Nonparametric Leverage Effects

Vast empirical evidence points to the existence of a negative correlation, named leverage effect, between shocks in volatility and shocks in returns. We provide a nonparametric theory of leverage estimation in the context of a continuous-time stochastic volatility model with jumps in returns, jumps in volatility, or both. Leverage is defined as a flexible function of the state of the firm, as summarized by the spot volatility level. We show that its point-wise functional estimates have asymptotic properties (in terms of rates of convergence, limiting biases, and limiting variances) which crucially depend on the likelihood of the individual jumps and co-jumps as well as on the features of the jump size distributions. Empirically, we find economically important time-variation in leverage with more negative values associated with higher volatility levels.