A Discrete Sine Transform Approach for Realized Volatility Measurement

Realized volatility afiords the ex-post empirical measurement of the latent notional volatility. However, the time-varying returns autocorrelation induced by microstructure efiects represents a challenging problem for standard volatility measures. In this study, a new nonparametric volatility measures based on the Discrete Sine Transform (DST) is proposed. We show that the DST exactly diagonalizes the covariance matrix of MA(1) process. This original result provides us an orthonomal basis decomposition of the return process which permits to optimally disentangle the underlying e‐cient price signal from the time-varying nuisance component contained in tick-by-tick return series. As a result, two nonparametric volatility estimators which fully exploit all the available information contained in high frequency data are constructed. Moreover the DST orthogonalization allow us to analytically compute the score and the Fischer information matrix of MA(1) processes. In discussing e‐cient numerical procedures for the likelihood maximizations we also suggest that DST estimator would represent the most valid starting point for the numerical maximization of the likelihood. Monte Carlo simulations based on a realistic model for microstructure efiects show the superiority of DST estimators, compared to alternative local volatility proxies for every level of the noise to signal ratio and a large class of noise contaminations. These properties make the DST approach a nonparametric method able to cope with time-varying autocorrelation, in a simple and e‐cient way, providing robust and accurate volatility estimates under a wide set of realistic conditions. Moreover, its computational e‐ciency makes it well suitable for real-time analysis of high frequency data.