Heuristic Optimisation in Financial Modelling

There is a large number of optimisation problems in theoretical and applied finance that are difficult to solve as they exhibit multiple local optima or are not ‘well- behaved’ in other ways (eg, discontinuities in the objective function). One way to deal with such problems is to adjust and to simplify them, for instance by dropping constraints, until they can be solved with standard numerical methods. This paper argues that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable to handle non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, the paper presents several actual problems where classical methods fail. Next, several well-known heuristic techniques that may be deployed in such cases are described. Since such presentations are quite general, the paper describes in some detail how a particular problem, portfolio selection, can be tackled by a particular heuristic method, Threshold Accepting. Finally, the stochastics of the solutions obtained from heuristics are discussed. It is shown, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computations.Optimisation heuristics, Financial Optimisation, Portfolio Optimisation

Algorithmic optimization and its application in finance

The goal of this thesis is to examine different issues in the area of finance and application of financial and mathematical models under consideration of optimization methods. Prior to the application of a model to its scope, the model results have to be adjusted according to the observed data. For this reason a target function is defined which is being minimized by using optimization algorithms. This allows finding the optimal model parameters. This procedure is called model calibration or model fitting and requires a suitable model for this application. In this thesis we apply financial and mathematical models such as Heston, CIR, geometric Brownian motion, as well as inverse transform sampling, and Chi-square test. Moreover, we test the following optimization methods: Genetic algorithms, Particle-Swarm, Levenberg-Marquardt, and Simplex algorithm. The first part of this thesis deals with the problem of finding a more accurate forecasting approach for market liquidity by using a calibrated Heston model for the simulation of the bid/ask paths instead of the standard Brownian motion and the inverse transformation method instead of compound Poisson process for the generation of the bid/ask volume distributions. We show that the simulated trading volumes converge to one single value which can be used as a liquidity estimator and we find that the calibrated Heston model as well as the inverse transform sampling are superior concerning the use of the standard Brownian motion, resp. compound Poisson process. In the second part, we examine the price markup for hedging or liquidity costs, that customers have to pay when they buy structured products by replicating the payoff of ten different structured products and comparing their fair values with the prices actually traded. For this purpose we use parallel computing, a new technology that was not possible in the past. This allows us to use a calibrated Heston model to calculate the fair values of structured products over a longer period of time. Our results show that the markup that clients pay for these ten products ranges from 0.9%-2.9%. We can also observe that products with higher payoff levels, or better capital protection, require higher costs. We also identify market volatility as a statistically significant driver of the markup. In the third part, we show that the tracking error of an passively managed ETF can be significantly reduced through the use of optimization methods if the correlation factor between Index and ETF is used as target function. By finding optimal weights of a self-constructed bond- and the DAX- index, the number of constituents can be reduced significantly, while keeping the tracking error small. In the fourth part, we develop a hedging strategy based on fuel prices that can be applied primarily to the end users of petrol and diesel fuels. This enables the fuel consumer to buy fuel at a certain price for a certain period of time by purchasing a call option. To price the American call option we use a geometric Brownian motion combined with a binomial model

GPU-Based Parallel Particle Swarm Optimization Methods for Graph Drawing

Particle Swarm Optimization (PSO) is a population-based stochastic search technique for solving optimization problems, which has been proven to be effective in a wide range of applications. However, the computational efficiency on large-scale problems is still unsatisfactory. A graph drawing is a pictorial representation of the vertices and edges of a graph. Two PSO heuristic procedures, one serial and the other parallel, are developed for undirected graph drawing. Each particle corresponds to a different layout of the graph. The particle fitness is defined based on the concept of the energy in the force-directed method. The serial PSO procedure is executed on a CPU and the parallel PSO procedure is executed on a GPU. Two PSO procedures have different data structures and strategies. The performance of the proposed methods is evaluated through several different graphs. The experimental results show that the two PSO procedures are both as effective as the force-directed method, and the parallel procedure is more advantageous than the serial procedure for larger graphs

Evolutionary multi-objective workflow scheduling in Cloud

Cloud computing provides promising platforms for executing large applications with enormous computational resources to offer on demand. In a Cloud model, users are charged based on their usage of resources and the required quality of service (QoS) specifications. Although there are many existing workflow scheduling algorithms in traditional distributed or heterogeneous computing environments, they have difficulties in being directly applied to the Cloud environments since Cloud differs from traditional heterogeneous environments by its service-based resource managing method and pay-per-use pricing strategies. In this paper, we highlight such difficulties, and model the workflow scheduling problem which optimizes both makespan and cost as a Multi-objective Optimization Problem (MOP) for the Cloud environments. We propose an evolutionary multi-objective optimization (EMO)-based algorithm to solve this workflow scheduling problem on an infrastructure as a service (IaaS) platform. Novel schemes for problem-specific encoding and population initialization, fitness evaluation and genetic operators are proposed in this algorithm. Extensive experiments on real world workflows and randomly generated workflows show that the schedules produced by our evolutionary algorithm present more stability on most of the workflows with the instance-based IaaS computing and pricing models. The results also show that our algorithm can achieve significantly better solutions than existing state-of-the-art QoS optimization scheduling algorithms in most cases. The conducted experiments are based on the on-demand instance types of Amazon EC2; however, the proposed algorithm are easy to be extended to the resources and pricing models of other IaaS services.This work is supported by the National Science Foundation of China under Grand no. 61272420 and the Provincial Science Foundation of Jiangsu Grand no. BK2011022

Portfolio Optimization Using Evolutionary Algorithms

Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced AnalyticsPortfolio optimization is a widely studied field in modern finance. It involves finding the optimal balance between two contradictory objectives, the risk and the return. As the number of assets rises, the complexity in portfolios increases considerably, making it a computational challenge. This report explores the application of the Multi-Objective Evolutionary Algorithm based on Decomposition (MOEA/D) and Genetic Algorithm (GA) in the field of portfolio optimization. MOEA/D and GA have proven to be effective at finding portfolios. However, it remains unclear how they perform when compared to traditional approaches used in finance. To achieve this, a framework for portfolio optimization is proposed, using MOEA/D, and GA separately as optimization algorithms and Capital Asset Pricing Model (CAPM) and Mean-Variance Model as methods to evaluate portfolios. The proposed framework is able to produce weighted portfolios successfully. These generated portfolios were evaluated using a simulation with subsequent (unseen) prices of the assets included in the portfolio. The simulation was compared with well known portfolios in the same market and other market benchmarks (Security Market Line and Market Portfolio). The results obtained in this investigation exceeded expectation by creating portfolios that perform better than the market. CAPM and Mean-Variance Model, although they fail to model all the variables that affect the stock market, provide a simple valuation for assets and portfolios. MOEA/D using Differential Evolution operators and the CAPM model produced the best portfolios in this research. Work can still be done to accommodate more variables that can affect markets and portfolios, such as taxes, investment horizon and costs for transactions

A metaheuristic for the capacity-pricing problem in the car rental business

A atenção ao problema de capacidade-preço no aluguer de carros tem vindo a aumentar à medida que as empresas começaram a investir em ferramentas avançadas de apoio à decisão para essas questões críticas. Ao planear um período de vendas, uma empresa deve decidir o número e o tipo de veículos necessários na sua frota de forma a atender à procura. A procura pelos veículos para aluguer é altamente sensível ao preço e, portanto, as decisões de capacidade e preço estão intimamente ligadas. Além disso, como os produtos são alugados, a capacidade "volta". Isso cria uma ligação entre a capacidade, a mobilização da frota e outras ferramentas que permitem à empresa atender à procura, tal como upgrades, transferência de veículos entre locais ou aluguer temporário de veículos adicionais. O impacto da solução desse complexo problema no lucro de uma empresa já foi estimado e avaliado, mas quando são tidos em conta os problemas do mundo real, o tamanho e a complexidade do problema tornam os métodos existentes lentos e inadequados para fornecer soluções num prazo razoável. O principal objetivo deste projeto é então selecionar, projetar e desenvolver uma meta-heurística eficiente que forneça boas soluções em curtos períodos de tempo.The capacity-pricing problem in car rental has increasingly been stepping in the spotlight as companies began investing in advanced decision-support tools for these critical issues. When planning a sales period, a company must decide the number and type of vehicles needed in its fleet in order to meet demand. The demand for rental vehicles is particularly price-sensitive and therefore capacity and pricing decisions are closely linked. In addition, as the products are rented, the capacity "returns". This creates an association between capacity, fleet mobilization and other tools that allow the company to meet demand, such as upgrades, transferring vehicles between locations or the temporary leasing of additional vehicles. The impact of solving this complex problem on a company's profit has already been estimated and evaluated, but when real-world problems are taken into account, the size and complexity of the problem makes existing methods slow and inadequate to provide solutions within a reasonable time. Therefore, the main objective of this dissertation is then to select, design and develop an efficient metaheuristic that provides similar or better results than the ones obtained in the literature

Energy aware hybrid flow shop scheduling

Only if humanity acts quickly and resolutely can we limit global warming' conclude more than 25,000 academics with the statement of SCIENTISTS FOR FUTURE. The concern about global warming and the extinction of species has steadily increased in recent years

A neural network-based framework for financial model calibration

A data-driven approach called CaNN (Calibration Neural Network) is proposed to calibrate financial asset price models using an Artificial Neural Network (ANN). Determining optimal values of the model parameters is formulated as training hidden neurons within a machine learning framework, based on available financial option prices. The framework consists of two parts: a forward pass in which we train the weights of the ANN off-line, valuing options under many different asset model parameter settings; and a backward pass, in which we evaluate the trained ANN-solver on-line, aiming to find the weights of the neurons in the input layer. The rapid on-line learning of implied volatility by ANNs, in combination with the use of an adapted parallel global optimization method, tackles the computation bottleneck and provides a fast and reliable technique for calibrating model parameters while avoiding, as much as possible, getting stuck in local minima. Numerical experiments confirm that this machine-learning framework can be employed to calibrate parameters of high-dimensional stochastic volatility models efficiently and accurately.Comment: 34 pages, 9 figures, 11 table