Toward a Unified Theory for Normal and Crash States in Financial Markets

Abstract: This paper offers a unified theory, which maps financial markets into a two dimension Banach space by quantizing the price fluctuation and trading volume of financial assets. In this space, we develop a new portfolio theory and capital asset pricing model. Then, we analyze normal and crash states at the same time, and find out a threshold above which a financial market crash occurs. Specifically, when financial markets are in normal states and the trading volume is ignored, this unified theory returns to the traditional theories—the modern portfolio theory and the CAPM, and theoretically challenges efficient-market hypothesis. Accordingly this paper paves the way to further research on asset pricing, systemic risk, market crisis, etc