Frontiers in financial dynamics

Abstract

In recent decades, mathematical motivated financial models have been used to understand the complexity and intermittent nature of financial market instruments. Typically, applied mathematics models a physical system by specifying and quantifying the physical laws to which the process should theoretically conform. Such theoretical models are often represented as differential equations. The solutions of these differential equations have been shown to have poor compliance with observed financial data which has been attributed to difficulties in correctly estimating the parameters of the differential equation. Generalised smoothing provides a comprehensive evaluation of financial dynamics as it accurately estimates data driven parameters for differential equations and produces a fitted curve that incorporates the theoretical specifications implied by the differential equation while adhering to the observed financial data. This article demonstrates the merit for a generalised smoothing approach to modeling financial dynamics by examining instantaneous forward yield curves within a generalised smoothing framework.