Pricing Multivariate European Equity Option Using Gaussians Mixture Distributions and EVT-Based Copulas

In this article, we present an approach which allows taking into account the effect of extreme values in the modeling of financial asset returns and in the valorisation of associated options. Specifically, the marginal distribution of asset returns is modelled by a mixture of two Gaussian distributions. Moreover, we model the joint dependence structure of the returns using a copula function, the extremal one, which is suitable for our financial data, particularly the extreme values copulas. Applications are made on the Atos and Dassault Systems actions of the CAC40 index. Monte Carlo method is used to compute the values of some equity options such as the call on maximum, the call on minimum, the digital option, and the spreads option with the basket (Atos, Dassault systems) as underlying.

Calibrating and Simulating Copula Functions in Financial Applications

Copula functions can be utilized in financial applications to determine the dependence structure of the financial asset returns in the portfolio. Empirical evidence has proved the inadequacy of the multi-normal distribution, traditionally adopted to model the financial asset returns distribution. Copula functions can be employed in a flexible way for building efficient algorithms and to simulate a more adequate distribution of the financial assets. This paper aims to describe some simple statistical procedures currently employed to calibrate the copula functions to the financial market data. Furthermore, we present some useful methods for choosing which copula function better fits the real financial data. Also, some algorithms to simulate random variates from certain types of copula functions are illustrated. Finally, for illustration purposes, the previous procedures described are applied to two Italian equities. In particular, we show how to generate efficient Monte Carlo scenarios of equity log-returns in the bivariate case using different types of copula functions.

Machine learning applied in the stock market through the Moving Average Convergence Divergence (MACD) indicator

The implementation of tools such as Genetic Algorithms has not been exploited for asset price prediction despite their power, robustness, and potential application in the stock market. This paper aims to fill the gap existing in the literature on the use of Genetic Algorithms for predicting asset pricing of investment strategies into stock markets and investigate its advantages over its peers Buy & Hold and traditional technical analysis. The Genetic Algorithms strategy applied to the MACD was carried out in two different validation periods and sought to optimize the parameters that generate the buy-sell signals. The performance between the machine learning-based approach, technical analysis with the MACD and B&H was compared. The results suggest that it is possible to find optimal values of the technical indicator parameters that result in a higher return on investment through Genetic Algorithms, beating the traditional technical analysis and B&H by around 4%. This study offers a new insight for practitioners, traders, and finance researchers to take advantage of Genetic Algorithms for trading rules application in forecasting financial asset returns under a more efficient and robust methodology based on historical data analysis.

PERAMALAN VOLATILITAS SAHAM MENGGUNAKAN MODEL EXPONENTIAL GARCH DAN THRESHOLD GARCH

In financial data there is asymmetric volatility, which denotes the different movements on conditional volatility of increase and decrease financial asset returns. The exponential GARCH and threshold GARCH models can be used to capture asymmetric volatility, called leverage effect. The aim of this research is to determine the best model between exponential GARCH and threshold GARCH models, and to know the results of forecasting volatility the LQ-45 stock index using the best model. The research showed that the best model to predicting volatility is EGARCH(2,1), because it has the smallest AIC value compared to other models. Then forecasting volatility of the LQ-45 stock index using EGARCH(2,1) showed that volatility increase from the first period until fourteenth period, this means that it has high volatility.

Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo

The Copula Multivariate GARCH (CMGARCH) model is based on a dynamic copula function with time-varying parameters. It is particularly suited for modelling dynamic dependence of non-elliptically distributed financial returns series. The model allows for capturing more flexible dependence patterns than a multivariate GARCH model and also generalizes static copula dependence models. Nonetheless, the model is subject to a number of parameter constraints that ensure positivity of variances and covariance stationarity of the modeled stochastic processes. As such, the resulting distribution of parameters of interest is highly irregular, characterized by skewness, asymmetry, and truncation, hindering the applicability and accuracy of asymptotic inference. In this paper, we propose Bayesian analysis of the CMGARCH model based on Constrained Hamiltonian Monte Carlo (CHMC), which has been shown in other contexts to yield efficient inference on complicated constrained dependence structures. In the CMGARCH context, we contrast CHMC with traditional random-walk sampling used in the previous literature and highlight the benefits of CHMC for applied researchers. We estimate the posterior mean, median and Bayesian confidence intervals for the coefficients of tail dependence. The analysis is performed in an application to a recent portfolio of S&P500 financial asset returns.

Investigating Causal Linkages Between International Stock Markets in Hungary and Austria in Terms of Economic Globalization

The main aim of this chapter is to examine causal linkages between selected stock markets of Hungary and Austria in terms of economic globalization. The sample databases cover a long time period from January 2000 to December 2013. The selected ATX stock index represents Austria index, while BUX represents the main stock index of Hungary. The empirical findings highlighted that stock market in Hungary is significantly more volatile and provides comparatively higher investing opportunities for financial asset returns. There are strong evidences of no casual linkages between selected markets of Austria and Hungary. The econometric analysis includes BDS and Granger causality tests. The results are classified in a comparative manner. This book chapter will support decision makings on escalation ratios depending on the international financial market transmitting patterns.

An EM algorithm for singular Gaussian mixture models

In this paper, we introduce finite mixture models with singular multivariate normal components. These models are useful when the observed data involves collinearities, that is when the covariance matrices are singular. They are also useful when the covariance matrices are ill-conditioned. In the latter case, the classical approaches may lead to numerical instabilities and give inaccurate estimations. Hence, an extension of the Expectation Maximization algorithm, with complete proof, is proposed to derive the maximum likelihood estimators and cluster the data instances for mixtures of singular multivariate normal distributions. The accuracy of the proposed algorithm is then demonstrated on the grounds of several numerical experiments. Finally, we discuss the application of the proposed distribution to financial asset returns modeling and portfolio selection.