*Article* **Generalized Mean-Reverting 4/2 Factor Model**

### **Yuyang Cheng †, Marcos Escobar-Anel \*,† and Zhenxian Gong †**

Department of Statistical and Actuarial Sciences, Western University, London, ON N6A 3K7, Canada;


Received: 13 September 2019; Accepted: 26 September 2019; Published: 8 October 2019

**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.

**Keywords:** stochastic covariance; 4/2 model; option pricing; risk measures
