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Seasonality in commodity prices: new approaches for pricing plain vanilla options

ANNALS OF OPERATIONS RESEARCH 2024年第1-2期336卷 1089-1131页

作者： Frau, Carme Fanelli, Viviana Univ Illes Balears Dept Business Econ Ctra Valldemossa Km 7-5 E-07122 Palma De Mallorca Spain Dept oc Econ Management & Business Law Largo Abbaz 53 I-70124 Bari Italy

We present a new term-structure model for commodity futures prices based on Trolle and Schwartz (2009), which we extend by incorporating seasonal stochastic volatility represented with two different sinusoidal expressions. We obtain a quasi-analytical representation of the characteristic function of the futures log-prices and closed-form expressions for standard European options' prices using the fast Fourier transform algorithm. We price plain vanilla options on the Henry Hub natural gas futures contracts, using our model and extant models. We obtain higher accuracy levels with our model than with the extant models.

关键词： Commodities Natural gas Futures prices Option pricing Fast Fourier transform Term-structure model Analytical solution Seasonal stochastic volatility sinusoidal functions

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Hybrid modeling approach for precise estimation of energy production and consumption based on temperature variations

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SCIENTIFIC REPORTS 2024年第1期14卷 1-22页

作者： Mbasso, Wulfran Fendzi Molu, Reagan Jean Jacques Harrison, Ambe Pushkarna, Mukesh Kemdoum, Fritz Nguemo Donfack, Emmanuel Fendzi Jangir, Pradeep Tiako, Pierre Tuka, Milkias Berhanu Univ Douala Technol & Appl Sci Lab UIT Douala POB 8689 Douala Cameroon Univ Buea Coll Technol COT Dept Elect & Elect Engn POB 63 Buea Cameroon GLA Univ Mathura Dept Elect Engn Mathura India Univ Yaounde I Higher Teachers Training Coll Dept Phys Nonlinear Phys & Complex Syst Grp POB 47 Yaounde Cameroon Univ Douala Fac Sci Dept Phys Pure Phys LabGrp Nonlinear Phys & Complex Syst POB 24157 Douala Cameroon Univ Yaounde I Fac Sci Dept Phys Lab Mech Mat & Struct POB 812 Yaounde Cameroon Saveetha Inst Med & Tech Sci Saveetha Sch Engn Dept Biosci Chennai 602105 Tamil Nadu India Chandigarh Univ Univ Ctr Res & Dev Gharuan 140413 Mohali India Appl Sci Private Univ Appl Sci Res Ctr Amman 11931 Jordan Tiako Univ Oklahoma Ctr IT Res & Dev Oklahoma City OK USA Addis Ababa Sci & Technol Univ Coll Engn Sustainable Energy Ctr Excellency Dept Elect & Comp Engn Addis Ababa Ethiopia

This study introduces an advanced mathematical methodology for predicting energy generation and consumption based on temperature variations in regions with diverse climatic conditions and increasing energy demands. Using a comprehensive dataset of monthly energy production, consumption, and temperature readings spanning ten years (2010-2020), we applied polynomial, sinusoidal, and hybrid modeling techniques to capture the non-linear and cyclical relationships between temperature and energy metrics. The hybrid model, which combines sinusoidal and polynomial functions, achieved an accuracy of 79.15% in estimating energy consumption using temperature as a predictor variable. This model effectively captures the seasonal and non-linear consumption patterns, demonstrating a significant improvement over conventional models. In contrast, the polynomial model for energy production, while yielding partial accuracy (R-2 = 0.65), highlights the need for more advanced techniques to fully capture the temperature-dependent nature of energy production. The results indicate that temperature variations significantly affect energy consumption, with higher temperatures driving increased energy demand for cooling, while lower temperatures affect production efficiency, particularly in systems like hydropower. These findings underscore the necessity for integrating sophisticated models into energy planning to ensure resilience in energy systems amidst climate variability. The study offers critical insights for policymakers to optimize energy generation and distribution in response to changing climatic conditions.

关键词： Energy modeling Temperature impact Hybrid models Polynomial regression sinusoidal functions Energy consumption Energy production Climatic variability Renewable energy planning

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Complex Numbers and Rhythmic Changes

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RESONANCE-JOURNAL OF SCIENCE EDUCATION 2021年第8期26卷 1059-1080页

作者： Geethamma, V. G. Gopinath, Deepa P. Daniel, Jacob K. Univ Illinois Chicago IL 60680 USA Univ Cambridge Cambridge England Univ Coll Engn Thodupuzha 685587 Kerala India Govt Engn Coll Barton Hill Thiruvananthapuram Kerala India Multimedia Univ Math Cyberjaya Malaysia 501 Sunny Palace Kochi 682024 Kerala India

The concept of complex numbers (CNs) is used in many disciplines. In many cases, students find it difficult to understand the logic behind CNs. Rotations, vibrations, and oscillations result in sine or cosine waves. Mathematical representation of rotation/vibration/oscillation is done in two ways-trigonometry and complex numbers. But the algebraic calculation is easier if CNs are used instead of trigonometric functions. The use of CNs as an effective representation of sinusoidal variations is discussed in this article.

关键词： Complex number harmonic motion sinusoidal functions phasor dynamic mechanical analysis vibration rotation

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Modelling and detection of live tree-related high impedance fault in distribution systems

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IET GENERATION TRANSMISSION & DISTRIBUTION 2018年第3期12卷 756-766页

作者： Bahador, Nooshin Namdari, Farhad Matinfar, Hamid Reza Lorestan Univ Lorestan Iran

Despite the importance of high-impedance fault (HIF) modelling as a key issue in numerous power system studies, there is no single model accurately representing the behaviour of each type of HIFs. Tree-related HIF (THIF) is a complex type that occurs when a power line comes in contact with a live tree. Given that available models for HIF cannot represent the expected behaviour of a live THIF, the need for a more accurate model seems obvious. So, in this study, based on experimental data obtained from measurements, the effective factors in HIF caused by live trees are studied and a new mathematical model of THIF provided in order to present the effects of both environmental conditions and biological classification. This model represents low and high frequency behaviours of THIFs, which are, respectively, derived in block-oriented feed-forward form and sinusoidal functions. Moreover, this study proposes a hybrid technique based on the combination of kernel density estimation and wavelet analysis to perform a feature extraction from THIF signals.

关键词： power distribution faults fault diagnosis feedforward trees (mathematics) live tree-related high impedance fault detection live tree-related high impedance fault modelling distribution systems power system tree-related HIF mathematical model environmental conditions biological classification high frequency behaviours block-oriented feedforward form sinusoidal functions kernel density estimation wavelet analysis feature extraction THIF signals

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A new fractional derivative involving the normalized sinc function without singular kernel

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EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS 2017年第16-18期226卷 3567-3575页

作者： Yang, Xiao-Jun Gao, Feng Machado, J. A. Tenreiro Baleanu, Dumitru China Univ Min & Technol State Key Lab Geomech & Deep Underground Engn Xuzhou 221116 Jiangsu Peoples R China China Univ Min & Technol Sch Mech & Civil Engn Xuzhou 221116 Jiangsu Peoples R China Polytech Porto Inst Engn Dept Elect Engn Rua Dr Antonio Bernardino de Almeida P-4249015 Porto Portugal Cankya Univ Dept Math Ogretmenler Cad 14 TR-06530 Ankara Turkey Inst Space Sci Bucharest Romania

In this paper, a new fractional derivative involving the normalized sinc function without singular kernel is proposed. The Laplace transform is used to find the analytical solution of the anomalous heat-diffusion problems. The comparative results between classical and fractional-order operators are presented. The results are significant in the analysis of one-dimensional anomalous heat-transfer problems.

关键词： Singular fractional order Anomalous sinusoidal functions Laplace transform

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Steering on SO(3) with sinusoidal inputs

Steering on SO(3) with sinusoidal inputs

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American Control Conference

作者： Shaoqian Wang Jesse B. Hoagg T. Michael Seigler Department of Mechanical Engineering University of Kentucky US

ISBN: (纸本)9781509045839

This paper presents steering control strategies for kinematic system q = RΩ on SO(3) for the case that input Ω is restricted to a class of sinusoidal functions. This restriction is motivated by the problem of rigid-body orientation control using vibrating internal-momentum actuators. A main result of this paper is a new closed-form solution of the kinematic system on SO(3). The solution is used to establish controllability of the kinematic system with the sinusoidal input restriction. We then present a feedback controller that globally asymptotically stabilizes the identity, and a feedback tracking controller that yields bounded error.

关键词： sinusoidal input Steering tracking controller kinematics controllability sinusoidal functions steering control Feedback personal identity

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Comparing Two Voltage Observers in a Sensorsystem using Repetitive Control

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IFAC-PapersOnLine 2016年第14期49卷 7-11页

作者： Schimmack, Manuel da Costa, Michel Lucio Mercorelli, Paolo Institute of Product and Process Innovation Leuphana University of Lueneburg Volgershall 1 LueneburgD-21339 Germany

In sensor systems one of the most crucial issues is represented by the insensibility of the sensors with respect to the disturbances to obtain precision in the detected measurements. This paper proposes two different observers to identify an input voltage disturbance in sensors for ferromagnetic particle monitoring. The disturbance is identified together with the state variables which can be used for a controller. Because of a sinusoidal function being chosen to be the reference signal of the sensor, the repetitive controller is proposed to make robust this periodic work function of the sensor. The tracking of this working point is realised using a classical feed-forward control, which is made robust using a resonant control loop. The resonant control loop provides not only for the robustness but in the meantime minimises the energy needed for the sensor. The resonance is maintained by using the repetitive controller. In this sense the resonance region of the system guarantees a structural robustness and optimality. The repetitive control provides a tracking throughout the cycles. Computer simulations are devoted to compare the obtained results and conclusion closes the paper. © 2016

关键词： Controllers Resonance Robustness (control systems) Sensors Ferromagnetic particles Input voltage disturbances Observers Repetitive control Repetitive controller Resonance controls sinusoidal functions Structural robustness

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A backstepping approach for an active suspension system

A backstepping approach for an active suspension system

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American Control Conference

作者： Halil Ibrahim Basturk Dept. of Mechanical Eng. Bogazici University Bebek 34342 Istanbul Turkey

ISBN: (纸本)9781467386838

In this paper, the control design problem for an active suspension system to maintain the comfort and safety of the vehicle body is considered. The road disturbance is modelled as a finite sum of sinusoidal functions with unknown frequencies, amplitudes and phases. The disturbance is parameterized and an adaptive controller is designed by using the backstepping technique. It is proven that the equilibrium of the closed loop system is stable and the vertical acceleration of the vehicle body tends to zero despite road disturbances. The effectiveness of the controller is illustrated with a simulation of a road test.

关键词： Roads Suspensions Automobiles Control design Zirconium Backstepping Vehicle body Backstepping Active Suspension Systems design control Road Automobiles Zirconium Suspensions Road tests Cars sinusoidal functions Suspension System normal acceleration

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Transmission of Analog Correlated Sources over MIMO Fading Channels

Transmission of Analog Correlated Sources over MIMO Fading C...

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WSA 2016;20th International ITG Workshop on Smart Antennas

作者： Pedro Suarez-Casal Oscar Fresnedo Luis Castedo Javier Garcia-Frias

In this work we address the transmission of correlated Gaussian sources over Multiple Input Multiple Output fading channels using analog Joint Source Channel Coding (JSCC). The source symbols are first compressed using a continuous parametric mapping based on a sinusoidal function that exploits the source correlation. Given that the data at the encoder output is also correlated, the information corresponding to the covariance matrix is incorporated into the design of the linear transmit and receive filters. The results obtained from the simulations confirm the suitability of analog JSCC techniques for the considered scenario.

关键词： transmission multiple input multiple output systems Fading channels variance covariance matrix sinusoidal functions receive filter

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A simple temporal magnetic hysteresis model for nonlinear magnetization control

A simple temporal magnetic hysteresis model for nonlinear ma...

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American Control Conference

作者： Bogdan Niemoczynski Saroj Biswas Naval Surface Warfare Center Philadelphia United States Department of Electrical and Computer Engineering Temple University Philadelphia PA 19122 United States

ISBN: (纸本)9781467386838

This paper presents a novel macroscopic model describing temporal evolution of hysteretic magnetization. The physical phenomena of domain rotation and hysteresis are described by a first order nonlinear differential equation and a decreasing gain function. By varying the model parameters, the proposed model can be used to represent hysteresis curves for a variety of magnetic materials. Particle swarm optimization has been used for model validation based on experimental hysteresis data. A tracking control system using feedback linearization method is derived to assure zero steady state error between the flux density with respect to the desired value. The proposed nonlinear control method is evaluated by simulation results for a desired constant set point and a sinusoidal function.

关键词： Magnetic hysteresis Mathematical model Magnetic domains Magnetization Saturation magnetization Differential equations Magnetic domain walls Magnetic hysteresis Magnetic domain walls Magnetic domain magnetization Saturation magnetization zero steady state error Differential equations Mathematical Model FLUX DENSITY Hysteresis gain function sinusoidal functions Differentiation nonlinear differential equations

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