Journal of Risk

A dynamic program under Lévy processes for valuing corporate securities

Hatem Ben-Ameur, Rim Chérif and Bruno N. Rémillard

  • We use dynamic programming and finite elements to design and solve an extended structural model that accommodates arbitrary Lévy dynamics for the underlying firm’s asset value, realistic debt payment schedules, multiple seniority classes, and various intangible assets.
  • We conduct a large numerical investigation under the jump-diffusion processes of Merton (1976) and Kou (2002) as well as the variance-gamma process of Madan et al. (1998).
  • We report major stylized facts reported in the empirical literature, and partially revisit the credit-spread puzzle.

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.

Sorry, our subscription options are not loading right now

Please try again later. Get in touch with our customer services team if this issue persists.

New to View our subscription options

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here