Stochastic Asset Price Dynamics and Volatility Using a Symmetric Supply and Demand Price Equation

A symmetric supply/demand model of price dynamics is developed and used to understand the relationship between price change and volatility. This differs from the classical approach in which the expected rate of price change and variance are assumed to be independent. The microeconomic and stochastic analysis leads to the conclusion that a particular measure of the marginal volatility has a minimum shortly before the expected log-price has an extremum. The maxi-mum of the volatility occurs when prices are likely to change most rapidly, and the supply/demand imbalance is greatest. The great bubble and collapse of Bitcoin's price serves as a test of this analysis. The volatility reached a mini-mum shortly prior to the peak of Bitcoin's price in December 2018. The model is further developed under the assumption that supply and demand depend on the fundamental value of the asset. Thus the paper is a key step in understand-ing the issue of whether volatility peaks can forecast trading price tops and bottoms. The methodology can be extended beyond log-normal returns and is further compared with an empirical study fo 40 sharp market boom/bust events studied by Sornette et. al. (2017)