Stochastic Volatility Models for Asset Returns with Leverage, Skewness and Heavy-Tails via Scale Mixture

We propose and estimate a new class of equity return models that incorporate scale mixtures of the skew-normal distribution for the error distribution into the standard stochastic volatility framework. The main advantage of our models is that they can simultaneously accommodate the skewness, heavy-tailedness, and leverage effect of equity index returns observed in the data. The proposed models are flexible and parsimonious, and include many asymmetrically heavy-tailed error distributions — such as skew-t and skew-slash distributions — as special cases. We estimate a variety of specifications of our models using the Bayesian Markov Chain Monte Carlo method, with data on daily returns of the S&P 500 index over 1987–2009. We find that the proposed models outperform existing ones of index returns.

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Bayesian Analysis of Additive Factor Volatility Models with Heavy-Tailed Distributions with Specific Reference to S&P 500 and SSEC Indices1

10.5772/intechopen.93685 ◽

2020 ◽

Author(s):

Verda Davasligil Atmaca ◽

Burcu Mestav

Keyword(s):

Normal Distribution ◽

Stochastic Volatility ◽

Specific Reference ◽

Financial Return ◽

Heavy Tailed Distributions ◽

Volatility Models ◽

Heavy Tailed Distribution ◽

Error Distributions ◽

Multivariate Stochastic Volatility ◽

Heavy Tailed

The distribution of the financial return series is unsuitable for normal distribution. The distribution of financial series is heavier than the normal distribution. In addition, parameter estimates obtained in the presence of outliers are unreliable. Therefore, models that allow heavy-tailed distribution should be preferred for modelling high kurtosis. Accordingly, univariate and multivariate stochastic volatility models, which allow heavy-tailed distribution, have been proposed to model time-varying volatility. One of the multivariate stochastic volatility (MSVOL) model structures is factor-MSVOL model. The aim of this study is to investigate the convenience of Bayesian estimation of additive factor-MSVOL (AFactor-MSVOL) models with normal, heavy-tailed Student-t and Slash distributions via financial return series. In this study, AFactor-MSVOL models that allow normal, Student-t, and Slash heavy-tailed distributions were estimated in the analysis of return series of S&P 500 and SSEC indices. The normal, Student-t, and Slash distributions were assigned to the error distributions as the prior distributions and full conditional distributions were obtained by using Gibbs sampling. Model comparisons were made by using DIC. Student-t and Slash distributions were shown as alternatives of normal AFactor-MSVOL model.

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Modeling of Stochastic Volatility to Validate IDR Anchor Currency

Gadjah Mada International Journal of Business ◽

10.22146/gamaijb.26006 ◽

2018 ◽

Vol 20 (2) ◽

pp. 165 ◽

Cited By ~ 4

Author(s):

Didit Budi Nugroho ◽

Tundjung Mahatma ◽

Yulius Pratomo

Keyword(s):

Stochastic Volatility ◽

Foreign Currency ◽

Foreign Exchange Rate ◽

Stochastic Volatility Models ◽

Daily Data ◽

Volatility Models ◽

Error Distributions ◽

T Distribution ◽

Negative Relationships ◽

Daily Returns

This study aims to assess the performance of stochastic volatility models for their estimation of foreign exchange rate returns' volatility using daily data from Bank Indonesia (BI). The model is then applied to validate the anchor currency of Indonesian rupiah (IDR). Two stylized facts are incorporated into the models: A correlation between the previous returns and their conditional variance, and return errors following four different error distributions namely Normal, Student-t, non-central Student-t, and generalized hyperbolic skew Student-t. The analysis is based on the application of daily returns data from nine foreign currency selling rates to IDR from 2010 to 2015, including the AUD, CHF, CNY, EUR, GBP, JPY, MYR, SGD, and USD. The main results are: (1) Mixed evidence of positive and negative relationships between the return and its variance were found, especially significant correlations being found for the IDR/AUD, IDR/CHF, IDR/JPY, IDR/SGD, and IDR/USD returns series; (2) the model with the generalized hyperbolic skew Student's t-distribution specification for the returns error provides the best performance; and (3) anchoring the IDR to established hard currencies is more appropriate than anchoring it to other currencies.

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Multivariate fractional phase–type distributions

Fractional Calculus and Applied Analysis ◽

10.1515/fca-2020-0071 ◽

2020 ◽

Vol 23 (5) ◽

pp. 1431-1451 ◽

Cited By ~ 1

Author(s):

Hansjörg Albrecher ◽

Martin Bladt ◽

Mogens Bladt

Keyword(s):

Tail Dependence ◽

Jump Process ◽

Multivariate Distributions ◽

New Class ◽

Natural Time ◽

Special Cases ◽

Phase Type ◽

Phase Type Distributions ◽

Markovian Jump Process ◽

Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

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