Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach

TL;DR

This paper develops a mathematical model for discrete coupon bonds with early redemption options using the structural approach, analyzing price estimates, default boundaries, and key financial metrics.

Contribution

It introduces a novel structural model for bonds with early redemption, providing existence, uniqueness, and analytic pricing formulas based on higher binary options.

Findings

Derived min-max and gradient estimates for bond prices

Proved existence and uniqueness of default and redemption boundaries

Provided analytic formulas for bond pricing, duration, and credit spread

Abstract

In this paper, using the structural approach is derived a mathematical model of the discrete coupon bond with the provision that allow the holder to demand early redemption at any coupon dates prior to the maturity and based on this model is provided some analysis including min-max and gradient estimates of the bond price. Using these estimates the existence and uniqueness of the default boundaries and some relationships between the design parameters of the discrete coupon bond with early redemption provision are described. Then under some assumptions the existence and uniqueness of the early redemption boundaries is proved and the analytic formula of the bond price is provided using higher binary options. Finally for our bond is provided the analysis on the duration and credit spread, which are used widely in financial reality. Our works provide a design guide of the discrete coupon bond with the early redemption provision