Comprehensive Unified Models of Structural and Reduced Form Models for Defaultable Fixed Income Bonds (Part 1: One factor-model, Part 2:Two factors-model)

TL;DR

This paper develops comprehensive models combining structural and reduced form approaches for defaultable fixed income bonds, considering government taxes, stochastic and deterministic coupons, and default events in one- and two-factor frameworks.

Contribution

It generalizes existing structural models into unified models incorporating reduced form elements, including stochastic interest rates and default intensities, for more accurate bond pricing.

Findings

Derived pricing formulas for defaultable bonds with discrete coupons.

Analyzed the impact of government taxes on bond valuation.

Calculated expected default barriers and bond durations.

Abstract

Pricing formulae for defaultable corporate bonds with discrete coupons under consideration of the government taxes in the united model of structural and reduced form models are provided. The aim of this paper is to generalize the comprehensive structural model for defaultable fixed income bonds (considered in [1]) into a comprehensive unified model of structural and reduced form models. Here we consider the one factor model and the two factor model. In the one factor model the bond holders receive the deterministic coupon at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under constant short rate. In the two factor model the bond holders receive the stochastic coupon (discounted value of that at the maturity) at predetermined coupon dates and the face value (debt) and the coupon at the maturity as well as the effect of government taxes which are paid on the proceeds of an investment in bonds is considered under stochastic short rate. The expected default event occurs when the equity value is not enough to pay coupon or debt at the coupon dates or maturity and unexpected default event can occur at the first jump time of a Poisson process with the given default intensity provided by a step function of time variable. We consider the model and pricing formula for equity value and using it calculate expected default barrier. Then we provide pricing model and formula for defaultable corporate bonds with discrete coupons and consider its duration and the effect of the government taxes.