On a convergent power series method to price defaultable bonds in a Vasicek-CIR model

19 Pages Posted: 1 Apr 2021

See all articles by Fabio Antonelli

Fabio Antonelli

Sapienza University of Rome

Alessandro Ramponi

Dept. Economics and Finance, University of Rome Tor Vergata

Sergio Scarlatti

University of Rome Tor Vergata

Date Written: March 31, 2021

Abstract

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

Suggested Citation

Antonelli, Fabio and Ramponi, Alessandro and Scarlatti, Sergio, On a convergent power series method to price defaultable bonds in a Vasicek-CIR model (March 31, 2021). Available at SSRN: https://ssrn.com/abstract=3816644 or http://dx.doi.org/10.2139/ssrn.3816644

Fabio Antonelli

Sapienza University of Rome ( email )

Piazzale Aldo Moro 5
Roma, Rome 00185
Italy

Alessandro Ramponi (Contact Author)

Dept. Economics and Finance, University of Rome Tor Vergata ( email )

Via Columbia, 2
Rome, Lazio 00133
Italy

Sergio Scarlatti

University of Rome Tor Vergata ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

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