Generalized Mean-Reverting 4/2 Factor Model

Abstract

This paper proposes and investigates a multivariate 4/2 Factor Model. The name 4/2 comes from the superposition of a CIR term and a 3/2-model component. Our model goes multidimensional along the lines of a principal component and factor covariance decomposition. We find conditions for well-defined changes of measure and we also find two key characteristic functions in closed-form, which help with pricing and risk measure calculations. In a numerical example, we demonstrate the significant impact of the newly added 3/2 component (parameter b) and the common factor (a), both with respect to changes on the implied volatility surface (up to 100%) and on two risk measures: value at risk and expected shortfall where an increase of up to 29% was detected.