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In this paper we present a novel methodology to perform Bayesian model selection in linear models with heavy-tailed distributions. We consider a finite mixture of distributions to model a latent variable where each component of the mixture corresponds to one possible model within the symmetrical class of normal independent distributions. Naturally, the Gaussian model is one of the possibilities. This allows for a simultaneous analysis based on the posterior probability of each model. Inference is performed via Markov chain Monte Carlo - a Gibbs sampler with Metropolis-Hastings steps for a class of parameters. Simulated examples highlight the advantages of this approach compared to a segregated analysis based on arbitrarily chosen model selection criteria. Examples with real data are presented and an extension to censored linear regression is introduced and discussed.

The application of stochastic volatility (SV) models in the option pricing literature usually assumes that the market has sufficient option data to calibrate the model’s risk-neutral parameters. When option data are insufficient or unavailable, market practitioners must estimate the model from the historical returns of the underlying asset and then transform the resulting model into its risk-neutral equivalent. However, the likelihood function of an SV model can only be expressed in a high-dimensional integration, which makes the estimation a highly challenging task. The Bayesian approach has been the classical way to estimate SV models under the data-generating (physical) probability measure, but the transformation from the estimated physical dynamic into its risk-neutral counterpart has not been addressed. Inspired by the generalized autoregressive conditional heteroskedasticity (GARCH) option pricing approach by Duan in 1995, we propose an SV model that enables us to simultaneously and conveniently perform Bayesian inference and transformation into risk-neutral dynamics. Our model relaxes the normality assumption on innovations of both return and volatility processes, and our empirical study shows that the estimated option prices generate realistic implied volatility smile shapes. In addition, the volatility premium is almost flat across strike prices, so adding a few option data to the historical time series of the underlying asset can greatly improve the estimation of option prices.

We describe two parametric classification tree methods, which allow formal selection of a member of a class of generalised distributions. In the paper we consider generalised Beta distributions for non-negative random variables and the generalised skew-Student distribution for random variables distributed on the real line. We introduce a class of symmetric generalised multivariate Student distributions, members of which may also be selected using the classification trees. We present two versions of the parametric classification tree: specific to general and general to specific. We apply the classification methods to daily returns on stocks from a selection of 15 major, mid-cap and emerging markets. The results show that the majority of return distributions follow Student's t, but that a non-negligible minority follow a symmetric generalised Student distribution. We confirm a well-known stylised fact about skewness: it tends not to be persistent. By contrast, kurtosis is persistent. Using the symmetric generalised multivariate Student distribution, we present a risk management study based on efficient portfolios constructed from UKFTSE250 stocks and specifically concerned with the computation of value at risk. The case study demonstrates that the model selection procedures based on the classification trees lead to more accurate computation of VaR than those based on the normal distribution or on non-parametric approaches. The study also shows that the normal distribution may be used for VaR computations for larger portfolios when the holding period is longer.

Cardiac disease is one of the major causes for death all over the world. Heart rate variability (HRV) is a significant parameter that used in assessing Autonomous Nervous System (ANS) activity. Generally, the 2D Poincare′ plot and 3D Poincaré plot of the HRV signals reflect the effect of different external stimuli on the ANS. Meditation is one of such external stimulus, which has different techniques with different types of effects on the ANS. Chinese Chi-meditation and Kundalini yoga are two different effective meditation techniques. The current work is interested with the analysis of the HRV signals under the effect of these two based on meditation techniques. The 2D and 3D Poincare′ plots are generally plotted by fitting respectively an ellipse/ellipsoid to the dense region of the constructed Poincare′ plot of HRV signals. However, the 2D and 3D Poincaré plots sometimes fail to describe the proper behaviour of the system. Thus in this study, a three-dimensional frequency-delay plot is proposed to properly distinguish these two famous meditation techniques by analyzing their effects on ANS. This proposed 3D frequency-delay plot is applied on HRV signals of eight persons practicing same Chi-meditation and four other persons practising same Kundalini yoga. To substantiate the result for larger sample of data, statistical Student t-test is applied, which shows a satisfactory result in this context. The experimental results established that the Chi-meditation has large impact on the HRVcompared to the Kundalini yoga.