We decompose UK market volatility into
short- and long-run components using EGARCH component model and examine the
cross-sectional prices of the two components. Our empirical results suggest
that these two components are significantly priced in the cross-section and the
negative risk premia are consistent with the existing literature. The Fama-French
three-factor model is improved by the inclusion of the two volatility
components. However, our ICAPM model using market excess return and the
decomposed volatility components as state variables compares inferiorly to the
traditional three-factor model.
We present an approach how to obtain solutions of arbitrary linear operator equation for unknown functions. The particular solution can be represented by the infinite operator series (Cyclic Operator Decomposition), which acts the generating function. The method allows us to choose the cyclic operators and corresponding generating function selectively, depending on initial problem for analytical or numerical study. Our approach includes, as a particular case, the perturbation theory, but generally does not require inside any small parameters and unperturbed solutions. We demonstrate the applicability of the method to the analysis of several differential equations in mathematical physics, namely, classical oscillator, Schrodinger equation, and wave equation in dispersive medium.