A dynamic program under Lévy processes for valuing corporate securities

Most structural models for valuing corporate securities assume a geometric Brownian motion to describe the value of a firm’s assets. However, this does not reflect market stylized features: the default is more often driven by unexpected information and sudden shocks, which are not captured by the Gaussian model assumption. To remedy this, we propose a dynamic program for valuing corporate securities under various Lévy processes. Specifically, we study two jump diffusions and a pure-jump process. Under these settings, we build and experiment with a flexible framework that accommodates the balance-sheet equality, arbitrary corporate debts, multiple seniority classes, tax benefits and bankruptcy costs. While our approach applies to several Lévy processes, we compute and detail the total value of equity, the total value of debt and the total value of the firm as well as the credit spreads of the debt by using Gaussian, double exponential and variance-gamma jump models.