Calibrating Option Pricing Models with Heuristics

Calibrating option pricing models to market prices often leads to optimisation problems to which standard methods (like such based on gradients) cannot be applied. We investigate two models: Heston’s stochastic volatility model, and Bates’s model which also includes jumps. We discuss how to price options under these models, and how to calibrate the parameters of the models with heuristic techniques.

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)

A long-term swarm intelligence hedging tool applied to electricity markets

This paper proposes a swarm intelligence long-term hedging tool to support electricity producers in competitive electricity markets. This tool investigates the long-term hedging opportunities available to electric power producers through the use of contracts with physical (spot and forward) and financial (options) settlement. To find the optimal portfolio the producer risk preference is stated by a utility function (U) expressing the trade-off between the expectation and the variance of the return. Variance estimation and the expected return are based on a forecasted scenario interval determined by a long-term price range forecast model, developed by the authors, whose explanation is outside the scope of this paper. The proposed tool makes use of Particle Swarm Optimization (PSO) and its performance has been evaluated by comparing it with a Genetic Algorithm (GA) based approach. To validate the risk management tool a case study, using real price historical data for mainland Spanish market, is presented to demonstrate the effectiveness of the proposed methodology

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

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

Pseudo-analytical solutions for stochastic options pricing using monte carlo simulation and breeding PSO-trained neural networks

We introduce a novel methodology for pricing options which uses a particle swarm trained neural network to approximate the solution of a stochastic pricing model. The performance of the network is compared to the analytical solution for European call options and the errors shown statistically comparable to Monte Carlo pricing. The work provides a proof of concept that can be extended to more complex options for which no analytical solutions exist, the pricing method presented here delivering results several orders of magnitude faster than the Monte Carlo pricing method used by default in the financial industry

A decision-support system based on particle swarm optimization for multiperiod hedging in electricity markets

This paper proposes a particle swarm optimization (PSO) approach to support electricity producers for multiperiod optimal contract allocation. The producer risk preference is stated by a utility function (U) expressing the tradeoff between the expectation and variance of the return. Variance estimation and expected return are based on a forecasted scenario interval determined by a price range forecasting model developed by the authors. A certain confidence level is associated to each forecasted scenario interval. The proposed model makes use of contracts with physical (spot and forward) and financial (options) settlement. PSO performance was evaluated by comparing it with a genetic algorithm-based approach. This model can be used by producers in deregulated electricity markets but can easily be adapted to load serving entities and retailers. Moreover, it can easily be adapted to the use of other type of contracts