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The Author shows that modelling the uncertain cash flow dynamics of an investment project deserves careful attention in real options valuation. Focusing on the case of commodity price uncertainty, a broad empirical study reveals that, contrary to common assumptions, prices are often non-stationary and exhibit non-normally distributed returns. Subsequently, more realistic stochastic volatility, jump diffusion, and Lévy processes are evaluated in the context of a stylised investment project. The valuation results suggest that stochastic process choice can have substantial implications for valuation results and optimal investment rules.



1. Introduction

The success or failure of businesses is determined by the ability of management to systematically seize value creating investment opportunities. To this end, an accurate investment valuation is of paramount importance as it resembles the only broad and long-term oriented criterion for investment decision making (Brealey, Allen, & Myers, 2011; Koller, Wessels, & Goedhart, 2010).

Max Schöne

2. Data

The task of setting up an appropriate dataset for my purposes involves decisions on the commodities to include, whether to use short-term future contracts or spot price data, what time period to analyse, and what data frequency to use.

Max Schöne

3. Empirical analysis

As a first step to a better understanding of commodity price dynamics, it is useful to exploit the rich set of information contained in historical price series via a range of econometric and statistical tests. Although, one may be sceptical that a backward looking analysis can yield valuable insights for the decision of how to model seemingly random price movements in the future, more than half a century of empirical studies have revealed that the statistical properties of such price variations are indeed common across numerous asset classes in different markets and time periods (Cont, 2001; Mantegna & Stanley, 2000).

Max Schöne

4. Modelling commodity prices

On the basis of the previous statistical findings, it is the objective of this section to propose models for the stochastic simulation of commodity prices that are theoretically consistent with empirical data. In this regard, recap that mean reversion cannot generally be proven in past prices over the last two decades. Even if a much longer time horizon would allow us to reject a unit root in prices, we concluded that the statistical properties of mean reversion seem to neither fit reality over the recent past (as shown by the backtest in fig. 3) nor the future outlook of uncertain and persistently volatile commodity markets.

Max Schöne

5. Capital budgeting implications

Having identified considerable differences in the ability of stochastic processes to replicate the properties of historical price series, we do not yet know to what extent process choice also influences the valuation of capital investments. While Lo and Wang (1995) show that the choice between GBM and a mean-reverting Ornstein-Uhlenbeck process can affect financial call option values in the order of 5%, Tsekrekos et al. (2012) identify much larger variations in a more complex real option investment ranging between -40 % and 25%. However, their analysis is entirely based on comparisons between the classical mean-reverting commodity price processes of Schwartz (1997) so that an analysis of valuation implications based on the different perspective advocated in this paper is yet unavailable in academic literature.

Max Schöne

6. Conclusion

This thesis aimed at providing practically relevant recommendations for the choice of stochastic commodity price models in capital investment valuation. The analysis of empirical price dynamics across a basket of 14 commodities led to the conclusion that popular mean-reverting processes and GBM are in several respects inconsistent with empirical data. In turn, the merits of alternative models known from financial options pricing were analysed in the application to commodity markets. In this context, a practical and flexible calibration scheme was proposed that allowed me to assess the relative goodness of fit of each process to a range of commodities. It was found that all new models deliver a considerably better fit to historical commodity price data than GBM.

Max Schöne


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