ASMBI – Applied Stochastic Models in Business and Industry has just published a special issue on Probabilistic and Statistical Methods in Commodity Risk Management, edited by Fabio Antonelli, Roy Cerqueti, Alessandro Ramponi and Sergio Scarlatti.
Editorial
The vast landscape of the financial sector is characterized by the continuous introduction of innovative financial instruments, providing investors with diverse opportunities for an efficient capital allocation. In this dynamic context, commodities emerge as a cornerstone, encapsulating an ancient financial exchange mechanism that carries profound contemporary implications. The historical significance of commodities as tradable assets intertwines with their crucial role in modern financial markets. Investments in commodities and their associated derivatives stand out as fundamental subjects in both academic and applied financial literature. The framework surrounding these investments has witnessed continual evolution, shaping the ongoing development of sophisticated models and methods to understand and predict their behavior.
Within the expansive theme of commodities market modeling, two closely interlinked aspects accentuate its specific relevance within the broader scope of investment theory and practical applications.
First, from a quantitative perspective, the intricacies of commodity price dynamics present a motivating challenge. The complexities arise from the distinctive features inherent in these prices, encompassing elements such as seasonality, the occurrence of pronounced peaks, and the dynamic nature of volatility over time. Consequently, the development of effective stochastic models for accurate price forecasting demands a specific approach. These models must exhibit a dual quality, being not only sufficiently comprehensive to encapsulate the nuanced idiosyncrasies of commodity price behavior but also maintaining a level of mathematical tractability that facilitates practical application and interpretation. Striking this delicate balance is imperative to ensure that the models not only accurately capture the multifaceted nature of commodity markets but also remain practical tools for decision-makers navigating the intricacies of financial decision-making. Therefore, building effective stochastic models for price prediction becomes a truly conceptual effort that requires models to be simultaneously suitable and mathematically tractable. Some of the papers within this Special Issue employ sophisticated stochastic models to describe the dynamics of the phenomena of interest.
In addition to traditional statistical approaches, the profound influence of machine learning methods on the financial landscape is unmistakable. Notably—as we will see in detail below—methodologies such as Reinforcement Learning are prominently featured in some of the presented papers, underscoring the transformative role these advanced techniques play in the realm of finance.
Second, from a more business perspective, commodities offer a rational alternative to conventional financial securities. This is particularly noteworthy in the aftermath of the recent financial crisis, where the vulnerabilities of traditional securities have been thoroughly examined. Commodities, by contrast, have gained prominence in the global financial industry, not only for their potential to enhance inflation-adjusted returns but also for the diversification benefits they can provide in comparison to more traditional fixed-income and equity investments. This underscores the multifaceted significance of commodities within the broader context of investment strategy and risk management.
The contributions in the special issue can be clustered into some relevant categories in a no unique way, according to different criteria. We here advance a detailed discussion of them in the light of a meaningful classification.
Bień-Barkowska and Cerqueti et al. describe the dynamics of the peaks of the commodities. The former paper offers an econometric approach to the extreme negative returns, while the latter one presents a stochastic model for the peaks based on a generalization of the spatial Poisson process.
Specifically, the former paper investigates extreme negative returns in gold and silver markets. The authors propose a discrete-duration version of the autoregressive conditional duration peaks-over-threshold (ACD-POT) model specifically designed for capturing market risk in precious metal markets. Unlike existing dynamic versions of peaks-over-threshold (POT) models, this model treats the time interval (duration) between extreme negative returns as a discrete variable, aligning with the unique dynamics of extreme events in precious metal markets. The discrete hazard function in the proposed model represents the daily probability of extreme loss events and can be utilized to generate 1-day-ahead forecasts for both value at risk and expected shortfall in gold and silver investments. The study employs formal backtesting methods, demonstrating that the discretized version of the POT model exhibits superior in-sample fit and forecasting performance compared to continuous-duration POT models.
In a different context, Cerqueti et al. introduce a probabilistic model designed to assess the peak components of commodity returns. The study is grounded in the observation that spikes in returns are a result of external shocks. The proposed approach employs a specific class of point processes known as Spatial Mixed Poisson Processes, leveraging an invariance property within this class. The theoretical framework is utilized to outline an estimation procedure for returns based on the existing information. To support the theoretical approach, the paper provides an empirical example using returns from various commodities and abnormal returns from the volatility index as external shocks.
Interestingly, Clemente et al. and Cretarola et al. provide a network-based perspective of the dynamics of the commodities and of the energy system.
In detail, Clemente et al. assess the resilience of energy systems by considering factors such as energy consumption, international resource transfers, the shift to renewable energies, and environmental sustainability. While existing literature has primarily concentrated on direct energy consumption, this study recognizes the significance of indirect energy consumption associated with the production of goods and services. The work involves analyzing various types of embodied energy sources and their temporal evolution within sectors and countries. To conduct this analysis, the study constructs a directed and weighted temporal multilayer network based on renewable and non-renewable sources. Sectors are represented as nodes, and layers correspond to countries. The research introduces a methodological approach using the Multi-Dimensional HITS algorithm to assess network reliability and resilience, identifying critical sectors and economies. Additionally, a novel topological indicator based on the maximum flow problem is proposed to evaluate central arcs in the network at each time-period. The research employs this approach to offer a comprehensive understanding of the roles played by economies, sectors, and connections over time in the network. The goal is to identify elements whose removal could significantly impact the stability of the system. The numerical analysis, based on embodied energy flows among countries and sectors from 1990 to 2016, demonstrates the effectiveness of the methods in capturing distinct patterns between renewable and non-renewable energy sources.
Cretarola et al. explore sentiment analysis as a valuable technique for analyzing economic and financial scenarios in the context of social networks, specialized forums, and online news. To capture the dynamics of commodities, the authors modify the mean-reverting 4/2 stochastic volatility model introduced in a prior study. In this new specification, jumps are permitted in the asset price dynamics, and the drift coefficient may switch between regimes associated with a sentiment indicator. The paper discusses the distributional characteristics of asset returns, presents a numerical procedure for model estimation, and offers preliminary results on the pricing of European-style derivatives within this framework. The model is then applied to market data for Gold and Crude Oil.
We notice that the attention paid by Cretarola et al. to volatility models lets this paper be close to Gianfreda and Scandolo and Bonnini et al., where the authors deal with risk and price volatility.
Indeed, Gianfreda and Scandolo assess the impact of model risk on risk measurement procedures, especially in complex markets with a variety of implemented models. The approach involves a normalized measure of model risk for daily Value-at-Risk forecasts, incorporating model selection and averaging procedures. By narrowing down plausible models on a daily basis, the method mitigates the sensitivity to the initial choice of competing models, leading to a more reliable assessment of model risk. The analysis employs AR-GARCH-type models with various distributions for innovations, examining the dynamics of model risk over 15 years for different financial assets and commodities, such as stocks, equity indices, exchange rates, electricity, crude oil, and natural gas.
Under a different perspective, Bonnini et al. focus on commodity price volatility’s negative impact on countries heavily dependent on commodities and its role in hindering economic growth. It highlights the relevance of commodities in environmental sustainability processes, particularly in the context of transitioning toward the Circular Economy to address supply disruptions. The study explores the relationship between firm size and the adoption of Circular Economy practices, proposing a nonparametric method for testing this effect. The methodology involves a multidimensional concept representing the propensity of companies to undertake Circular Economy activities, and the study’s findings are supported by a Monte Carlo simulation. Case studies involving Italian small and medium enterprises in strategic sectors are also discussed.
The ethical aspects realized by the circular economy in Bonnini et al. are close to the viewpoint offered by D’Amato et al.
In detail, D’Amato et al. investigate the impact of Corporate Social Responsibility (CSR), specifically measured by the Environmental, Social, and Governance (ESG) score, on firms’ profitability. While existing literature has established the positive influence of CSR on various aspects of firm performance, there is limited evidence regarding its relationship with profitability, often assessed by earnings before interest and taxes (EBIT). The study analyzes approximately 400 companies in the EuroStoxx-600 index from 2011 to 2020, utilizing machine learning models to investigate this relationship. A key novelty of this study is the use of machine learning interpretability tools, including partial dependence plots and individual conditional expectation, to assess the influence of the ESG score on profitability. These tools facilitate the measurement of the functional relationship between the predicted response and features, providing insights into the contribution of the ESG score to the prediction. The findings indicate that the model exhibits high accuracy in predicting EBIT, and the ESG score emerges as a promising predictor compared to traditional accounting variables.
Guarino et al. and Giorgi et al. share the same target of focusing on trading strategies.
In particular, Guarino et al. examine the trading strategies of five advanced agents based on reinforcement learning across six commodity futures: Brent oil, corn, gold, coal, natural gas, and sugar. The analysis spans periods before and after the 2022 Russia–Ukraine conflict, with agents evaluated using various financial indicators. The most successful strategy from the top-performing traders is used to train a newly introduced neuro-fuzzy agent, capable of adjusting its strategy through “herd behavior” by learning from competitors. Results indicate the excellence of reinforcement learning agents and demonstrate that the neuro-fuzzy agent can enhance its strategy by incorporating information on competitors’ movements. Additionally, experiments with transaction costs reveal that—despite the presence of these costs implies fewer transactions—yet the intelligent agents, particularly the neuro-fuzzy agent, still exhibit outstanding performance.
Giorgi et al. present a Reinforcement Learning (RL) algorithm designed to formulate a trading strategy within a realistic framework that incorporates transaction costs and factors influencing asset dynamics. The authors compare the outcome of the proposed algorithm to the analytical optimal solution, for scenarios with linear factors and quadratic transaction costs. The results demonstrate that RL effectively replicates the optimal strategy. Furthermore, in a more realistic context involving non-linear dynamics, reflective of WTI spot prices time series, where an optimal strategy is unknown, RL emerges as a practical alternative. Utilizing synthetic data generated from WTI spot prices, the paper reveals that the RL agent surpasses a trader employing linearization to implement the theoretically optimal strategy.
Giorgi et al. is in line with Daluiso et al., where the authors present a stochastic model for derivatives in the context of energy.
More specifically, Daluiso et al. deal with swing options in commodity and energy markets, particularly focusing on the natural gas market. Swing options offer buyers the ability to hedge against price fluctuations in futures and choose their preferred delivery strategy within daily or periodic constraints, potentially determined by quoted futures contracts. The study introduces a dynamic model for commodity futures prices, specifically in the natural gas market. The model is designed to calibrate to liquid market quotes and imply a volatility smile for futures contracts with varying delivery periods. The numerical problem is tackled using a least-square Monte Carlo simulation, and alternative approaches involving reinforcement learning algorithms are explored.