The volatility is a key parameter that is difficult to estimate, but has a major influence in economic evaluation. Under the traditional investment view, volatility increases project risk, and the discount rate via a higher risk premium. In investment decision under the real option theory, volatility may aggregate value to the project, since the downside potential is limited whereas the upside is theoretically unbounded. In addition, volatility is an important indicator in oil project risk management, especially when oil prices present high levels of fluctuation. Volatility is hard to estimate. Oil price volatility can be estimated using historical data, but the procedure for estimating project volatility is more complex. This paper presents a framework to estimate the volatility of oil production projects employing a numerical technique based on project cash flows and the simulation of the evolution of oil prices using the Monte Carlo technique. Three stochastic processes to track oil price dynamics were used: Geometric Brownian Motion, Mean Reversion, and a pure Independent Lognormal Model. Since price is uncertain, NPV will also be an uncertain variable, so that its standard deviation is used as estimation of the true project volatility. This approach is applied to a portfolio composed of 12 deep-waters oil projects located in offshore Brazilian basins. These projects have different characteristics in terms of oil quality, water-depths, CAPEX, OPEX, infrastructure, etc. In order to reveal differences in results of project volatility, several correlations were evaluated regarding CAPEX, oil price and volatility of oil price. Preliminary results indicate that the project volatility is equal or higher than that of oil prices, especially in the case of high CAPEX and low price. In the simulations used in this study, project volatility ranged from 1 to 3 times oil price volatility. In case of oil volume of less than 300 MM bbl, the project volatility is around 1.8 times that of crude oil spot price. Therefore, this paper shows that the traditional assumption of using the oil price volatility, as a proxy for the project volatility may not give realistic results since most projects may not present a linear relationship between long-run average price and OPEX.

Key-words: uncertainty, real options, volatility, capital budgeting.


Future volatility of the underlying asset is one of the most important inputs in the real options model of valuation and decision, but this parameter cannot be easily observed in the market. One of the main difficulties is the availability of the historical time series of project market values, especially when valuing the option to invest, since in this case the potential project does not yet exist. Davis[1] pointed out that if the potential project is identical to others owned and operated by listed companies, it may be possible to estimate the rate of volatility of the project's value from a historical series of company values. If there are options on these listed companies, an implied volatility could also be estimated[2].

In another attempt Pickles and Smith[3] model de value of developed oil reserves by using reported reserves transactions values, finding a reserve's value volatility value of 0.23 very close to volatility of crude oil prices of 0.22. However, the authors pointed out this methodology cannot be a general rule for all oil projects.For example, Dixit and Pindyck[4] recommend an annual volatility between 15% and 25%. Some authors (e.g. Baker et al.[5]) used an annual volatility value higher than 30%.

These constraints force the real options practitioners to adopt informed guesses about the project's volatility from market information. Several authors[6] recognized that miss-estimation of the project's volatility may have important impacts on the estimated option value.

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