Higher Order Binaries with Time Dependent Coefficients and Two Factors - Model for Defaultable Bond with Discrete Default Information

TL;DR

This paper develops a sophisticated model for pricing defaultable bonds using higher order binaries with time-dependent coefficients, accounting for discrete default information and two stochastic factors, providing explicit pricing formulas.

Contribution

It introduces a novel approach employing higher order binaries with time-dependent coefficients to price defaultable bonds with discrete default information and two stochastic factors.

Findings

Derived explicit pricing formulas for defaultable bonds.

Analyzed credit spreads under different default recovery assumptions.

Extended binary option pricing techniques to complex bond models.

Abstract

In this article, we consider a 2 factors-model for pricing defaultable bond with discrete default intensity and barrier where the 2 factors are stochastic risk free short rate process and firm value process. We assume that the default event occurs in an expected manner when the firm value reaches a given default barrier at predetermined discrete announcing dates or in an unexpected manner at the first jump time of a Poisson process with given default intensity given by a step function of time variable. Then our pricing model is given by a solving problem of several linear PDEs with variable coefficients and terminal value of binary type in every subinterval between the two adjacent announcing dates. Our main approach is to use higher order binaries. We first provide the pricing formulae of higher order binaries with time dependent coefficients and consider their integrals on the last expiry date variable. Then using the pricing formulae of higher binary options and their integrals, we give the pricing formulae of defaultable bonds in both cases of exogenous and endogenous default recoveries and credit spread analysis.