Getting Inside the Latent Volatility

This chapter introduces the reader into some recent financial applications of the Fourier estimator. We exploit here the ability of the method to reconstruct the volatility as a stochastic function of time in the univariate and multivariate case; in other words, we can handle the volatility function as an observable variable. This property makes it possible to have insights into various volatility related financial quantities, such as volatility of volatility and leverage. The chapter begins with an empirical exercise in which the latent volatility is estimated; we discuss in some extent the issue of the presence of jumps in the financial data. Then, in Sections 6.2 and 6.3 it is shown how to iterate the procedure for the purpose of parameter identification and calibration of stochastic volatility models and how to estimate in a model-free fashion a second order effect, known as price-volatility feedback rate. Finally, in Section 6.4 we analyze the forecasting power of the Fourier estimator of integrated volatility by a simple Monte Carlo experiment and an empirical application. Further directions for additional applications are given in Section 6.5.