A two-factor structural model for valuing corporate securities

Malek Ben-Abdellatif (), Hatem Ben-Ameur (), Rim Chérif () and Bruno Rémillard ()
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Malek Ben-Abdellatif: ESLSCA University
Hatem Ben-Ameur: Department of Management Sciences, HEC Montréal
Rim Chérif: American University in Cairo
Bruno Rémillard: Department of Management Sciences, HEC Montréal

Review of Derivatives Research, 2024, vol. 27, issue 2, No 3, 203-225

Abstract: Abstract We propose a general structural model for valuing risky corporate debt securities within a two-dimensional framework. The state variables in our model include the firm’s asset value, described as a geometric Brownian motion stochastic process, and the short-term interest rate, following a mean-reverting Ornstein–Uhlenbeck stochastic process. Our model accommodates flexible debt structure, multiple seniority classes, tax benefits, bankruptcy costs, and a stochastic endogenous default barrier. The proposed methodology relies on a two-dimensional dynamic program coupled with finite elements where key transition parameters are computed in closed form, and effective approximations using local interpolations are made during backward recursion. Our design incorporates space discretization without imposing time discretization, which is advantageous, particularly in the valuation of corporate bonds where exercise opportunities are often distant. Our methodology distinguishes itself by assuming a numerical error, setting it apart from statistical methods. Together, the above features establish dynamic programming coupled with finite elements as a competitive valuation approach as compared to its counterparts in the existing literature. We use parallel computing to enhance the efficiency of our methodology. We conduct a numerical and and an empirical investigation, both of which show consistency with several empirical evidence documented in the literature.

Keywords: Structural model; Stochastic interest rate; Dynamic programming; Finite elements; Parallel computing; Primary 60F05; Secondary 62E20 (search for similar items in EconPapers)
JEL-codes: C6 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11147-024-09203-2

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