On a convergent power series method to price defaultable bonds in a Vasicek-CIR model
19 Pages Posted: 1 Apr 2021
Date Written: March 31, 2021
In this paper we prove that the price of a defaultable bond, under a Vasicek short rate dynamic coupled with a Cox-Ingersoll-Ross default intensity model, is a real analytic function, in a neighborhood of the origin, of the correlation parameter between the Brownian motions driving the processes, used to express the dependence between the short rate and the default intensity of the bond issuer. Employing conditioning and a change of num\'eraire technique, we obtain a manageable representation of the bond price in this non-affine model which allows us to control its derivatives and assess the convergence of the series. By truncating the expansion at the second order, a quadratic approximation formula for the price is then provided. Finally, practical applications of the result are highlighted by performing a numerical comparison with alternative pricing methodologies.
Keywords: Credit Risk, Defaultable Bond Pricing, Non-Affine Models, Analytical Functions, Hazard Process, Change of Numéraire, Monte-Carlo Methods.
JEL Classification: C02, C63
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