A Default Risk Model in a Fuzzy Framework

A default risk model is provided by using option pricing theory in a fuzzy framework in consideration of a simple company comprised of a single type of the debt that is free from profit payment and a single type of capital that is liberated from dividend. The model is based on the assumption that asset value of a company is the sum of total market value of stock and debt value, considering a situation where the asset value becomes below the debt value is default. For constructing the default risk model, a new variable is defined to derive a formula to evaluate the probability of default. Thus, an EDP (estimated default probability) model with the first and second moment is proposed and since debt value is fluctuated as asset price some bounds are established to somehow admit the fluctuation of the debt values, employing fuzzy number in the total market value of asset value.