On statistical indistinguishability of complete and incomplete discrete time market models

Abstract

We investigate the possibility of statistical evaluation of the market completeness
for discrete time
stock market models. It is known that the market completeness is
not a robust property: small random deviations of the coefficients
convert a complete market model into a incomplete one. The paper
shows that market incompleteness is also non-robust.
We show that, for any incomplete market from a wide
class of discrete time models, there exists a complete market model with
arbitrarily close stock prices. This means that incomplete markets are indistinguishable from the complete markets
in the terms of market statistics.

Keywords: price statistics, market completeness, market incompleteness, forecasting

JEL Classification: C52, C53, C53, G13