On statistical indistinguishability of complete and incomplete market models

Purpose: This paper aims to investigate possibility of statistical detection of market completeness for continuous time diffusion stock market models. Design/methodology/approach: The paper uses theory of forecasting to find criteria of predictability of market parameters such as volatilities and the appreciation rates. Findings: 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. Originality/value: The paper results lead to a counterintuitive conclusion that the incomplete markets are indistinguishable in the terms of the market statistics.