Search Results (279)

This study presents a self-contained derivation and solution of the Black and Scholes partial differential equation (PDE), replacing the standard Wiener process with a smoothed Wiener process, which is a differentiable stochastic process constructed via normal kernel smoothing. By presenting a self-contained, Itô-free derivation, this study bridges the gap between heuristic financial reasoning and rigorous mathematics, bringing forth fresh insights into one of the most influential models in quantitative finance. The smoothed Wiener process does not merely simplify the technical machinery but further reaffirms the robustness of the Black and Scholes framework under alternative mathematical formulations. This approach is particularly valuable for instructors, apprentices, and practitioners who may seek a deeper understanding of derivative pricing without relying on the full machinery of stochastic calculus. The derivation underscores the universality of the Black and Scholes PDE, irrespective of the specific stochastic process adopted, under the condition that the essential properties of stochasticity, volatility, and of no arbitrage may be preserved. Full article

This study investigates the optimal sizing of photovoltaic (PV) and battery storage (BAT) systems for Estonian households operating under grid constraints that prevent selling surplus energy. We develop and compare three sizing models of increasing complexity, ranging from a simple heuristic to a full simulation based optimization. Their performance is evaluated using a multi-criteria decision analysis (MCDA) framework that integrates Net Present Value (NPV), Internal Rate of Return (IRR), Profitability Index Ratio (PIR), and payback period. Sensitivity analyses are used to test the robustness of each configuration against electricity price shifts and market volatility. Our findings reveal that standalone PV-only systems are the most economically robust investment. They consistently outperform combined PV + BAT and BAT-only configurations in terms of investment efficiency and overall financial attractiveness. Key results demonstrate that the simplest heuristic-based model (Model 1) identifies configurations with a better balance of financial returns and capital efficiency than the more complex simulation-based approach (Model 3). While the optimization model achieves the highest absolute NPV, it requires significantly higher investment and results in lower overall efficiency. The economic case for batteries remains weak, with viability depending heavily on price volatility and arbitrage potential. These results provide practical guidance, suggesting that for grid constrained households, a well-sized PV-only system identified with a simple model offers the most effective path to cost savings and energy self-sufficiency. Full article

The increasing integration of intermittent renewable energy sources necessitates effective energy storage solutions, with battery energy storage systems (BESSs) emerging as promising candidates for energy arbitrage operations. This study conducted a comprehensive comparative analysis of 29 European electricity markets to identify optimal locations for utility-scale BESS-enabled energy arbitrage ventures. Using hourly wholesale electricity price data spanning January 2015 to December 2023, we employed statistical analysis techniques, 3D surface plots, and developed a novel energy arbitrage feasibility (EAF) score-based ranking system that integrates electricity market volatility metrics with regulatory and economic variables including gross domestic product per capita, index of economic freedom, and electricity supply-origin risk (ESOR). Five investor preference scenarios were analyzed: risk-averse, ESOR-sensitive, economy-sensitive, volatility-sensitive, and equally weighted approaches. Results demonstrated that Estonia ranked highest in three scenarios, achieving the maximum absolute EAF score of 0.558197 in the volatility-sensitive scenario, while Luxembourg led in the ESOR and economy-sensitive scenarios. Estonia’s market characteristics support single daily charge–discharge cycles, whereas Luxembourg enables dual cycles, offering different operational strategies. The EAF scoring methodology provides a standardized framework for cross-country investment decision-making in energy arbitrage ventures. These findings indicate that market selection significantly impacts the BESS arbitrage profitability, with Estonia and Luxembourg representing the most favorable investment destinations. Full article

The rapid development of digital technology is reshaping the global economic landscape. However, its impact on firms’ capacity utilization rate (CUR), particularly through technological innovation, remains unclear. This study investigates this issue by developing an endogenous growth model that connects digital technology to CUR. The empirical analysis is based on data from Chinese A-share manufacturing firms. The methods employed include quantile regression, instrumental variable techniques, and various tests to explore underlying mechanisms. CUR is calculated using a special model that looks at random variations, and digital transformation is assessed using text analysis powered by machine learning. The findings indicate that digital transformation significantly enhances CUR, especially for firms with average capacity utilization levels, but has a limited effect on low- and high-end firms. Moreover, technological innovation mediates this relationship; however, factors like “double arbitrage” (involving policy and capital markets) and “herd effects” tend to prioritize quantity over quality, which constrains innovation potential. Improvements in CUR lead to enhanced firm performance and productivity, generating industry spillovers and demonstrating the broader economic externalities of digitalization. This study uniquely applies endogenous growth theory to examine the role of digital transformation in optimizing CUR. It introduces the “quantity-quality” technology innovation paradox as a crucial mechanism and highlights industry spillovers to address overcapacity while offering insights for fostering sustainable economic and social development in emerging markets. Full article

In the context of urban decarbonization, multi-energy microgrids (MEMGs) are gaining increasing relevance due to their ability to enhance synergies across multiple energy vectors. This study presents a block-based MILP framework developed to optimize the operations of a real MEMG, with a particular focus on accurately modeling the structure of electricity and natural gas bills. The objective is to assess the added economic value of integrating a battery energy storage system (BESS) under the assumption it is employed to provide implicit flexibility—namely, bill management, energy arbitrage, and peak shaving. Results show that under assumed market conditions, tariff schemes, and BESS costs, none of the analyzed BESS configurations achieve a positive net present value. However, a 2 MW/4 MWh BESS yields a 3.8% reduction in annual operating costs compared to the base case without storage, driven by increased self-consumption (+2.8%), reduced thermal energy waste (–6.4%), and a substantial decrease in power-based electricity charges (–77.9%). The performed sensitivity analyses indicate that even with a significantly higher day-ahead market price spread, the BESS is not sufficiently incentivized to perform pure energy arbitrage and that the effectiveness of a time-of-use power-based tariff depends not only on the level of price differentiation but also on the BESS size. Overall, this study provides insights into the role of BESS in MEMGs and highlights the need for electricity bill designs that better reward the provision of implicit flexibility by storage systems. Full article

Hydrogen is increasingly recognized as a key element of the transition to a low-carbon energy system, leading to a growing interest in accurate and sustainable assessment of its economic viability. Levelized Cost of Hydrogen (LCOH) is one of the most widely used metrics for comparing hydrogen production technologies and informing investment decisions. However, traditional LCOH calculation methods apply a single discount rate to all cash flows without distinguishing between the risks associated with outflows and inflows. This approach may yield a systematic overestimation of costs, especially in capital-intensive projects. In this study, we adapt a binary cash flow discounting model, previously proposed in the finance literature, for hydrogen energy systems. The model employs two distinct discount rates, one for costs and one for revenues, with a rate structure based on the required return and the risk-free rate, thereby ensuring that arbitrage conditions are not present. Our approach allows the range of possible LCOH values to be determined, eliminating the methodological errors inherent in traditional formulas. A numerical analysis is performed to assess the impact of a change in the general rate of return on the final LCOH value. The method is tested on five typical hydrogen production technologies with fixed productivity and cost parameters. The results show that the traditional approach consistently overestimates costs, whereas the binary model provides a more balanced and risk-adjusted representation of costs, particularly for projects with high capital expenditures. These findings may be useful for investors, policymakers, and researchers developing tools to support and evaluate hydrogen energy projects. Full article

Recent European regulations promote distributed energy resources as alternatives to centralized generation. This study compares utility-scale and distributed photovoltaic (PV) systems coupled with Battery Energy-Storage Systems (BESSs) in the Italian electricity market, analyzing different battery sizes. A multistage stochastic mixed-integer linear programming model, using Monte Carlo PV production scenarios, optimizes day-ahead and intra-day market offers while incorporating PV forecast updates. In real time, battery flexibility reduces imbalances. Here we show that, to ensure dispatchability—defined as keeping annual imbalances below 5% of PV output—a 1 MW PV system requires 220 kWh of storage for utility-scale and 50 kWh for distributed systems, increasing the levelized cost of electricity by +13.1% and +1.94%, respectively. Net present value is negative for BESSs performing imbalance netting only. Therefore, a multiple service strategy, including imbalance netting and energy arbitrage, is introduced. Performing arbitrage while keeping dispatchability reaches an economic optimum with a 1.7 MWh BESS for utility-scale systems and 1.1 MWh BESS for distributed systems. These results show lower PV firming costs than previous studies, and highlight that under a multiple-service strategy, better economic outcomes are obtained with larger storage capacities. Full article

This paper examines arbitrage opportunities available in one of the largest wholesale electricity markets in the world, the Midcontinent Independent System Operator (MISO) electricity exchange. While prior research suggests that market efficiency on the exchange has increased over time, this study reveals that historical pricing information can still be used to generate positive returns. I find that a trading rule based on prior spot and forward prices generates statistically and economically significant risk-adjusted returns across the entire MISO footprint. These returns may in part be explained by the relatively small number of financial traders in the market and the ability of generation owners to exercise market power. Full article

Shared energy storage (SES) represents a transformative approach to advancing sustainable energy systems through improved resource utilization and renewable energy integration. In order to enhance the economic benefits of energy storage and prosumers, as well as to increase the consumption rate of renewable energy, this paper proposes a bilevel optimization model for multi-prosumer power complementarity based on SES. The upper level is the long-term energy storage capacity configuration optimization, aiming to minimize the investment and operational costs of energy storage. The lower level is the intra-day operation optimization for prosumers, which reduces electricity costs through peer-to-peer (P2P) transactions among prosumers and the coordinated dispatch of SES. Meanwhile, an improved Nash bargaining method is introduced to reasonably allocate the P2P transaction benefits among prosumers based on their contributions to the transaction process. The case study shows that the proposed model can reduce the SES configuration capacity by 46.3% and decrease the annual electricity costs of prosumers by 0.98% to 27.30% compared with traditional SES, and the renewable energy consumption rate has reached 100%. Through peak–valley electricity price arbitrage, the annual revenue of the SES operator increases by 71.1%, achieving a win–win situation for prosumers and SES. This article, by optimizing the storage configuration and trading mechanism to make energy storage more accessible to users, enhances the local consumption of renewable energy, reduces both users′ energy costs and the investment costs of energy storage, and thereby promotes a more sustainable, resilient, and equitable energy future. Full article

Battery energy storage systems (BESS) rely on accurate electricity price forecasts to maximize arbitrage profits in day-ahead markets. We examined whether specific forecasting models, ranging from statistical benchmarks to machine learning methods, consistently deliver superior financial outcomes for storage operators. Using real market data from the Italian day-ahead electricity market over 2020–2024, we compared univariate singular spectrum analysis (SSA), ARIMA, SARIMA, random forests, and a 30-day simple moving average under a unified trading framework. All models were evaluated based on their ability to generate arbitrage profits. Univariate SSA clearly outperformed all alternatives, achieving on average 98% of the theoretical maximum profit while maintaining the lowest forecast error. Among the other models, simpler approaches performed surprisingly well: they achieved comparable, if not superior, profit performance to more complex, hour-specific, or computationally intensive configurations. These results were robust to plausible variations in battery parameters and retraining schedules, suggesting that univariate SSA offers a uniquely effective forecasting solution for battery arbitrage and that simplicity can often be more effective than complexity in operational revenue terms. Full article

This study presents a comprehensive life-cycle assessment of Vehicle-to-Grid (V2G) economic viability, explicitly integrating the costs of both battery cycling degradation and calendar aging. While V2G offers revenue through energy arbitrage, its net profitability is critically dependent on regional electricity price differentials and the associated battery degradation costs. We develop a dynamic cost–benefit model, validated over a 10-year horizon across five diverse regions (Shanghai, Chengdu, the U.S., the U.K., and Australia). The results reveal stark regional disparities: Chengdu (0.65 USD/kWh peak–valley gap) and Australia (0.53 USD/kWh) achieve substantial net revenues of up to USD 25,000 per vehicle, whereas Shanghai’s narrow price differential (0.03 USD/kWh) renders V2G unprofitable. Sensitivity analysis quantifies critical break-even price differentials, varying by EV model and annual mileage (e.g., 0.12 USD/kWh minimum for Tesla Model Y). Crucially, calendar aging emerged as the dominant degradation cost (67% at 10,000 km/year), indicating significant battery underutilization potential. Policy insights emphasize the necessity of targeted interventions, such as Chengdu’s discharge incentives (0.69 USD/kWh), to bridge profitability gaps. This research provides actionable guidance for policymakers, grid operators, and EV owners by quantifying the trade-offs between V2G revenue and battery longevity, enabling optimized deployment strategies. Full article

This paper demonstrates that perfectly calibrating a multi-asset model to observed market prices of all basket call options is insufficient to uniquely determine the price of a best-of call option. Previous research on multi-asset option pricing has primarily focused on complete market settings or assumed specific parametric models, leaving fundamental questions about model risk and pricing uniqueness in incomplete markets inadequately addressed. This limitation has critical practical implications: derivatives practitioners who hedge best-of options using basket-equivalent instruments face fundamental distributional uncertainty that compounds the well-recognized non-linearity challenges. We establish this non-uniqueness using convex analysis (extreme ray characterization demonstrating geometric incompatibility between payoff structures), measure theory (explicit construction of distinct equivalent probability measures), and geometric analysis (payoff structure comparison). Specifically, we prove that the set of equivalent probability measures consistent with observed basket prices contains distinct measures yielding different best-of option prices, with explicit no-arbitrage bounds $[a_K,b_K]$ quantifying this uncertainty. Our theoretical contribution provides the first rigorous mathematical foundation for several empirically observed market phenomena: wide bid-ask spreads on extremal options, practitioners’ preference for over-hedging strategies, and substantial model reserves for exotic derivatives. We demonstrate through concrete examples that substantial model risk persists even with perfect basket calibration and equivalent measure constraints. For risk-neutral pricing applications, equivalent martingale measure constraints can be imposed using optimal transport theory, though this requires additional mathematical complexity via Schrödinger bridge techniques while preserving our fundamental non-uniqueness results. The findings establish that additional market instruments beyond basket options are mathematically necessary for robust exotic derivative pricing. Full article

The configuration of energy storage systems in offshore wind farms can effectively suppress fluctuations in wind power and enhance the stability of the power grid. However, the economic balance between the cost of energy storage systems and the fluctuations in wind power remains an urgent challenge to be addressed, especially against the backdrop of widespread spot trading in the electricity market. How to achieve effective wind power stabilization at the lowest cost has become a key issue. This paper proposes three different energy storage configuration strategies and adopts the non-dominated sorting genetic algorithm (NSGA-II) to conduct multi-objective optimization of the system. NSGA-II performed stably in dual-objective scenarios and effectively balanced the relationship between the investment cost of the energy storage system and power fluctuations through the explicit elite strategy. Furthermore, this study analyzed the correlation between the rated power and rated capacity of the energy storage system and the battery life, and corrected the battery life of the Pareto frontier solution obtained by NSGA-II. The research results show that when only considering the investment cost of the energy storage, the optimal configuration was a rated power of 4 MW and a rated capacity of 28 MWh, which could better balance the investment economy and power fluctuation. When further considering the participation of energy storage systems in the electricity spot market, the economic efficiency of the energy storage systems could be significantly improved through the fixed-period electricity price arbitrage method. At this point, the optimal configuration was a rated power of 8 MW and a rated capacity of 37 MWh. The corresponding project investment cost was CNY 242.77 million, and the annual fluctuation rate of the wind power output decreased to 17.84%. Full article

A robust model for natural gas prices should simultaneously capture the observed prices of both futures and options. While incorporating a seasonal factor in the convenience yield of the spot price effectively replicates forward curves, it proves insufficient for accurately modelling the options price surface. The latter is more sensitive to the volatility structure of the spot price process, which has a limited impact on futures pricing. In this paper, we analyse European natural gas spot, futures, and options prices throughout 2024 and propose a no-arbitrage model that integrates both a seasonal stochastic convenience yield and a local volatility factor. This framework enables a simultaneous and accurate fit of both forward curves and options prices. Full article

Electricity markets with a high share of variable renewable energy require significant balancing reserves to ensure stability by preserving the balance of supply and demand. However, they were originally conceived for dispatchable technologies, which operate with predictable and controllable generation. As a result, adapting market mechanisms to accommodate the characteristics of variable renewables is essential for enhancing grid reliability and efficiency. This work studies the strategic behavior of a wind power producer (WPP) in the Iberian electricity market (MIBEL) and the Portuguese balancing markets (BMs), where wind farms are economically responsible for deviations and do not have support schemes. In addition to exploring current market dynamics, the study proposes new market designs for the balancing markets, with separate procurement of upward and downward secondary balancing capacity, aligning with European Electricity Regulation guidelines. The difference between market designs considers that the wind farm can hourly bid in both (New 1) or only one (New 2) balancing direction. The study considers seven strategies (S1–S7) for the participation of a wind farm in the past (S1), actual (S2 and S3), New 1 (S4) and New 2 (S5–S7) market designs. The results demonstrate that new market designs can increase the wind market value by 2% compared to the optimal scenario and by 31% compared to the operational scenario. Among the tested approaches, New 2 delivers the best operational and economic outcomes. In S7, the wind farm achieves the lowest imbalance and curtailment while maintaining the same remuneration of S4. Additionally, the difference between the optimal and operational remuneration of the WPP under the New 2 design is only 22%, indicating that this design enables the WPP to achieve remuneration levels close to the optimal case. Full article