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High-Frequency Options Trading ∣ With Portfolio optimization

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arXiv 2024年

作者： Bhatia, Sid Stevens Institute of Technology United States

This paper explores the effectiveness of high-frequency options tradingstrategies enhanced by advanced portfolio optimization techniques,investigating their ability to consistently generate positive returns comparedto traditional long or short positions on options. Utilizing SPY options datarecorded in five-minute intervals over a one-month period, we calculate keymetrics such as Option Greeks and implied volatility, applying the BinomialTree model for American options pricing and the Newton-Raphson algorithm forimplied volatility calculation. Investment universes are constructed based oncriteria like implied volatility and Greeks, followed by the application ofvarious portfolio optimization models, including Standard Mean-Variance andRobust Methods. Our research finds that while basic long-short strategiescentered on implied volatility and Greeks generally underperform, moresophisticated strategies incorporating advanced Greeks, such as Vega and Rho,along with dynamic portfolio optimization, show potential in effectivelynavigating the complexities of the options market. The study highlights theimportance of adaptability and responsiveness in dynamic portfolio strategieswithin the high-frequency trading environment, particularly under volatilemarket conditions. Future research could refine strategy parameters and exploreless frequently traded options, offering new insights into high-frequencyoptions trading and portfolio management. © 2024, CC BY.

关键词： optimization algorithms

High dimensional Bayesian optimization via Condensing-Expansion Projection

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arXiv 2024年

作者： Lu, Jiaming Zhu, Rong J.B. ISTBI Fudan University Shanghai China

In high-dimensional settings, Bayesian optimization (BO) can be expensive and infeasible. The random embedding Bayesian optimization algorithm is commonly used to address high-dimensional BO challenges. However, this method relies on the effective subspace assumption on the optimization problem's objective function, which limits its applicability. In this paper, we introduce Condensing-Expansion Projection Bayesian optimization (CEPBO), a novel random projection-based approach for high-dimensional BO that does not reply on the effective subspace assumption. The approach is both simple to implement and highly practical. We present two algorithms based on different random projection matrices: the Gaussian projection matrix and the hashing projection matrix. Experimental results demonstrate that both algorithms outperform existing random embedding-based algorithms in most cases, achieving superior performance on high-dimensional BO problems. The code is available in https://***/r/CEPBO-14429. © 2024, CC BY.

关键词： optimization algorithms

Distributed Online Bandit Nonconvex optimization with One-Point Residual Feedback via Dynamic Regret

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arXiv 2024年

作者： Hua, Youqing Liu, Shuai Hong, Yiguang Johansson, Karl Henrik Wang, Guangchen School of Control Science and Engineering Shandong University Jinan China Nanyang Technological University Singapore Department of Control Science and Engineering Shanghai Research Institute for Intelligent Autonomous Systems Tongji University Shanghai China School of Electrical Engineering and Computer Science KTH Royal Institute of Technology Stockholm Sweden

This paper considers the distributed online bandit optimization problem with nonconvex loss functions over a time-varying digraph. This problem can be viewed as a repeated game between a group of online players and an adversary. At each round, each player selects a decision from the constraint set, and then the adversary assigns an arbitrary, possibly nonconvex, loss function to this player. Only the loss value at the current round, rather than the entire loss function or any other information (e.g. gradient), is privately revealed to the player. Players aim to minimize a sequence of global loss functions, which are the sum of local losses. We observe that traditional multi-point bandit algorithms are unsuitable for online optimization, where the data for the loss function are not all a priori, while the one-point bandit algorithms suffer from poor regret guarantees. To address these issues, we propose a novel one-point residual feedback distributed online algorithm. This algorithm estimates the gradient using residuals from two points, effectively reducing the regret bound while maintaining O(1) sampling complexity per iteration. We employ a rigorous metric, dynamic regret, to evaluate the algorithm's performance. By appropriately selecting the step size and smoothing parameters, we demonstrate that the expected dynamic regret of our algorithm is comparable to existing algorithms that use two-point feedback, provided the deviation in the objective function sequence and the path length of the minimization grows sublinearly. Finally, we validate the effectiveness of the proposed algorithm through numerical simulations. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

ORS: A NOVEL OLIVE RIDLEY SURVIVAL INSPIRED META-HEURISTIC optimization ALGORITHM

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arXiv 2024年

作者： Panigrahi, Niranjan Bhoi, Sourav Kumar Mohapatra, Debasis Sahoo, Rashmi Ranjan Sahoo, Kshira Sagar Mohapatra, Anil Department of CSE PMEC Berhampur761003 India Department of Computing Science Umeå University Umeå901 87 Sweden Estuarine Biology Regional Center Zoological Survey of India Gopalpur-on-Sea Ganjam 761002 India

Meta-heuristic algorithmic development has been a thrust area of research since its inception. In this paper, a novel meta-heuristic optimization algorithm, Olive Ridley Survival (ORS), is proposed which is inspired from survival challenges faced by hatchlings of Olive Ridley sea turtle. A major fact about survival of Olive Ridley reveals that out of one thousand Olive Ridley hatchlings which emerge from nest, only one survive at sea due to various environmental and other factors. This fact acts as the backbone for developing the proposed algorithm. The algorithm has two major phases: hatchlings survival through environmental factors and impact of movement trajectory on its survival. The phases are mathematically modelled and implemented along with suitable input representation and fitness function. The algorithm is analysed theoretically. To validate the algorithm, fourteen mathematical benchmark functions from standard CEC test suites are evaluated and statistically tested. Also, to study the efficacy of ORS on recent complex benchmark functions, ten benchmark functions of CEC-06-2019 are evaluated. Further, three well-known engineering problems are solved by ORS and compared with other state-of-the-art meta-heuristics. Simulation results show that in many cases, the proposed ORS algorithm outperforms some state-of-the-art meta-heuristic optimization algorithms. The sub-optimal behavior of ORS in some recent benchmark functions is also observed. © 2024, CC BY.

关键词： optimization algorithms

A Double Tracking Method for optimization with Decentralized Generalized Orthogonality Constraints

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arXiv 2024年

作者： Wang, Lei Xiao, Nachuan Liu, Xin Department of Statistics Pennsylvania State University University ParkPA United States Institute of Operational Research and Analytics National University of Singapore Singapore State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences Beijing China

In this paper, we consider the decentralized optimization problems with generalized orthogonality constraints, where both the objective function and the constraint exhibit a distributed structure. Such optimization problems, albeit ubiquitous in practical applications, remain unsolvable by existing algorithms in the presence of distributed constraints. To address this issue, we convert the original problem into an unconstrained penalty model by resorting to the recently proposed constraint-dissolving operator. However, this transformation compromises the essential property of separability in the resulting penalty function, rendering it impossible to employ existing algorithms to solve. We overcome this difficulty by introducing a novel algorithm that tracks the gradient of the objective function and the Jacobian of the constraint mapping simultaneously. The global convergence guarantee is rigorously established with an iteration complexity. To substantiate the effectiveness and efficiency of our proposed algorithm, we present numerical results on both synthetic and real-world datasets. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

A deterministic optimization algorithm for nonconvex and combinatorial bi-objective programming

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arXiv 2024年

作者： Lee, Ye Seol Jackson, George Galindo, Amparo Adjiman, Claire S. Department of Chemical Engineering Sargent Centre for Process Systems Engineering Institute for Molecular Science and Engineering Imperial College London South Kensington Campus LondonSW7 2AZ United Kingdom Department of Chemical Engineering University College London Torrington Pl LondonWC1E 7JE United Kingdom

Many practical multiobjective optimization (MOO) problems include discrete decision variables and/or nonlinear model equations and exhibit disconnected or smooth but nonconvex Pareto surfaces. Scalarization methods, such as the weighted-sum and sandwich (SD) algorithms, are common approaches to solving MOO problems but may fail on nonconvex or discontinuous Pareto fronts. In the current work, motivated by the well-known normal boundary intersection (NBI) method and the SD algorithm, we present SDNBI, a new algorithm for bi-objective optimization (BOO) designed to address the theoretical and numerical challenges associated with the reliable solution of general nonconvex and discrete BOO problems. The main improvements in the algorithm are the effective exploration of the nonconvex regions of the Pareto front and, uniquely, the early identification of regions where no additional Pareto solutions exist. The performance of the SDNBI algorithm is assessed based on the accuracy of the approximation of the Pareto front constructed over the disconnected nonconvex objective domains. The new algorithm is compared with two MOO approaches, the modified NBI method and the SD algorithm, using published benchmark problems. The results indicate that the SDNBI algorithm outperforms the modified NBI and SD algorithms in solving convex, nonconvex-continuous, and combinatorial problems, both in terms of computational cost and of the overall quality of the Pareto-optimal set, suggesting that the SDNBI algorithm is a promising alternative for solving BOO problems. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

Memory-Efficient optimization with Factorized Hamiltonian Descent

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arXiv 2024年

作者： Nguyen, Son Chen, Lizhang Liu, Bo Liu, Qiang The University of Texas Austin United States

Modern deep learning heavily depends on adaptive optimizers such as Adam and its variants, which are renowned for their capacity to handle model scaling and streamline hyperparameter tuning. However, these algorithms typically experience high memory overhead caused by the accumulation of optimization states, leading to a critical challenge in training large-scale network models. In this study, we introduce a novel adaptive optimizer, H-Fac, which incorporates a memory-efficient factorization approach to address this challenge. By employing a rank-1 parameterization for both momentum and scaling parameter estimators, H-Fac reduces memory costs to a sublinear level while maintaining competitive performance across a wide range of architectures. We develop our algorithms based on principles derived from Hamiltonian dynamics, providing robust theoretical underpinnings in optimization dynamics and convergence guarantees. These optimization algorithms are designed to be both straightforward and adaptable, facilitating easy implementation in diverse settings © 2024, CC BY.

关键词： optimization algorithms

A Review of Non-dominating Sorting algorithms

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A Review of Non-dominating Sorting Algorithms

International Conference on Business Intelligence and Information Technology, BIIT 2023

作者： Kong, Lingping Pan, Jeng-Shyang Snášel, Václav Faculty of Electrical Engineering and Computer Science VSB-Technical University of Ostrava Ostrava Czech Republic School of Artificial Intelligence Nanjing University of Information Science and Technology Nanjing China

ISBN: (纸本)9789819739790

The concept of non-dominated sorting (NDS) involves organizing a popu-lation’s solutions based on the Pareto dominance principle, a critical element influencing the computational efficiency of various multi-objective evolutionary algorithms. The roots of multi-objective optimization using a non-dominated sorting scheme can be traced back to the early days of Goldenberg’s book. Over time, enhancements have been made to non-dominated sorting methods, achieving a best-case complexity of.O(MN log N), with . N representing the population size and . M denoting the number of objectives. This study presents a comprehensive literature review, examining existing papers on non-dominated sorting and categorizing methods into tree-based NDS, first objective sorted list-based NDS, full objective sorted lists-based NDS, divide-and-conquer-based NDS, and labeling and deleting-based NDS. Additionally, the exploration includes a detailed division between front-by-front procedure-based NDS and solution-by-solution procedure-based NDS. The review assesses the strengths and weaknesses of these methods, concluding with suggestions for promising avenues in future research on non-dominated sorting. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.

关键词： optimization algorithms

Optimized PV-Battery Systems using Backtracking Search Algorithm for Sustainable Energy Solutions

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Optimized PV-Battery Systems using Backtracking Search Algor...

2023 IEEE International Conference on Energy Technologies for Future Grids, ETFG 2023

作者： Abdolrasol, M.G.M. Jern Ker, Pin Hannan, M.A. Tiong, S.K. Ayob, Afida Almadani, J.F.S. Sunway University School of Engineering and Technology Petaling Jaya Bandar Sunway47500 Malaysia Universiti Tenaga Nasional Institute of Sustainable Energy Kajang43000 Malaysia Universiti Kebangsaan Malaysia Department of Electric Electronics and Sys. Eng. Bangi43600 Malaysia Universiti Putra Malaysia Department of Computer and Communication Systems Engineering Serdang43400 Malaysia

ISBN: (纸本)9781665471640

This study explores the integration of photovoltaic (PV) systems with battery storage for sustainable energy solutions. Employing the Backtracking Search Algorithm (BSA), the research optimizes PI controller parameters to enhance system efficiency and reliability. Real-world energy demand and weather data are integrated for practical relevance. Rigorous simulations within MATLAB/Simulink establish a robust analytical framework, evaluating optimization algorithms and identifying optimal configurations. By analysing objectives and simulation outcomes, the study provides insights for system refinement. The research strategically applies advanced algorithms to elevate PV-battery system performance and compares outcomes with Particle Swarm optimization (PSO) and other studies, offering a comprehensive benchmark for evaluation. © 2023 IEEE.

关键词： Backtracking Search Algorithm (BSA) modulation index control optimization algorithms photovoltaic-Battery System Sustainable Energy Solutions