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Weekly UpdatesINTRODUCTION
Good decision-making practices in complex and difficult situations are crucial to the success of a firm. In oil and gas investment projects, the difference between a good decision and a bad one can be the difference between success and failure. A good investment decision-making process is the one that is able to assess risk and uncertainty and manage them in a balanced manner. In order to improve performance through good investment decisions, there is a need to know where the oil and gas industry currently is in terms of its management of risk and uncertainty and what are the possible ways to move forward to achieve quality investment decisions.
Bos (2005) presented current oil and gas practice as a "modeling cube" with three axes: precision, integration, and uncertainty. This cube is characterized with high precision, medium integration, and low-to-medium uncertainty modeling. Current practice puts more emphasis on deterministic rather than stochastic models. In addition, the industry is more concerned with modeling "below-ground" uncertainties while seemingly ignoring the "above-ground" uncertainties. Limited views to below-ground uncertainties and ignoring above-ground uncertainties such as oil price, production, development schemes, environmental concerns, and fiscal regimes can have a huge impact on the overall value of the project. Brashear, Becker, and Gabriel (1999) indicated that some projects that were selected to have expected returns of 10-20% ended up yielding returns in the region of 5%. They attributed the poor outcomes to an inadequate appreciation of the above-ground uncertainties, such as oil price.
Simpson et al. (2000) conducted a survey of companies operating in the UK and concluded that most of the companies (82.5%) use Monte Carlo simulation for reserves calculations, recognizing uncertainties in input variables, but only 7.5% used simulation in economic evaluation. In general, companies use deterministic approximations for production, cost, and oil price. These studies clearly indicate the need to capture uncertainty in economics models and specifically in oil price.
The focus of this article is on the impact of stochastic oil price models on a project's NPV as well as the impact of uncertainty in the input parameters of these oil price models. This is accomplished by comparing and contrasting the impact of the following oil price models: geometric Brownian motion (GBM), mean reversion (MR), and mean reversion with jumps. Many studies have concluded that oil price has a significant impact on the NPV of oil and gas projects but do not investigate the magnitude of the output uncertainty using the three oil price models. Furthermore, to our knowledge, none of the previous studies have considered the uncertainty in the input parameters such as volatility, drift, and reversion speed.
STOCHASTIC OIL PRICE MODELS
This article focuses on three 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.
Geometric Brownian Motion (GBM)
The GBM stochastic oil price model has been used in many applications of real options valuation in the literature (Rutherford 2002; Dezen and Morooka 2001). 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:
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 a. Dixit and Pindyck (1994) indicated 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 estimation procedures have been discussed extensively in the literature and will not be considered in this article.
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 more evidence from Bessembinder et al. (1995) 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 such as Pindyck (1999) suggest a reversion speed of 5 years.
Mean Reversion with Jumps
Dias and Rocha (1998) observed the price of oil from the early 1970s to the late 1990s and found that the price tends to jump due to abnormal events, such as war. They proposed a 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. Dias and Rocha (1998) indicated that 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. Dias and Rocha (1998) considered the mean reversion model with jumps 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.
With the introduction of three stochastic oil price models, the aim of this article is to address the following questions: Do oil price models have the same impact on the output uncertainty of the project NPV? 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?
OFFSHORE OIL FIELD DEVELOPMENT
In order to answer the above questions, a hypothetical integrated offshore oil field with submodels of reserves, production, and economics is used (Al-Harthy et al., 2006). Although the model is a fully integrated stochastic model, all factors up to the oil price will be held constant in the experiments so as to see clearly the impact of the price models on the project NPV.
The reserves model calculates field output using the volumetric equation with an assumed recovery factor of 20%. This yields reserves of 42 MMSTB (Million Stock Tank Barrel). The field will start to produce in 3 years, reaching a peak of 15,000 barrels per day (4.92 million barrels per year) and then exponentially decline until it reaches the economic field rate of 1200 barrels per day (Figure 1). The production profile is used as an input into the economic model, which assumes capital expenditures in the first 3 years of $300 million and a fixed cost of $15 million per year and operating costs of $2 per barrel. The model assumes a 15% discount rate and the oil price depends on the price model.
[FIGURE 1 OMITTED]
EXPERIMENTS
The NPV of the offshore oil field is evaluated using the three stochastic oil price models discussed before, with input parameters as shown in Table 1. The following experiments are conducted:
* The first experiment will run the three oil price models with no uncertain parameters except the Wiener process.
* The second experiment will introduce uncertainty in the volatility by modeling it as a triangular distribution instead of a deterministic value.
* The third experiment replicates the second experiment with the addition of drift as an uncertain input parameter in the GBM model and reversion speed as an uncertain factor for MR and MR with jumps models.
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