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Risks
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Financial Derivatives and Hedging in Energy Markets
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Financial Derivatives and Hedging in Energy Markets

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: 31 August 2025 | Viewed by 3244

Special Issue Editors

Dr. Viviana Fanelli

E-Mail Website
Guest Editor
Department of Economics, University of Foggia, 71121 Foggia, Italy
Interests: stochastic models; asset pricing; arbitrage strategies; dynamic models; commodity finance and markets; interest rate and credit risk modelling.
Dr. Michele Bufalo

E-Mail Website
Guest Editor
Department of Economics and Finance, University of Bari, 70121 Bari, Italy
Interests: stochastic processes; stochastic models for interest rates; Skew-Geometric Brownian motions and applications in finance; forecasting: interest rates forecasting; natural catastrophes (NatCat) forecasting; option pricing in incomplete markets; generalized Trotter-Kato formulas for option pricing problems in incomplete markets; option pricing under changes of numeraire; Expected transaction costs; and generalized Barone-Adesi Whaley formula for turbolent markets

Special Issue Information

Dear Colleagues,

The liberalization of energy markets has given rise to new patterns of financial product prices and the need for models that could accurately describe price dynamics as they grew exponentially to improve decision-making for all the agents involved in energy issues.

Energy derivatives play an important role in the modern financial system and are widely used for speculation, industrial production planning, and risk hedging. In the global energy markets, energy derivatives enable participants to manage the risk associated with volatile prices, speculate on future price movements, and achieve investment diversification. Definitively, they encourage better price discovery and risk transfer.

Therefore, mathematical and statistical tools are important for estimating, implementing and calibrating quantitative models, pricing and trading energy-linked products, and managing basic and complex portfolio risks.

Topics for consideration in this Special Issue include, among others, the following:

  • The pricing of energy derivatives;
  • Hedging with futures, options, and swaps;
  • Portfolio risk management;
  • Modeling dynamic hedge ratios;
  • Mathematical finance;
  • Advanced hedging measures;
  • Risk-neutral valuation;
  • The arbitrage theory;
  • Derivative trading.

Dr. Viviana Fanelli
Dr. Michele Bufalo
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Risks is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1800 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • energy derivatives
  • pricing
  • risk management
  • hedging

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Published Papers (5 papers)

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Research

21 pages, 1012 KiB  
Article
Advanced Operator Theory for Energy Market Trading: A New Framework
by Michele Bufalo and Viviana Fanelli
Risks 2025, 13(7), 118; https://doi.org/10.3390/risks13070118 - 20 Jun 2025
Viewed by 120
Abstract
This paper analyzes a parabolic operator L that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with L and derive its explicit analytical representation. The theoretical framework developed in this study [...] Read more.
This paper analyzes a parabolic operator L that generalizes several well-known operators commonly used in financial mathematics. We establish the existence and uniqueness of the Feller semigroup associated with L and derive its explicit analytical representation. The theoretical framework developed in this study provides a robust foundation for modeling stochastic processes relevant to financial markets. Furthermore, we apply these findings to energy market trading by developing specialized simulation algorithms and forecasting models. These methodologies were tested across all assets comprising the S&P 500 Energy Index, evaluating their predictive accuracy and effectiveness in capturing market dynamics. The empirical analysis demonstrated the practical advantages of employing generalized semigroups in modeling non-Gaussian market behaviors and extreme price fluctuations. Full article
(This article belongs to the Special Issue Financial Derivatives and Hedging in Energy Markets)
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20 pages, 2552 KiB  
Article
Evaluation of Perpetual American Put Options with General Payoff
by Luca Anzilli and Lucianna Cananà
Risks 2025, 13(6), 112; https://doi.org/10.3390/risks13060112 - 13 Jun 2025
Viewed by 176
Abstract
In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms [...] Read more.
In this paper, we study perpetual American put options with a generalized standard put payoff and establish sufficient conditions for the existence and uniqueness of the solution to the associated pricing problem. As a key tool, we express the Black–Scholes operator in terms of elasticity. This formulation enables us to demonstrate that the considered pricing problem admits a unique solution when the payoff function exhibits strictly decreasing elasticity with respect to the underlying asset. Furthermore, this approach allows us to derive closed-form solutions for option pricing. Full article
(This article belongs to the Special Issue Financial Derivatives and Hedging in Energy Markets)
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28 pages, 4030 KiB  
Article
Linking Futures and Options Pricing in the Natural Gas Market
by Francesco Rotondi
Risks 2025, 13(6), 107; https://doi.org/10.3390/risks13060107 - 3 Jun 2025
Viewed by 478
Abstract
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 [...] Read more.
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
(This article belongs to the Special Issue Financial Derivatives and Hedging in Energy Markets)
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18 pages, 4380 KiB  
Article
Gaussian Process Regression with a Hybrid Risk Measure for Dynamic Risk Management in the Electricity Market
by Abhinav Das and Stephan Schlüter
Risks 2025, 13(1), 13; https://doi.org/10.3390/risks13010013 - 16 Jan 2025
Viewed by 947
Abstract
In this work, we introduce an innovative approach to managing electricity costs within Germany’s evolving energy market, where dynamic tariffs are becoming increasingly normal. In line with recent German governmental policies, particularly the Energiewende (Energy Transition) and European Union directives on clean energy, [...] Read more.
In this work, we introduce an innovative approach to managing electricity costs within Germany’s evolving energy market, where dynamic tariffs are becoming increasingly normal. In line with recent German governmental policies, particularly the Energiewende (Energy Transition) and European Union directives on clean energy, this work introduces a risk management strategy based on a combination of the well-known risk measures of the Value at Risk (VaR) and Conditional Value at Risk (CVaR). The goal is to optimize electricity procurement by forecasting hourly prices over a certain horizon and allocating a fixed budget using the aforementioned measures to minimize the financial risk. To generate price predictions, a Gaussian process regression model is used. The aim of this hybrid approach is to design a model that is easily understandable but allows for a comprehensive evaluation of potential financial exposure. It enables consumers to adjust their consumption patterns or market traders to invest and allows more cost-effective and risk-aware decision-making. The potential of our approach is shown in a case study based on the German market. Moreover, by discussing the political and economical implications, we show how the implementation of our method can contribute to the realization of a sustainable, flexible, and efficient energy market, as outlined in Germany’s Renewable Energy Act. Full article
(This article belongs to the Special Issue Financial Derivatives and Hedging in Energy Markets)
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20 pages, 598 KiB  
Article
Empirical Evidence of the Market Price of Risk for Delivery Periods
by Annika Kemper and Maren Diane Schmeck
Risks 2025, 13(1), 7; https://doi.org/10.3390/risks13010007 - 3 Jan 2025
Cited by 1 | Viewed by 804
Abstract
In this paper, we provide empirical evidence of the market price of risk for delivery periods (MPDP) of electricity swap contracts. The MPDP enables an accurate pricing of such contracts in the presence of the delivery period such that the typical approximations can [...] Read more.
In this paper, we provide empirical evidence of the market price of risk for delivery periods (MPDP) of electricity swap contracts. The MPDP enables an accurate pricing of such contracts in the presence of the delivery period such that the typical approximations can be avoided. In our empirical study, we focus on term-structure effects and identify the resulting MPDP. In presence of the Samuelson effect, we find the most pronounced MPDP close to maturity, while the MPDP disappears proportional to the Samuelson effect far away from maturity. Thus, our theory improves the pricing accuracy close to maturity. Full article
(This article belongs to the Special Issue Financial Derivatives and Hedging in Energy Markets)
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