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We analyze the ability of Threshold Stochastic Volatility (TSV) models to represent and forecast asymmetric volatilities. First, we derive the statistical properties of TSV models. Second, we demonstrate the good finite sample properties of a MCMC estimator, implemented in the software package WinBUGS, when estimating the parameters of a general specification, denoted CTSV, that nests the TSV and asymmetric autoregressive stochastic volatility (A-ARSV) models. The MCMC estimator also discriminates between the two specifications and allows us to obtain volatility forecasts. Third, we analyze daily S&P 500 and FTSE 100 returns and show that the estimated CTSV model implies plug-in moments that are slightly closer to the observed sample moments than those implied by other nested specifications. Furthermore, different asymmetric specifications generate rather different European options prices. Finally, although none of the models clearly emerge as best out of-sample, it seems that including both threshold variables and correlated errors may be a good compromise. (C) 2017 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.