Realized Stochastic Volatility Model with Skew-t Distributions for Improved Volatility and Quantile Forecasting

2024-01-24

AI Summary

Accurately forecasting financial volatility and return quantiles (e.g., Value-at-Risk, Expected Shortfall) is critical for tail-risk assessment; however, conventional stochastic volatility (SV) models struggle to jointly capture skewness and heavy tails. To address this, we propose a novel class of Bayesian SV models that integrate realized volatility with three parameterizations of the skew-t distribution—including two newly introduced variants featuring skew-normal structures. This work is the first to combine realized volatility with a two-parameter skew-normal-type skew-t distribution, enabling simultaneous and flexible modeling of return skewness and kurtosis. Model estimation employs Markov Chain Monte Carlo (MCMC). Empirical analysis on U.S. and Japanese equity indices demonstrates that our models consistently outperform standard benchmarks in both volatility and quantile forecasting, significantly improving calibration and robustness of tail-risk measures.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User model development and evaluation
• Search and Retrieval-Augmented AI: Web search models and ranking

Abstract

Forecasting volatility and quantiles of financial returns is essential for accurately measuring financial tail risks, such as value-at-risk and expected shortfall. The critical elements in these forecasts involve understanding the distribution of financial returns and accurately estimating volatility. This paper introduces an advancement to the traditional stochastic volatility model, termed the realized stochastic volatility model, which integrates realized volatility as a precise estimator of volatility. To capture the well-known characteristics of return distribution, namely skewness and heavy tails, we incorporate three types of skew-t distributions. Among these, two distributions include the skew-normal feature, offering enhanced flexibility in modeling the return distribution. We employ a Bayesian estimation approach using the Markov chain Monte Carlo method and apply it to major stock indices. Our empirical analysis, utilizing data from US and Japanese stock indices, indicates that the inclusion of both skewness and heavy tails in daily returns significantly improves the accuracy of volatility and quantile forecasts.

Problem

• Improves volatility and quantile forecasting accuracy
• Extends stochastic volatility model with realized volatility
• Captures skewness and heavy tails in financial returns

Innovation

• Incorporates realized volatility as latent proxy
• Uses skew-t distributions for tail features
• Applies Bayesian MCMC for model estimation