On statistical indistinguishability of complete and incomplete market models

This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models.

The paper uses theory of forecasting to find criteria of predictability of market parameters such as volatilities and the appreciation rates.

It is known that the market completeness is not a robust property: small random deviations of the coefficients convert a complete market model into an incomplete one. The paper shows that market incompleteness is also non-robust: for any incomplete market from a wide class of models, there exists a complete market model with arbitrarily close paths of the stock prices and the market parameters.

The paper results lead to a counterintuitive conclusion that the incomplete markets are indistinguishable in the terms of the market statistics.