Leverage at different time scales: a stochastic volatility perspective

This paper proposes a stochastic volatility model in which leverage evolves through a heterogeneous autoregressive (HAR) structure that combines daily and weekly return innovations. The resulting HARA specification can be viewed as a parsimonious restriction of multi-lag leverage drivers used in the stochastic volatility literature, delivering an interpretable multiscale decomposition of leverage dynamics and a closed-form leverage-propagation function. Parameters are estimated using data cloning, providing stable likelihood-based inference. Monte Carlo experiments confirm accurate recovery of the daily/weekly leverage components under both Gaussian and heavy-tailed innovations. Empirically, estimates for four international equity indices reveal substantial cross-asset heterogeneity in the horizon and persistence of leverage propagation. Benchmark comparisons are reported in an appendix as validation.