Dynamics of asset price changes: Statistical and differential equations models

This dissertation is comprised of two related tracts: (i) Quantitative Modeling and (ii) Analysis of Asset Flow Differential Equations. In the former a data set of over 100,000 daily closed-end fund prices is analyzed using mixed-effects regressions with the objective of understanding price dynamics. This analysis provides strong statistical evidence that relative daily price change is positively influenced by valuation, recent price trend, short term volatility, volume trend, and the M2 money supply. There is a strong nonlinearity in the influence of the price trend, so that a significantly large recent uptrend has a negative influence on the subsequent day's relative price change. The nonlinearity is the key to an understanding of the competing role of price trend, since a single large data set exhibits both under- and overreaction in different regimes of the independent variables. The role of long term volatility is not a clear-cut risk/return inverse relation; rather there is an ambiguous and complicated relationship between volatility and return. Standardization of the independent regression variables allows for a more direct comparison of each factor's influence on the return.In the latter a two-group asset flow model of a financial instrument with one group focused on price trend, the other on value, is considered. The existence of both stable and unstable regions for the system of differential equations is proven. It is shown that a strong motivation based on (recent) price trend is associated with instability. Numerical computations using a set of typical parameters describe regions of stability and instability. A precise limiting connection between the discrete and differential equations is also established.