A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model.

Area of Science:

• Financial econometrics
• Statistical modeling
• Probability theory

Background:

• Traditional stochastic volatility (SV) models often assume global heavy-tailed distributions.
• Existing models may not adequately capture the nuanced characteristics of financial time series, such as localized kurtosis and fat tails.
• There is a need for more flexible distributions in financial volatility modeling.

Purpose of the Study:

• To introduce a novel scale mixture of normal distribution with local leptokurticity and fat-tailedness (LLFT).
• To integrate the LLFT distribution into a stochastic volatility (SV) model, creating the LLFT-SV model.
• To provide a flexible alternative for financial volatility modeling, especially for non-standard financial data.

Main Methods:

• Development of a novel locally leptokurtic and fat-tailed (LLFT) distribution.
• Incorporation of the LLFT distribution into a basic stochastic volatility (SV) model.
• Application of a Bayesian statistical framework with Markov Chain Monte Carlo (MCMC) methods for parameter estimation and latent variable sampling.

Main Results:

• The LLFT-SV model demonstrates validity in modeling financial time series with repeating zero returns and typical index data (S&P 500, DAX).
• The LLFT-SV model significantly outperforms a standard t-SV model in density forecasting for non-standard financial data.
• The proposed LLFT distribution shows potential for broader applications in advanced SV models.

Conclusions:

• The LLFT-SV model offers a superior and flexible approach to financial volatility modeling.
• The LLFT distribution effectively addresses limitations of globally heavy-tailed distributions in capturing specific financial data characteristics.
• The developed Bayesian framework and MCMC methods provide effective tools for analyzing the LLFT-SV model.