A stochastic delay model for pricing debt and equity: Numerical techniques and applications

• We consider a delayed nonlinear model for pricing corporate liabilities.
• We solve numerically the delayed nonlinear model for firm market value.
• We propose robust numerical method for RPDEs modeling the debt and equity values.
• We forecast and compare numerical solutions from the nonlinear model and Merton model.
• We compare the numerical solutions with the real corporate data.

Delayed nonlinear models for pricing corporate liabilities and European options were recently developed. Using self-financed strategy and duplication we were able to derive a Random Partial Differential Equation (RPDE) whose solutions describe the evolution of debt and equity values of a corporate in the last delay period interval in the accompanied paper (Kemajou et al., 2012) [14]. In this paper, we provide robust numerical techniques to solve the delayed nonlinear model for the corporate value, along with the corresponding RPDEs modeling the debt and equity values of the corporate.Using financial data from some firms, we forecast and compare numerical solutions from both the nonlinear delayed model and classical Merton model with the real corporate data. From this comparison, it comes up that in corporate finance the past dependence of the firm value process may be an important feature and therefore should not be ignored.