Volatility of Futures Contract in Iran Mercantile Market

Most financial theories are relying on estimation of volatility. Volatility is not directly observable and must be estimated. In this research we investigate the volatility of gold, trading as a futures contract on the Iran Mercantile Exchange (IME) using intraday (high frequency) data from 5 January 2009 to May 2012. This paper uses several models for the calculation of volatility based on range prices. The results show that a simple measure of volatility (defined as the first logarithmic difference between the high and low prices) overestimates the other three measures. Comparing values of RMSE, MSE, MAD and MAPE we find out that Garman-Klass and Rogers-Satchell Models are more accurate estimator of volatility. Keywords: volatility, range-based models, futures contract

On High-Performance Benders-Decomposition-Based Exact Methods with Application to Mixed-Integer and Stochastic Problems

RÉSUMÉ : La programmation stochastique en nombres entiers (SIP) combine la difficulté de l’incertitude et de la non-convexité et constitue une catégorie de problèmes extrêmement difficiles à résoudre. La résolution efficace des problèmes SIP est d’une grande importance en raison de leur vaste applicabilité. Par conséquent, l’intérêt principal de cette dissertation porte sur les méthodes de résolution pour les SIP. Nous considérons les SIP en deux étapes et présentons plusieurs algorithmes de décomposition améliorés pour les résoudre. Notre objectif principal est de développer de nouveaux schémas de décomposition et plusieurs techniques pour améliorer les méthodes de décomposition classiques, pouvant conduire à résoudre optimalement divers problèmes SIP. Dans le premier essai de cette thèse, nous présentons une revue de littérature actualisée sur l’algorithme de décomposition de Benders. Nous fournissons une taxonomie des améliorations algorithmiques et des stratégies d’accélération de cet algorithme pour synthétiser la littérature et pour identifier les lacunes, les tendances et les directions de recherche potentielles. En outre, nous discutons de l’utilisation de la décomposition de Benders pour développer une (méta- )heuristique efficace, décrire les limites de l’algorithme classique et présenter des extensions permettant son application à un plus large éventail de problèmes. Ensuite, nous développons diverses techniques pour surmonter plusieurs des principaux inconvénients de l’algorithme de décomposition de Benders. Nous proposons l’utilisation de plans de coupe, de décomposition partielle, d’heuristiques, de coupes plus fortes, de réductions et de stratégies de démarrage à chaud pour pallier les difficultés numériques dues aux instabilités, aux inefficacités primales, aux faibles coupes d’optimalité ou de réalisabilité, et à la faible relaxation linéaire. Nous testons les stratégies proposées sur des instances de référence de problèmes de conception de réseau stochastique. Des expériences numériques illustrent l’efficacité des techniques proposées. Dans le troisième essai de cette thèse, nous proposons une nouvelle approche de décomposition appelée méthode de décomposition primale-duale. Le développement de cette méthode est fondé sur une reformulation spécifique des sous-problèmes de Benders, où des copies locales des variables maîtresses sont introduites, puis relâchées dans la fonction objective. Nous montrons que la méthode proposée atténue significativement les inefficacités primales et duales de la méthode de décomposition de Benders et qu’elle est étroitement liée à la méthode de décomposition duale lagrangienne. Les résultats de calcul sur divers problèmes SIP montrent la supériorité de cette méthode par rapport aux méthodes classiques de décomposition. Enfin, nous étudions la parallélisation de la méthode de décomposition de Benders pour étendre ses performances numériques à des instances plus larges des problèmes SIP. Les variantes parallèles disponibles de cette méthode appliquent une synchronisation rigide entre les processeurs maître et esclave. De ce fait, elles souffrent d’un important déséquilibre de charge lorsqu’elles sont appliquées aux problèmes SIP. Cela est dû à un problème maître difficile qui provoque un important déséquilibre entre processeur et charge de travail. Nous proposons une méthode Benders parallèle asynchrone dans un cadre de type branche-et-coupe. L’assouplissement des exigences de synchronisation entraine des problèmes de convergence et d’efficacité divers auxquels nous répondons en introduisant plusieurs techniques d’accélération et de recherche. Les résultats indiquent que notre algorithme atteint des taux d’accélération plus élevés que les méthodes synchronisées conventionnelles et qu’il est plus rapide de plusieurs ordres de grandeur que CPLEX 12.7.----------ABSTRACT : Stochastic integer programming (SIP) combines the difficulty of uncertainty and non-convexity, and constitutes a class of extremely challenging problems to solve. Efficiently solving SIP problems is of high importance due to their vast applicability. Therefore, the primary focus of this dissertation is on solution methods for SIPs. We consider two-stage SIPs and present several enhanced decomposition algorithms for solving them. Our main goal is to develop new decomposition schemes and several acceleration techniques to enhance the classical decomposition methods, which can lead to efficiently solving various SIP problems to optimality. In the first essay of this dissertation, we present a state-of-the-art survey of the Benders decomposition algorithm. We provide a taxonomy of the algorithmic enhancements and the acceleration strategies of this algorithm to synthesize the literature, and to identify shortcomings, trends and potential research directions. In addition, we discuss the use of Benders decomposition to develop efficient (meta-)heuristics, describe the limitations of the classical algorithm, and present extensions enabling its application to a broader range of problems. Next, we develop various techniques to overcome some of the main shortfalls of the Benders decomposition algorithm. We propose the use of cutting planes, partial decomposition, heuristics, stronger cuts, and warm-start strategies to alleviate the numerical challenges arising from instabilities, primal inefficiencies, weak optimality/feasibility cuts, and weak linear relaxation. We test the proposed strategies with benchmark instances from stochastic network design problems. Numerical experiments illustrate the computational efficiency of the proposed techniques. In the third essay of this dissertation, we propose a new and high-performance decomposition approach, called Benders dual decomposition method. The development of this method is based on a specific reformulation of the Benders subproblems, where local copies of the master variables are introduced and then priced out into the objective function. We show that the proposed method significantly alleviates the primal and dual shortfalls of the Benders decomposition method and it is closely related to the Lagrangian dual decomposition method. Computational results on various SIP problems show the superiority of this method compared to the classical decomposition methods as well as CPLEX 12.7. Finally, we study parallelization of the Benders decomposition method. The available parallel variants of this method implement a rigid synchronization among the master and slave processors. Thus, it suffers from significant load imbalance when applied to the SIP problems. This is mainly due to having a hard mixed-integer master problem that can take hours to be optimized. We thus propose an asynchronous parallel Benders method in a branchand- cut framework. However, relaxing the synchronization requirements entails convergence and various efficiency problems which we address them by introducing several acceleration techniques and search strategies. In particular, we propose the use of artificial subproblems, cut generation, cut aggregation, cut management, and cut propagation. The results indicate that our algorithm reaches higher speedup rates compared to the conventional synchronized methods and it is several orders of magnitude faster than CPLEX 12.7

A Simulated Annealing Algorithm within the Variable Neighbourhood Search Framework to Solve the Capacitated Facility Location-Allocation Problem

In this study, we discuss the capacitated facility location-allocation problem with uncertain parameters in which the uncertainty is characterized by given finite numbers of scenarios. In this model, the objective function minimizes the total expected costs of transportation and opening facilities subject to the robustness constraint. To tackle the problem efficiently and effectively, an efficient hybrid solution algorithm based on several meta-heuristics and an exact algorithm is put forward. This algorithm generates neighborhoodsby combining the main concepts of variable neighborhood search, simulated annealing, and tabu search and finds the local optima by using an algorithm that uses an exact method in its framework. Finally, to test the algorithms’ performance, we apply numerical experiments on both randomly generated and standard test problems. Computational experiments show that our algorithm is more effective and efficient in term of CPU time and solutions quality in comparison with CPLEX solver

Renewing the Budget: Recommendations for Louisiana’s Renewable Energy Tax Credit

Long-term operation of energy systems is a complex optimization task. Often, such long-term operational optimizations are solved by direct decomposing the problem into smaller subproblems. However, direct decomposition is not possible for problems with time-coupling constraints and variables. Such time-coupling is common in energy systems, e.g., due to peak power prices and (seasonal) energy storage. To efficiently solve coupled long-term operational optimization problems, we propose a time-series decomposition method. The proposed method calculates lower and upper bounds to obtain a feasible solution of the original problem with known quality. We compute lower bounds by the Branch-and-Cut algorithm. For the upper bound, we decompose complicating constraints and variables into smaller subproblems. The solution of these subproblems are recombined to obtain a feasible solution for the long-term operational optimization. To tighten the upper bound, we iteratively decrease the number of subproblems. In a case study for an industrial energy system, we show that the proposed time-series decomposition method converges fast, outperforming a commercial state-of-the-art solver

Research trends in combinatorial optimization

Acknowledgments This work has been partially funded by the Spanish Ministry of Science, Innovation, and Universities through the project COGDRIVE (DPI2017-86915-C3-3-R). In this context, we would also like to thank the Karlsruhe Institute of Technology. Open access funding enabled and organized by Projekt DEAL.Peer reviewedPublisher PD

Large-scale unit commitment under uncertainty: an updated literature survey

The Unit Commitment problem in energy management aims at finding the optimal production schedule of a set of generation units, while meeting various system-wide constraints. It has always been a large-scale, non-convex, difficult problem, especially in view of the fact that, due to operational requirements, it has to be solved in an unreasonably small time for its size. Recently, growing renewable energy shares have strongly increased the level of uncertainty in the system, making the (ideal) Unit Commitment model a large-scale, non-convex and uncertain (stochastic, robust, chance-constrained) program. We provide a survey of the literature on methods for the Uncertain Unit Commitment problem, in all its variants. We start with a review of the main contributions on solution methods for the deterministic versions of the problem, focussing on those based on mathematical programming techniques that are more relevant for the uncertain versions of the problem. We then present and categorize the approaches to the latter, while providing entry points to the relevant literature on optimization under uncertainty. This is an updated version of the paper "Large-scale Unit Commitment under uncertainty: a literature survey" that appeared in 4OR 13(2), 115--171 (2015); this version has over 170 more citations, most of which appeared in the last three years, proving how fast the literature on uncertain Unit Commitment evolves, and therefore the interest in this subject

Modeling the Dynamics of Correlations Between International Equity Volatility Indices

I show that volatility indices are more volatile than equity indices, and correlation is higher during periods of high market uncertainty. In this thesis, I consider correlation between volatility markets around the world. This thesis introduces a one-factor model to examine the correlations between volatility markets. I show that for markets where there is a higher level of stock market integration, there is a correspondingly higher degree of volatility market integration. My findings suggest that investors’ expectations about future uncertainty are highly integrated. Applying the dynamic conditional correlation model developed by Engle (2002) to 10 volatility indices across different countries, I show that there is a positive and time-varying correlation between all volatility indices and that the correlation with the underlying equity market index is one factor associated with volatility market integration. I document some evidence of regional integration in volatility markets which suggests that macroeconomic factors should be examined further in future research

Modeling the Dynamics of Correlations Between International Equity Volatility Indices

I show that volatility indices are more volatile than equity indices, and correlation is higher during periods of high market uncertainty. In this thesis, I consider correlation between volatility markets around the world. This thesis introduces a one-factor model to examine the correlations between volatility markets. I show that for markets where there is a higher level of stock market integration, there is a correspondingly higher degree of volatility market integration. My findings suggest that investors’ expectations about future uncertainty are highly integrated. Applying the dynamic conditional correlation model developed by Engle (2002) to 10 volatility indices across different countries, I show that there is a positive and time-varying correlation between all volatility indices and that the correlation with the underlying equity market index is one factor associated with volatility market integration. I document some evidence of regional integration in volatility markets which suggests that macroeconomic factors should be examined further in future research