# Evaluation of equity-based debt obligations

## TL;DR

This paper analyzes equity-based debt obligations (EbDO), a type of performance-linked financial instrument, addressing their accounting and pricing challenges through mathematical modeling in discrete and continuous time.

## Contribution

It formulates and solves the pricing problem for EbDOs using FBSDEs and decoupling fields, providing new methods for their valuation.

## Key findings

- Successfully models EbDO pricing in discrete and continuous time.
- Reduces continuous-time problem to a solvable FBSDE.
- Provides a mathematical framework for accounting and valuation of EbDOs.

## Abstract

We consider a class of participation rights, i.e. obligations issued by a company to investors who are interested in performance-based compensation. Albeit having desirable economic properties equity-based debt obligations (EbDO) pose challenges in accounting and contract pricing. We formulate and solve the associated mathematical problem in a discrete time, as well as a continuous time setting. In the latter case the problem is reduced to a forward-backward stochastic differential equation (FBSDE) and solved using the method of decoupling fields.