Valuation of Corporate Debt and Equity in Uncertain Markets

Abstract

In practice, financial decisions are made in the context of indeterminacy. Randomness, uncertainty, and fuzziness are three basic types of indeterminacy. A multiplicity of differential equations have been designed to depict various processes powered by different kinds of indeterminacy. Among others, these differential equations include uncertain differential equations, stochastic differential equations, and fuzzy differential equations. In this study, we propose that the value of a firm can be described by an uncertain differential equation powered by a geometric canonical Liu process. Uncertain differential equations describe processes driven by uncertainty. Implementing the uncertain Liu option pricing theory, we develop and analyse a framework for valuing debt and equity for a levered firm in uncertain markets. Numerical calculations are demonstrated.