Calibration and Analysis of Structural Credit Risk Models with Occupation Time

Abstract

Credit risk is concerned with analyzing financial losses occurring due to changes in the credit quality of a firm. A rare occurrence of such sort is the default event that often leads to bankruptcy or liquidation, resulting in large financial losses to investors. In structural credit risk models, the asset value is compared to firm’s liabilities at any time, and the default event occurs when the asset value falls dangerously low. In this paper, we consider a structural credit risk model based on occupation time, which is defined as the time the firm asset value V spends below a default barrier. Here, we assume the geometric Brownian motion dynamics for V. Liquidation is declared if the firm value drops below a liquidation barrier or if it spends too much time below the default barrier. The main purpose of this paper is to calibrate the occupation-time model parameters using default probabilities derived from Credit Default Swaps (CDS) spreads available through Bloomberg Finance L.P.. This is done by applying the non-linear least-squares method. We also compare the occupation-time model with another well-known structural model of credit risk, namely, the Black–Cox model (1976).