The Optimal Analysis of Default Probability for a Credit Risk Model

Abstract

A credit risk mathematical model is investigated. Under regular conditions, a different recovery scheme is proposed, which is an extension of the recovery of treasury value scheme $(\text{RTV})$ with time-continuous liquidation. Assuming that a function depends on the optimal time for the liquidation and the recovery rate, we obtain the functional expression of the risky bond price. When the firm value follows a jump-diffusion process with a Log-exponentially distributed jump, we develop a method to obtain the optimal default probability with time-continuous liquidation.