Risk premia in commodity price forecasts and their impact on valuation

Abstract

Commodity price driven valuation models require a stochastic price input if the value of managerial flexibility, such as the option to defer investment until the optimal time and the option to abandon a project, is to be estimated. The risk-neutral version of the stochastic price model is typically used in academic work; however, risk-adjusted models of the expected spot price are often used in practice. These two approaches are connected by a risk premium which is unfortunately often difficult to estimate. In this work, we use natural gas futures prices in a Kalman filter approach with maximum likelihood estimation to parameterize the Schwartz and Smith (2000) stochastic price model, and then apply an asset pricing model to address the large uncertainty of the risk premia parameter estimates. To evaluate the impact of the risk premia and other parameters in the two-factor price model on project valuation, we apply the price model to a prototypical shale gas investment, both for a base reference case as well as for cases where there are real options to optimally time decisions to invest or to abandon the project. Using this approach, we are able to determine the implied risk-adjusted discount rate that would be used with the spot price forecast, given the two-factor model risk premia, and we also discuss the impact of the risk premia on project value relative to other model parameters.

Review of stochastic differential equations in statistical arbitrage pairs trading

“…For further research, the GBM model could be expanded for a regime-switching component as proposed by Tie et al (2017) or for a jump component as presented in Göncü and Akyildirim (2014). The two-factor model gains attention recently (see, e.g., Farkas et al 2017 andHahn et al 2018), providing additional flexibility by allowing for two stochastic factors, e.g., short-term variations and long-term behavior. The two factors can be estimated from two different data bases (see Schwartz and Smith 2000).…”

Looking for Accurate Forecasting of Copper TC/RC Benchmark Levels

“…way of modelling prices that are believed not to follow any specific rule or pattern and hence seen as random. Black and Scholes [23] first used GBM to model stock prices and since then others have used it to model asset prices as well as commodities, these being perhaps the most common of all, in which prices are expected to increase over time, as does their variance [11]. Hence, following our first premise, concerning whether TC/RC might vary randomly, there should not exist a main driving factor that would determine TC/RC future benchmark levels and therefore GBM could to a certain extent be a feasible model for them.…”

“…Then, their forecasting accuracy at different time horizons will be tested and compared. These techniques (Geometric Brownian Motion -GBM-; the Mean Reversion -MR-; Linear Exponential Smoothing -LES-), have been chosen primarily because they are common in modelling commodities prices and their future expected behaviour, as well as in stock indices' predictive works, among other practical applications [10][11][12][13]. The selection of these models is further justified by the similarities shared by TC/RC with indices, interest rates, or some economic variables that these models have already been applied to.…”

Green bonds and US shale gas prices: Evidence from a novel time-varying causality

“…Although some researchers have expressed ongoing concerns about the relationship between the SGPI and GBI, they have not reached the same conclusions. Some researchers claim that the SGPI has positive effects on the GBI [ 10 ], while there is a conflicting view [ 11 ]. Some argue that the SGPI does not have causality with the GBI [ 12 ].…”