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2022 On a convergent power series method to price defaultable bonds in a Vasicek-CIR model
Fabio Antonelli, Alessandro Ramponi, Sergio Scarlatti
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Electron. Commun. Probab. 27: 1-12 (2022). DOI: 10.1214/22-ECP458

Abstract

In this paper, we prove that the price of a defaultable bond, under a Vasicek short rate dynamics 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 numéraire 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.

Funding Statement

The Authors F. Antonelli and A. Ramponi are members of INdAM-GNAMPA.

Acknowledgments

We thank the anonymous Referee for the careful reading of the paper.

Citation

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Fabio Antonelli. Alessandro Ramponi. Sergio Scarlatti. "On a convergent power series method to price defaultable bonds in a Vasicek-CIR model." Electron. Commun. Probab. 27 1 - 12, 2022. https://doi.org/10.1214/22-ECP458

Information

Received: 30 September 2021; Accepted: 22 February 2022; Published: 2022
First available in Project Euclid: 7 March 2022

Digital Object Identifier: 10.1214/22-ECP458

Subjects:
Primary: 26E05 , 91G30 , 91G60

Keywords: analytical functions , change of numéraire , credit risk , defaultable bond pricing , Hazard process , non-affine models

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