Shock‐Triggered Asymmetric Response Stochastic Volatility

We propose a novel asymmetric stochastic volatility model (STAR‐SV) in which the leverage parameter adjusts to the magnitude of past shocks. This flexible specification captures both the leverage effects and their propagation more effectively than standard asymmetric volatility models. To estimate the STAR‐SV parameters, we implement a data cloning algorithm that approximates the maximum likelihood estimates and their asymptotic variances. In finite‐sample simulations, data cloning consistently leads to reliable estimates and small standard errors. Empirically, we fit the model to Bitcoin, Nasdaq, and S&P 500 returns and evaluate 1‐ and 10‐day volatility forecasts using unconditional and conditional tests of predictive ability. STAR‐SV using data cloning proves to be the most adequate forecaster, outperforming the most stringent confidence thresholds and weakly dominating in several variance regimes. Finally, we show the performance of the model in predicting the 99% value‐at‐risk. STAR‐SV, using data cloning, seems to respond quickly to volatility spikes and passes backtests for both time horizons.