Neural network based models for value-at-risk analysis with applications in emerging markets

Abstract

Value-at-Risk (VaR) is a highly comprehensive risk measure which summarises the overall market risk exposure throughout one single quantitative parameter. In recent years it has become the most widely used technique for measuring future expected risk in both ¯nancial and commercial institutions. However, despite its conceptual simplicity, VaR estimation is actually a very tough statistical proposition and, un- fortunately, none of the traditional methods has achieved convincing results. The main reason is that they overlook the stylised facts of ¯nancial time series, such as heavy-tailedness, skewness, heteroskedasticity, etc., and then misspecify model as- sumptions. For instance, the normal VaR method might seriously underestimate VaR in the presence of fatter tails than predicted by a normal distribution. The GARCH model families based on conditional volatility achieve some degree of success, but the problem of heavy-tailedness still remains. On the other hand, the historical simulation method has gained popularity in practice because it is free from the non-normality problem. Nevertheless, raw returns cannot be used in the simulation unless they are independently and identically distributed. Unfortunately, such a characteristic is seldom found in ¯nancial time series. These di±culties make it attractive to consider arti¯cial neural network (ANN) as a new alternative modelling technology to more traditional econometric and sta- tistical approaches. ANN can approximate any function up to any desired degree of accuracy. However, in the presence of stochastic noise, this ability as a univer- sal function approximator makes the speci¯cation of the neural network model very di±cult. Despite the huge amount of theoretical and applied research on neural net- works, there is little in terms of a model building paradigm. In addition, even after an ANN is ¯tted, the model o®ers no information on the relative importance of the input variables or description of the data generating process. This study ¯lls the gap by developing new methodologies based on ANN for VaR modelling. Applying ANN in VaR estimation generates at least two bene¯ts. First, ANN models can better capture the nonlinear patterns of ¯nancial time series. Sec- ond, one can make the least assumptions about the underlying distributions. In this thesis the usefulness of ANN is investigated from several aspects. For univariate time series analysis, both single and hybrid ANN models are constructed. In a single ANN approach, a statistical procedure for model selection is developed. The statistical ANN reduces the need to ¯t a comprehensive set of models when compared to the ad hoc nature of choosing neural network architecture. Also, it can help the user better understand the data generating process. Experiment results show that the statistical ANN outperforms other forecasting methods on stock index return series. In a hybrid ANN approach, econometric models (i.e. ARMA and GARCH) and ANN are combined for VaR estimation. Two ANN models are built to estimate the conditional mean and conditional volatility respectively. The hybrid model achieves better e±ciency in selecting input variables because they are newly created by time series models. The performance of traditional time series models could be further enhanced by the forecasting power of ANN models. Empirical study shows that the hybrid model can improve the predictive power in the framework of both accuracy and reliability. For multivariate time series, a novel approach is proposed based on Independent Component Analysis (ICA) and Mixture Density Network (MDN). Speci¯cally, the original data is ¯rst transformed into separate signals which are in- dependent from each other through ICA. Then using MDN their conditional density functions are ¯tted, from which the joint distribution function of the multivariate time series could be derived. Finally VaR estimates are calculated based on Monte Carlo simulation. This method successfully circumvents the di±cult correlation issue within multivariate time analysis and it achieves superior performance compared to traditional EWMA and MVGARCH techniques in empirical study. As a whole, the proposed ANN models could be regarded as alternative approaches to estimate VaR which outperforms traditional methods.