smaller shock events. The red curve shows the underlying mean value to which the Brownian process is trying to revert. Again, note the oscillations caused by the actions of the market players to perceived changes in oil price.

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