A dynamic program under Lévy processes for valuing corporate securities

Abstract

Most structural models for valuing corporate securities assume a geometric-Brownian motion to describe the firm’s assets value. However, this does not reflect market-stylized features; the default is more often conducted by sudden informations and 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, which 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 equity’s, debt’s, and firm’s total values, as well as the debt’s credit-spreads under Gaussian, double exponential, and variance-gamma-jump models.