Stock prices as branching processes in random environments: estimation

Epps (1996) introduced a variant of the Bienayme-Galton-Watson branching process to study the evolution of daily closing prices in the stock market. We indicate here that this model is actually a particular branching process in random environments of the iid type and use Dion and Esty's (1979) results to estimate explicitly some of the parameters. These estimators are known to be consistent; but we find through extensive simulations that some of them have substantial bias in this application. A comparison with Epps' iterative estimators is made.