Ordinary differential equations of the first order linear differential equations complex numbers and linear algebra simultaneous linear differential equations numerical methods the descriptive theory of nonlinear differential equations mechanical systems and electric circuits Fourier series Fourier integrals and Fourier transforms the Laplace transformation partial differential equations Bessel functions and Legendre polynomials applications and further properties of matrices vector analysis the calculus of variations analytic functions of a complex variable infinite series in the complex plane the theory of residues conformal mapping.

Advanced Engineering Mathematics. By C. R. Wylie. Pp. xiv, 813. 1966. (McGraw-Hill.)

In this paper, we present a new strategy for pricing average value options, i.e. options whose payoff depends on the average price of the underlying asset over a fixed period leading up to the maturity date. Such options are of particular interest and importance for thinly-traded assets (e.g. crude oil), since price manipulation is inhibited, and both the investor and issuer enjoy a welcome degree of protection from the vagaries of the market. These options are often implicit in a bond contract, although they also appear in a straightforward form. Our results suggest that the price of an average-value option will always be lower than that of a standard European option. Our pricing strategy involves Monte Carlo simulation with variance reduction elements and offers an enhanced pricing method to both arbitragers and hedgers, as well as to the issuers of such bonds.

A Pricing Method for Options Based on Average Asset Values

A data mining procedure to forecast daily stock market return is proposed.The raw data includes 60 financial and economic features over a 10-year period.Combining ANNs with PCA gives slightly higher classification accuracy.Combining ANNs with PCA provides significantly higher risk-adjusted profits. In financial markets, it is both important and challenging to forecast the daily direction of the stock market return. Among the few studies that focus on predicting daily stock market returns, the data mining procedures utilized are either incomplete or inefficient, especially when a large amount of features are involved. This paper presents a complete and efficient data mining process to forecast the daily direction of the S&P 500 Index ETF (SPY) return based on 60 financial and economic features. Three mature dimensionality reduction techniques, including principal component analysis (PCA), fuzzy robust principal component analysis (FRPCA), and kernel-based principal component analysis (KPCA) are applied to the whole data set to simplify and rearrange the original data structure. Corresponding to different levels of the dimensionality reduction, twelve new data sets are generated from the entire cleaned data using each of the three different dimensionality reduction methods. Artificial neural networks (ANNs) are then used with the thirty-six transformed data sets for classification to forecast the daily direction of future market returns. Moreover, the three different dimensionality reduction methods are compared with respect to the natural data set. A group of hypothesis tests are then performed over the classification and simulation results to show that combining the ANNs with the PCA gives slightly higher classification accuracy than the other two combinations, and that the trading strategies guided by the comprehensive classification mining procedures based on PCA and ANNs gain significantly higher risk-adjusted profits than the comparison benchmarks, while also being slightly higher than those strategies guided by the forecasts based on the FRPCA and KPCA models.

Forecasting daily stock market return using dimensionality reduction

Forecasting energy consumption using ensemble ARIMA-ANFIS hybrid algorithm

Review of swarm intelligence-based feature selection methods

Application of Japanese Candlestick for data transformation and attribute generation.Developing wrapper ANFIS-ICA method.Stock market timing and feature selection with wrapper ANFIS-ICA.Comparison of results with base study and other wrapper algorithms. Predicting stock prices is an important objective in the financial world. This paper presents a novel forecasting model for stock markets on the basis of the wrapper ANFIS (Adaptive Neural Fuzzy Inference System)-ICA (Imperialist Competitive Algorithm) and technical analysis of Japanese Candlestick. Two approaches of Raw-based and Signal-based are devised to extract the model's input variables with 15 and 24 features, respectively. The correct predictions percentages for periods of 1-6 days with the total number of buy and sell signals are considered as output variables. In proposed model, the ANFIS prediction results are used as a cost function of wrapper model and ICA is used to select the most appropriate features. This novel combination of feature selection not only takes advantage of ICA optimization swiftness, but also the ANFIS prediction accuracy. The emitted buy and sell signals of the model revealed that Signal databases approach gets better results with 87% prediction accuracy and the wrapper features selection obtains 12% improvement in predictive performance regarding to the base study. In addition, since the wrapper-based feature selection models are considerably more time-consuming, our presented wrapper ANFIS-ICA algorithm's results have superiority in time decreasing as well as increasing prediction accuracy as compared to other algorithms such as wrapper Genetic algorithm (GA).

Wrapper ANFIS-ICA method to do stock market timing and feature selection on the basis of Japanese Candlestick

Two alternative approaches for selecting performance measures in data envelopment analysis

A smoothing filter based on fuzzy transform

Financial risk modeling and management are very important and challenging tasks for financial institutions’ quantitative units. Owing to the complex nature of portfolios, and given recent financial market developments, contemporary research is focused on tail modeling and/or dependency modeling. The main objective of this paper is to examine the potential contribution of Levy-based subordinated models coupled by ordinary elliptical copula functions to the estimation of the distribution pattern of international equity portfolios. The authors observe that the subordinated NIG model coupled with the Student copula function, and in particular its combined estimation version, allows them to get very good estimates of portfolio risk measures.

International equity portfolio risk modeling: the case of the NIG model and ordinary copula functions

Option pricing models are an important part of financial markets worldwide. The PDE formulation of these models leads to analytical solutions only under very strong simplifications. For more general models the option price needs to be evaluated by numerical techniques. First, based on an ideal pure diffusion process for two risky asset prices with an additional path-dependent variable for continuous arithmetic average, we present a general form of PDE for pricing of Asian option contracts on two assets. Further, we focus only on one subclass—Asian options with floating strike—and introduce the concept of the dimensionality reduction with respect to the payoff leading to PDE with two spatial variables. Then the numerical option pricing scheme arising from the discontinuous Galerkin method is developed and some theoretical results are also mentioned. Finally, the aforementioned model is supplemented with numerical results on real market data.

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Tomáš Tichý

Papers

Wrapper ANFIS-ICA method to do stock market timing and feature selection on the basis of Japanese Candlestick

Two alternative approaches for selecting performance measures in data envelopment analysis

A smoothing filter based on fuzzy transform

International equity portfolio risk modeling: the case of the NIG model and ordinary copula functions

DG method for numerical pricing of multi-asset Asian options—The case of options with floating strike