Stochastic Volatility in Mean Models with Heavy Tails: A Fast Approximate Bayesian Inference Using Hidden Markov Models

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Highly relevant for quantitative trading applications involving volatility modeling, risk management, and VaR estimation. The SVM framework captures the volatility feedback effect important for understanding return-volatility dynamics. The 10x speedup over MCMC makes real-time or near-real-time model fitting feasible. Heavy-tailed distributions (Student-t, Slash, Variance Gamma) better capture extreme market events critical for risk management. The out-of-sample VaR backtesting demonstrates practical applicability for position sizing and risk limits.

Moderate to high complexity. Requires understanding of HMM forward algorithm, importance sampling, SMN distributions, and special functions. Implementation uses Rcpp/RcppArmadillo for C++ integration, RcppParallel for parallelization, and RcppGSL for special functions. The R package svHMM provides a user-friendly interface, but custom implementation requires significant statistical and programming expertise. Parameter reparameterization for constrained spaces adds complexity.

All computational routines are publicly available through the R package svHMM on GitHub (https://github.com/svHMM/svHMM.git). Data is available at https://github.com/svHMM/Data. The paper provides detailed algorithm descriptions, prior specifications, and supplementary material with full technical derivations. Implementation uses Rcpp, RcppArmadillo, RcppParallel, and RcppGSL packages.