A Stochastic Delay Model for Pricing Debt and Equity: Numerical Techniques and Applications

TL;DR

This paper introduces numerical methods for solving a delayed nonlinear model for corporate debt and equity pricing, highlighting the importance of past dependence in firm value modeling through comparison with classical models.

Contribution

It provides novel numerical techniques for a delayed nonlinear model and demonstrates their application to real financial data, emphasizing the significance of past dependence.

Findings

Delayed nonlinear model aligns better with real data than classical models.

Past dependence significantly impacts corporate liability valuation.

Numerical solutions effectively solve the proposed RPDEs.

Abstract

In the accompanied paper [14], a delayed nonlinear model for pricing corporate liabilities was developed. Using self-financed strategy and duplication we were able to derive two Random Partial Differential Equations (RPDEs) describing the evolution of debt and equity values of the corporate in the last delay period interval. In this paper, we provide numerical techniques to solve our delayed nonlinear model along with the corresponding RPDEs modeling the debt and equity values of the corporate. Using financial data from some firms, we compare numerical solutions from both our nonlinear model and classical Merton model [7] to 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.