Estimation of NIG and VG Models for High Frequency Financial Data

Numerous empirical studies have shown that certain exponential Levy models are able to fit the empirical distribution of daily financial returns quite well. By contrast, very few papers have considered intraday data in spite of their growing importance. In this paper, we fill this gap by studying the ability of the Normal Inverse Gaussian (NIG) and the Variance Gamma (VG) models to fit the statistical features of intraday data at different sampling frequencies. We propose to assess the suitability of the model by analyzing the signature plots of the point estimates at different sampling frequencies. Using high frequency transaction data from the U.S. equity market, we find the estimator of the volatility parameter to be quite stable at a wide range of intraday frequencies, in sharp contrast to the estimator of the kurtosis parameter, which is more sensitive to market microstructure effects. As a secondary contribution, we also assess the performance of the two most favored parametric estimation methods, the Method of Moments Estimators (MME) and the Maximum Likelihood Estimators (MLE), when dealing with high frequency observations. By Monte Carlo simulations, we show that neither high frequency sampling nor maxi- mum likelihood estimation significantly reduces the estimation error of the volatility parameter of the model. On the contrary, the estimation error of the parameter controlling the kurtosis of log returns can be significantly reduced by using MLE and high-frequency sampling. Both of these results appear to be new in the literature on statistical analysis of high frequency data