Sensitivity Analysis of Asset Flow Differential Equations and Volatility Comparison of Two Related Variables

Abstract

In this study I apply forward sensitivity analysis to the dynamical system of nonlinear asset flow differential equations (AFDE). I find that all parameters in AFDE are needed and can be estimated from market prices and net asset values data. Moreover, the market price is the most fluctuating state variable and the coefficient for the trend-based investors' sentiment is the dominant parameter. Furthermore, I define and compare the extreme value based volatilities of market price and net asset value for closed-end funds. I find that the extreme value based volatility of market price is higher than that of net asset value for the vast majority of closed-end funds for both overlapping and non-overlapping cases.

Keywords: parametric sensitivity analysis, extreme value based volatility, nonlinear dynamical systems, numerical solution of differential equations market dynamics, mathematical finance and economics, quantitative finance

JEL Classification: C61, G12, D52, C12, C63, C81