An intensity‐based approach for equity modeling

Abstract

This paper analyzes an intensity-based approach for equity modeling. We use the Cox-Ingersoll-Ross (CIR) process to describe the intensity of the firm's default process. The intensity is purposely linked to the assets of the firm and consequently is also used to explain the equity. We examine two different approaches to link assets and intensity and derive closed-form expressions for the firms' equity under both models. We use the Kalman filter to estimate the parameters of the unobservable intensity process. We demonstrate our approach using historical equity time series data from Merrill Lynch.