A conditional distribution model for limited stock index returns

When a price limit regime exists for all of the stocks involved in an index, the index return is an aggregate of limited variables and thereby it is restricted to the same limits. We argue that neither a censored nor a truncated distribution model is appropriate for the aggregate return. The proposed mixed beta distribution allows for varying conditional mean and volatility, and with increasing volatility it changes from leptokurtic to platykurtic densities. The model is illustrated and statistically evaluated with an empirical application to the Shanghai stock market index returns under a 10% price change limit regime.