Measuring the leverage effect in a high-frequency trading framework

Multi-factor stochastic volatility models of the financial time series can have important applications in portfolio management and pricing/hedging of financial instruments. Based on the semi-martingale paradigm, we focus on the study and the estimation of the leverage effect, defined as the covariance between the price and the volatility process and modeled as a stochastic process. Our estimation procedure is based only on a pre-estimation of the Fourier coefficients of the volatility process. This approach constitutes a novelty in comparison with the non-parametric leverage estimators proposed in the literature, generally based on a pre-estimation of the spot volatility, and it can be directly applied to estimate the leverage effect in the case of irregular trading observations and in the presence of microstructure noise contaminations, i.e. in a high frequency framework. The finite sample performances of the Fourier estimator of the leverage are tested in numerical simulations and in an empirical application to S&P 500 index futures.