Leandro Maciel

Evolving fuzzy systems for pricing fixed income options

During the recent decades, option pricing became an important topic in computational finance. The main issue is to obtain a model of option prices that reflects price movements observed in the real world. In this paper we address option pricing using an evolving fuzzy system model and Brazilian interest rate options pricing data. Evolving models are particularly appropriate since it gradually develops the model structure and its parameters from a stream of data. Therefore, evolving fuzzy models provide a higher level of system adaptation and learns the system dynamics continuously, an essential attribute in pricing option estimation. In particular, we emphasize the use of the evolving participatory learning method. The model suggested in this paper is compared against the traditional Black closed-form formula, artificial neural networks structures and alternative evolving fuzzy system approaches. Actual daily data used in the experiments cover the period from January 2003 to June 2008. We measure forecast performance of all models based on summary measures of forecast accuracy and statistical tests for competing models. The results show that the evolving fuzzy system model is effective especially for out-of-the-money options.

Enhanced evolving participatory learning fuzzy modeling: an application for asset returns volatility forecasting

Evolving participatory learning (ePL) modeling joins the concepts of participatory learning and evolving fuzzy systems. It uses data streams to continuously adapt the structure and functionality of fuzzy models. This paper suggests an enhanced version of the ePL approach, called ePL+, which includes both an utility measure to shrink rule bases, and a variable cluster radius mechanism to improve the cluster structure. These features are useful in adaptive fuzzy rule-based modeling to recursively construct local fuzzy models with variable zone of influence. Moreover, ePL+ extends ePL to multi-input, multi-output fuzzy system modeling. Computational experiments considering financial returns volatility modeling and forecasting are conducted to compare the performance of the ePL+ approach with state of the art fuzzy modeling methods and with GARCH modeling. The experiments use actual data of S&P 500 and Ibovespa stock market indexes. The results suggest that the ePL+ approach is highly capable to model volatility dynamics, in a robust, flexible, parcimonious, and autonomous way.

Recursive possibilistic fuzzy modeling

This paper suggests a recursive possibilistic approach for fuzzy modeling of time-varying processes. The approach is based on an extension of the possibilistic fuzzy c-means clustering and functional fuzzy rule-based modeling. Recursive possibilistic fuzzy modeling (rPFM) employs memberships and typicalities to cluster data. Functional fuzzy models uses affine functions in the fuzzy rule consequents. The parameters of the consequent functions are computed using the recursive least squares. Two classic benchmarks, Mackey-Glass time series and Box & Jenkins furnace data, are studied to illustrate the rPFM modeling and applicability. Data produced by a synthetic model with parameter drift is used to show the usefulness of rPFM to model time-varying processes. Performance of rPFM is compared with well established recursive fuzzy and neural fuzzy modeling and identification. The results show that recursive possibilistic fuzzy modeling produces parsimonious models with comparable or better accuracy than the alternative approaches.

MIMO evolving functional fuzzy models for interest rate forecasting

Forecasting the term structure of interest rates plays a crucial role in portfolio management, household finance decisions, business investment planning, and policy formulation. This paper proposes the use of evolving fuzzy inference systems for interest rate forecasting in the US and Brazilian markets. Evolving models provide a high level of system adaptation and learns the system dynamic continuously, which is essential for uncertain environments as fixed income markets. Besides the usefulness evaluation of evolving methods to forecast yields, this paper suggests the interest rate factors forecasting taking into account multi-input-multi-output (MIMO) evolving systems, which reduces computational time complexity and provides more accurate forecasts. Results based on mean squared forecast errors showed that MIMO evolving methods perform better than traditional benchmark for short and long-term maturities, for both fixed income markets evaluated.

Evolving hybrid neural fuzzy network for realized volatility forecasting with jumps

Equity assets volatility modeling and forecasting are fundamental in risk management, portfolio construction, financial decision making and derivative pricing. The use of realized volatility models outperforms GARCH and related stochastic volatility models in out-of-sample forecasting. Gains in performance can be achieved by separately considering volatility jump components. This paper suggests an evolving hybrid neural fuzzy network (eHFN) modeling approach for realized volatility forecasting with jumps. The eHFN model is nonlinear, time-raying, and uses neurons based on uninorms and sigmoidal activation functions in a feedforward network topology. The approach simultaneously chooses the number of hidden layer neurons and corresponding neural networks weights. This is of outmost importance in dynamic environments such as in volatility forecasting using data streams. Computational experiments were performed to evaluate and to compare the performance of eHFN with multilayer feedforward neural network, linear regression, and evolving fuzzy models representative of the current state of the art. The experiments use actual data from the main equity market indexes in global markets, namely, S&P 500 and Nasdaq (United States), FTSE (United Kingdom), DAX (Germany), IBEX (Spain) and Ibovespa (Brazil). The results show that the evolving hybrid neural fuzzy network is highly capable to model time-varying realized volatility with jumps.

Simplified evolving rule-based fuzzy modeling of realized volatility forecasting with jumps

Financial asset volatility modeling and forecasting play a central role in risk management, portfolio selection, and derivative pricing. The increasing availability of market data at intraday frequencies has led to the development of improved volatility measurements such as realized volatility. The literature has shown that simple realized volatility models outperform the popular GARCH and related stochastic volatility models in out-of-sample forecasting. Moreover, gains in performance are achieved by separately considering volatility jump components. This paper suggests a nonlinear approach for realized volatility forecasting with jumps using a simplified evolving fuzzy system based on the concept of data clouds. Such an approach offers an alternative nonparametric form of fuzzy rule antecedents that reflects the real data distribution without requiring any explicit aggregation operations or membership functions, thus providing a more autonomous and efficient algorithm. Empirical results based on the Brazilian stock market index Ibovespa reveal the high potential of the evolving cloud-based fuzzy approach in modeling time-varying realized volatility with jump components, outperforming a traditional benchmark based on a linear regression, as well as alternative evolving fuzzy systems.

Evolving Possibilistic Fuzzy Modeling for Realized Volatility Forecasting With Jumps

Equity asset volatility modeling and forecasting provide key information for risk management, portfolio construction, financial decision making, and derivative pricing. Realized volatility models outperform autoregressive conditional heteroskedasticity and stochastic volatility models in out-of-sample forecasting. Gain in forecasting performance is achieved when models comprise volatility jump components. This paper suggests evolving possibilistic fuzzy modeling to forecast realized volatility with jumps. The modeling approach is based on an extension of the possibilistic fuzzy c-means clustering and on functional fuzzy rule-based models. It employs memberships and typicalities to recursively update cluster centers. The evolving nature of the model allows adding or removing clusters using statistical distance-like criteria to update the model as dictated by input data. The possibilistic model improves robustness to noisy data and outliers, an essential requirement in financial markets volatility modeling and forecasting. Computational experiments and statistical analysis are done using value-at-risk estimates to evaluate and compare the performance of the evolving possibilistic fuzzy modeling with the heterogeneous autoregressive model, neural networks and current state-of-the-art evolving fuzzy models. The experiments use actual data from S&P 500 and Nasdaq (U.S.), FTSE (U.K.), DAX (Germany), IBEX (Spain), and Ibovespa (Brazil), major equity market indexes in global markets. The results show that the evolving possibilistic fuzzy model is highly efficient to model realized volatility with jumps in terms of forecasting accuracy.

MIMO evolving participatory learning fuzzy modeling

Evolving participatory learning fuzzy modeling is a flexible and effective method to handle real world complex systems. It is capable to process and learn from streams of data online, and is a natural candidate to find fuzzy rule-based model structures in dynamic environments. This paper extends the evolving participatory learning fuzzy approach for multi-input multi-output - MIMO - processes modeling and suggests the use of subtractive clustering (SC) algorithm to obtain an initial rule base when a priori knowledge is available. SC improves autonomy because it adds learning flexibility. Modeling uses the participatory learning fuzzy clustering algorithm to find rule antecedents, and the recursive MIMO least squares algorithm to estimate the parameters of the linear rules consequents. A novel application concerning modeling the term structure of interest rates and forecasting is also included. Computational results based on the US fixed income market data show that the MIMO evolving participatory learning fuzzy model describes the interest rate behavior accurately, revealing a high potential to forecast complex nonlinear dynamics in uncertain environments.

A Hybrid Fuzzy GJR-GARCH Modeling Approach for Stock Market Volatility Forecasting

Forecasting stock market returns volatility is a challenging task that has attracted the attention of market practitioners, regulators and academics in recent years. This paper proposes a Fuzzy GJR-GARCH model to forecast the volatility of S&P 500 and Ibovespa indexes. The model comprises both the concept of fuzzy inference systems and GJR-GARCH modeling approach in order to consider the principles of time-varying volatility, leverage effects and volatility clustering, in which changes are cataloged by similarity. Moreover, a differential evolution (DE) algorithm is suggested to solve the problem of Fuzzy GJR-GARCH parameters estimation. The results indicate that the proposed method offers significant improvements in volatility forecasting performance in comparison with GARCH-type models and with a current Fuzzy-GARCH model reported in the literature. Furthermore, the DE-based algorithm aims to achieve an optimal solution with a rapid convergence rate.

Estimating the Brazilian Central Bank’s Reaction Function by Fuzzy Inference System

A modelling strategy based on the application of fuzzy inference system is shown to provide a powerful and efficient method for the identification of non-linear and linear economic relationships. The procedure is particularly suitable for the estimation of ill-defined systems in which there is considerable uncertainty about the nature and range of key input variables. In addition, no prior knowledge is required about the form of the underlying relationships. Trend, cyclical and irregular components of the model can all be processed in a single pass. The potential benefits of the fuzzy logic approach are illustrated using a model to explain regime changes in Brazilian nominal interest rates. The results suggest that the relationships in the model are basically non-linear.