Paper: arXiv 2404.13986

Authors: Daichi Hiraki, Siddhartha Chib, Yasuhiro Omori

Abstract

In this paper we consider the simulation-based Bayesian analysis of stochastic volatility in mean (SVM) models. Extending the highly efficient Markov chain Monte Carlo mixture sampler for the SV model proposed in Kim et al. (1998) and Omori et al. (2007), we develop an accurate approximation of the non-central chi-squared distribution as a mixture of thirty normal distributions. Under this mixture representation, we sample the parameters and latent volatilities in one block. We also detail a correction of the small approximation error by using additional Metropolis-Hastings steps. The proposed method is extended to the SVM model with leverage. The methodology and models are applied to excess holding yields and S&P500 returns in empirical studies, and the SVM models are shown to outperform other volatility models based on marginal likelihoods.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 7.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a mathematically sophisticated extension of the MCMC mixture sampler to Stochastic Volatility in Mean (SVM) models using a 30-component normal mixture. It features strong empirical validation on real-world asset returns, outperforming baseline models in marginal likelihood comparisons.

Research Flowchart

  flowchart TD
    A[Research Goal: Efficient Bayesian Analysis of Stochastic Volatility in Mean SVM Models] --> B[Methodology: Approximate Non-Central Chi-Squared Distribution using 30-Normal Mixture]
    B --> C[Data Inputs: Excess Holding Yields & S&P500 Returns]
    C --> D[Computational Engine: Block Sampler with MCMC Mixture Sampling & MH Correction Steps]
    D --> E[Extension: SVM Model with Leverage Effects]
    E --> F[Key Outcome: Superior Fit & Marginal Likelihood vs Other Volatility Models]

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0 of 36 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.