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.

Antonelli, F., Ramponi, A., Scarlatti, S. (2022). On a convergent power series method to price defaultable bonds in a Vasicek-CIR model. ELECTRONIC COMMUNICATIONS IN PROBABILITY.

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

Alessandro Ramponi
;
Sergio Scarlatti
2022-01-01

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.
2022
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/06 - PROBABILITA' E STATISTICA MATEMATICA
English
analytical functions, change of numéraire, credit risk, defaultable bond pricing, Hazard process, non-affine models
Antonelli, F., Ramponi, A., Scarlatti, S. (2022). On a convergent power series method to price defaultable bonds in a Vasicek-CIR model. ELECTRONIC COMMUNICATIONS IN PROBABILITY.
Antonelli, F; Ramponi, A; Scarlatti, S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/295091
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