This paper extends the approximate Bayesian estimation framework for Stochastic Volatility in Mean (SVM) models to accommodate heavy-tailed distributions from the Scale Mixture of Normals (SMN) family. To overcome the computational challenges arising from these models, we propose a numerically stable estimation procedure that exploits special functions to eliminate the need for direct numerical integration. Furthermore, the implementation incorporates parallel computing strategies that substantially reduce computational costs. Simulation studies and empirical applications demonstrate that the proposed approach delivers accurate inference while achieving computational times that are approximately an order of magnitude smaller than those required by conventional Markov chain Monte Carlo (MCMC) methods.

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