China - Economics
Prices of oil in 2009? Make your own forecast
Ashley Jenner argues that it is safe to predict an event and it is safe to predict a date, but very risky to forecast both an event and a date. In the same vein he uses the example of oil prices to tell how to foresee risks. From São Paulo.
The present economic woes are inflicting huge stress on the BRIC economies, particularly their stock markets. One of the main focuses of the turbulence is the unprecedented level of volatility in the price of oil. The main casualty is Russia whose narrowly based oil and gas economy was due to take a hit sooner or later but Brazil, China and India, as oil importers should have been benefited by the drop in the price of oil but any benefits are being offset by the rise in the dollar. This normally would benefit exporters but not this time because the main importers of their products have almost disappeared. In fact, oil has acted as a lead weight on almost all commodities including agribusiness and mining. For this reason oil price patterns need to be closely examined.
The performance of the price of crude oil over the past twelve months shown by the attached graph appears to defy all logic. In fact, it seems to show random behavior. If understanding the past is difficult forecasting the price for 2009 seems beyond the scope of human intelligence. Experts cannot even forecast next month let alone next year. For example, the U.S. energy statistics department says “The current U.S. and global economic downturn has led to a decrease in global energy demand and a rapid and substantial reduction in crude oil and other energy prices. As a result, projections for both energy demand and prices are considerably lower than last month’s Outlook”. The annual average Texan oil price is now projected to be $101.45 per barrel in 2008 and $63.50 in 2009. Citigroup lowered its forecast to $65 per barrel. Goldman Sachs Group cut its forecast for the average price of New York-traded crude oil in 2009 to $80 a barrel from $86, adding that it was closing all its trading recommendations for oil. “Over the past week, macroeconomic data confirmed the severity of recent economic weakness, reinforcing the concerns flagged by extremely weak physical commodities markets. A price average of $50 a barrel for most of 2009 is possible if economic and industrial activity in Asia fails to stabilize", the weekly report said.
Everyman´s guide to forecasting the price of oil using RANDOM STOCHASTIC OIL PRICE MODELS
Since the past price shows random behavior, it is reasonable to also forecast the future price using Random Models generally called Monte Carlo models, just like in its casinos. These methods of forecasting prices of traded assets are very commonplace nowadays. They are no longer restricted to Rocket Scientist eggheads with unlimited computing power which can calculate millions of scenarios of random numbers making it possible to form a normal statistical distribution which may mimic the random behavior of markets.
Since the past price shows random behavior, it is reasonable to forecast the future price using Random Models generally called Monte Carlo models.
There are three basic stochastic oil price models: geometric Brownian motion, mean reversion, and mean reversion with jumps. These oil price models are known as stochastic processes, which is a way to mathematically model how price evolves through time in a random fashion. This piece uses Mr Al-Harthy Mansoor Hamood´s work as well as that of Marco.Ind from PUC Rio.
Geometric Brownian Motion (GBM)
The GBM stochastic oil price model has been used in many applications of real options valuation. The famous Black and Scholes equation underlies the assumption of the GBM. The GBM is common in real options applications due to its simplicity and fewer parameters in modeling oil price. The GBM is a stochastic process that is mathematically described by the following equation 1):
1) dP = [alpha]P dt + [sigma]P dz (1) where:
dz = [epsilon] [square root of dt], [epsilon] = Wiener process, which is normally distributed with a mean of zero and a standard deviation of 1, N (0,1); P = the current oil price; dt = represents the change in time; dP = represents the change in price; [alpha] = the drift and [sigma] = volatility.
If [alpha] > 0, the drift or trend of oil price is positive and if [alpha] < 0, the trend is negative. Volatility represents the variance of the lognormal price distribution, which increases as time passes. This change in variance represents an increase in the uncertainty of oil price as time evolves. In order to model GBM, two parameters need to be estimated: drift [alpha] and volatility. Some indicate that volatility ranges between 15 and 25% per year, whereas others use a volatility of 30% per year. The drift has been estimated to be around 0-1% per year. The main problem with GBM is that is does not account for reversion to the average price over time (i.e. it has no memory of previous prices), which is a real problem in commodity price forecasting. This is resolved by the next method.
Mean Reversion (MR)
The MR stochastic oil price model is mathematically described as
dP = [eta]P([bar.P] - P)dt + [sigma] P dz (2)
where
[bar.P] = the long-term oil price equilibrium;
[eta] = the reversion speed which is the number of years for price to revert to the long-term equilibrium.
The remaining variables are defined as in Equation 1). If the current oil price is lower than the long-term equilibrium, then the price will be pulled up or revert to the long-term equilibrium, and if the current price is higher than the equilibrium price, then the current price will be pulled down to the long-term equilibrium level. The MR model is considered to be a better model than the GBM model because it argues that price will revert to the long-term equilibrium, which tends to make sense with market conditions. For example, if the long-run equilibrium is $40 per barrel and if price increased to $60 per barrel, then OPEC will increase production to sell more oil and price will go down or revert to the long-run equilibrium. On the other hand, if the price falls below $40 per barrel, then OPEC will restrict, and again the price will revert to the long-term equilibrium. There is much evidence that supports the view that oil price tends to follow a mean reversion process. The variance of oil price in the MR model increases and eventually stabilizes. This is different from the GBM model where the variance grows continuously. The MR model requires the estimation of the reversion speed, which ranges between 1 and 2 years. Others suggest a reversion speed of 5 years.
Mean Reversion with Jumps
The price of oil from the early 1970s to the late 1990s has tended to jump due to abnormal events, such as war (as is the case today and is clearly shown in the attached graph). This led to stochastic model known as mean reversion with jumps. This is an extension of the mean reversion model by adding a jump component. Mathematically this process is described as follows:
dP = [eta]P([bar.P] - P) dt + [sigma]P dz + Pdq (3)
where dq = the jump factor modelled using the Poisson process, which is discrete.
The additional parameters in the MR with jumps are the jump frequency, jump size, and direction. One way to model the jump size could be by assuming that prices will double as a jump up and halve as a jump down. Another way is by assuming a normal distribution for both the jump up and down using a mean and standard deviation. The mean reversion model with jumps is considered to be a better model than the MR and the GBM models because it considers the normal events modeled by MR as well as the abnormal events that cause jumps in oil price.
The questions these three stochastic oil price models must address are the following: Do oil price models have the same impact on the output uncertainty of new project value? If they are different, which one has a bigger impact and why? If uncertainty is introduced in the input parameters of the oil price models, which parameters are the most sensitive (have a bigger impact on the output)? What if one of the input parameters cannot be estimated accurately? Does that reduce the quality of the output of the oil price model?
Do oil price models have the same impact on the output uncertainty of new project value? If they are different, which one has a bigger impact and why?
Using the attached Excel Mean-Reversion with Jumps - Marlim Model forecasting Simulation (please see download link below)
The Marlin model is actually from a large Brazilian oil-field called Marlin. As can be seen, all the user has to do is input the assumptions correctly on the first page and many scenarios will be created on the graph of the second page. The most important assumption was that the long-term price of oil will be $90 with a present price of $50. Once the assumptions have been fed in, it is necessary to repeatedly press F9 on the keyboard in order to generate scenarios. If this is done a million times and all the results fitted onto a Gaussian distribution, the price of oil can be forecast by almost anyone. Apart from the long-term price input and the present price input, the volatility is crucial; at the 20% level, the price does not really get above $100 in 2009 but at 40% volatility the price begins to go into an epileptic fit. This is due to the Jumping effect of the reversion to mean process.
Conclusion
The world is very fortunate to have accessible Rocket scientists and Excel models which allow the rest of humanity to know what is coming around the corner. Forecasting has shown that it is safe to predict an event and it is safe to predict a date but very risky to forecast both an event and a date. Therefore it is left up to the reader to work out the 2009 price of crude oil for him or her self thereby providing him or her not with an answer but with the means to obtaining an answer.
Download here to make your own forecast
Please disable the macros on the Excel model in order to use it.
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