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On a convergent power series method to price defaultable bonds in a Vašíček-CIR model. (English) Zbl 1484.91466

Summary: In this paper, we prove that the price of a defaultable bond, under a Vašíček 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G40 Credit risk
91G30 Interest rates, asset pricing, etc. (stochastic models)
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