Modelling asset returns under price limits with mixture of truncated Gaussian distribution

In this paper, we propose to use the mixture of truncated Gaussian distribution in modelling the financial asset return distribution under price limits. Theoretically, while retaining many convenient statistical properties of the Gaussian distribution, the proposed model assumes a flexible structure accommodating some important special features of the return data under price restrictions, such as the clusters near the bounds (due to the ‘bound effect’) and peaked shape around zero (due to the minimum-tick size effect). It can also allow for a wide range of variances and kurtosis even with a bounded domain. These are the salient features that the conventional models (such as the Normal, Truncated Normal and Censored Normal) do not have. For empirical illustration, we apply our proposed model to stocks under different price restrictions. Some common interesting features have been found. Furthermore, in our Value-at-Risk analysis, we find that ignoring the bound cluster in the tail of the distribution could lead to a significant overestimation of the number of violations and produce unreliable Value-at-Risk measures. In addition, we also find that the proposed model has a better empirical performance when the data are highly asymmetric and heavy-tailed.