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

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 (e.g., 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. We argue that an alternative approach is the application of optimisation heuristics like Simulated Annealing or Genetic Algorithms. These methods have been shown to be capable of handling non-convex optimisation problems with all kinds of constraints. To motivate the use of such techniques in finance, we present 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, we then describe 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. We show, again for the example from portfolio selection, how this random character of the solutions can be exploited to inform the distribution of computation

Application of Guided Local Search (GLS) in Portfolio Optimization

Portfolio optimization is a major activity in any operating business. Conventional portfolio optimization research makes simplifying assumptions; for example, they assume no constraint in how many assets one holds (cardinality constraint). They also assume no minimum and maximum holding sizes (holding size constraint). Once these assumptions are relaxed, conventional methods become inapplicable, and hence new methods are needed to tackle this challenge. Threshold Accepting is an established algorithm in the extended portfolio optimization problem. In this paper, an algorithm called Guided Local Search (GLS) is applied using an accurate and efficient designed hill climbing algorithm, named HC-C-R. GLS sitting on HC-C-R is for the purpose of solving the extended portfolio optimization problem. The improved hill climbing algorithm is tested on standard portfolio optimization problem. Results are compared (benchmarked) with the Threshold Accepting (TA) algorithm, a well-known algorithm for portfolio optimization and are also compared with its original algorithm HC-C-R. Results show that GLS sitting on HC-C-R is more effective than HC-C-R and the algorithms are more effective than TA. Keywords: Portfolio Optimization; Algorithm; Guided Local Search; GLS, Threshold Acceptanc

Efficient and Simple Heuristic Algorithm for Portfolio Optimization

Markowitz model considers what is termed as standard portfolio optimization. The portfolio optimization problem is a problem which based on asset allocation and diversification for maximum return with minimum risk. Thus, the standard portfolio optimization problem happens when the constraints considered are budget and no-short selling. In reality however, portfolio optimization has realistic constraints to be incorporated such as holding sizes, cardinality and transaction cost. When realistic constraints are added into portfolio optimization problem, it becomes too complex to be solved by standard optimization methods which in this case turns to be an extended portfolio optimization problem. Markowitz solution and the standard methods like quadratic programming become inapplicable. With such limitation, heuristic methods are usually used to deal with this extended portfolio optimization problem. Therefore, this paper proposes a heuristic algorithm for the extended portfolio optimization problem. It is a hill climbing algorithm named Hill Climbing Simple (HC-S) which is then validated by solving the standard Markowitz model. In fact, the proposed algorithm is benchmarked with the quadratic programming (QP), which is a standard method. By benchmarking HC-S with QP, it showed that HC-S can attains similar accurate solutions. Also, HC-S demonstrated to be more effective and efficient than threshold accepting (TA), an established algorithm for portfolio optimization since HC-S find solutions with significant higher objective value and require less computing time as compared to standard methods

SWIFT Calibration of the Heston model

In the present work, the SWIFT method for pricing European options is extended to Heston model calibration. The computation of the option price gradient is simplified thanks to the knowledge of the characteristic function in closed form. The proposed calibration machinery appears to be extremely fast, in particular for a single expiry and multiple strikes, outperforming the state-of-the-art method we compare it with. Further, the a priori knowledge of SWIFT parameters makes a reliable and practical implementation of the presented calibration method possible. A wide range of stress, speed and convergence numerical experiments is carried out, with deep in-the-money, at-the-money and deep out-of-the-money options for very short and very long maturitie

Numerical estimates of risk factors contingent on credit ratings

AbstractAssuming a favorable or an adverse outcome for every combination of a credit class and an industry sector, a binary string, termed as a macroeconomic scenario, is considered. Given historical transition counts and a model for dependence among credit-rating migrations, a probability is assigned to each of the scenarios by maximizing a likelihood function. Applications of this distribution in financial risk analysis are suggested. Two classifications are considered: 7 non-default credit classes with 6 industry sectors and 2 non-default credit classes with 12 industry sectors. We propose a heuristic algorithm for solving the corresponding maximization problems of combinatorial complexity. Probabilities and correlations characterizing riskiness of random events involving several industry sectors and credit classes are reported

Applying Dynamic Training-Subset Selection Methods Using Genetic Programming for Forecasting Implied Volatility

International audienceVolatility is a key variable in option pricing, trading, and hedging strategies. The purpose of this article is to improve the accuracy of forecasting implied volatility using an extension of genetic programming (GP) by means of dynamic training-subset selection methods. These methods manipulate the training data in order to improve the out-of-sample patterns fitting. When applied with the static subset selection method using a single training data sample, GP could generate forecasting models, which are not adapted to some out-of-sample fitness cases. In order to improve the predictive accuracy of generated GP patterns, dynamic subset selection methods are introduced to the GP algorithm allowing a regular change of the training sample during evolution. Four dynamic training-subset selection methods are proposed based on random, sequential, or adaptive subset selection. The latest approach uses an adaptive subset weight measuring the sample difficulty according to the fitness cases' errors. Using real data from S&P500 index options, these techniques are compared with the static subset selection method. Based on mean squared error total and percentage of non-fitted observations, results show that the dynamic approach improves the forecasting performance of the generated GP models, especially those obtained from the adaptive-random training-subset selection method applied to the whole set of training samples

A survey on financial applications of metaheuristics

Modern heuristics or metaheuristics are optimization algorithms that have been increasingly used during the last decades to support complex decision-making in a number of fields, such as logistics and transportation, telecommunication networks, bioinformatics, finance, and the like. The continuous increase in computing power, together with advancements in metaheuristics frameworks and parallelization strategies, are empowering these types of algorithms as one of the best alternatives to solve rich and real-life combinatorial optimization problems that arise in a number of financial and banking activities. This article reviews some of the works related to the use of metaheuristics in solving both classical and emergent problems in the finance arena. A non-exhaustive list of examples includes rich portfolio optimization, index tracking, enhanced indexation, credit risk, stock investments, financial project scheduling, option pricing, feature selection, bankruptcy and financial distress prediction, and credit risk assessment. This article also discusses some open opportunities for researchers in the field, and forecast the evolution of metaheuristics to include real-life uncertainty conditions into the optimization problems being considered.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (TRA2013-48180-C3-P, TRA2015-71883-REDT), FEDER, and the Universitat Jaume I mobility program (E-2015-36)