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2014 | OriginalPaper | Chapter

Conditional Default Probability and Density

Authors : N. El Karoui, M. Jeanblanc, Y. Jiao, B. Zargari

Published in: Inspired by Finance

Publisher: Springer International Publishing

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Abstract

We construct explicit models of conditional probability and density processes given a reference filtration for one or several default times. For this purpose, different methods are proposed such as the dynamic copula, change of time, change of probability measure and filtering.

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previous chapter Mean Square Error and Limit Theorem for the Modified Leland Hedging Strategy with a Constant Transaction Costs Coefficient

next chapter Yield Curve Smoothing and Residual Variance of Fixed Income Positions

More results on that model, in an enlargement of filtration setting, can be found in Chaleyat-Maurel and Jeulin [3] and Yor [17].

We recall that H-hypothesis stands for any F-martingale is a G=F∨H martingale.

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Chaleyat-Maurel, M., Jeulin, T.: Grossissement Gaussien de la filtration Brownienne. Lecture Notes in Math., vol. 1118, pp. 59–109. Springer, Berlin (1985) CrossRef

El Karoui, N., Jeanblanc, M., Jiao, Y.: What happens after a default: the conditional density approach. Stoch. Process. Appl. 120, 1011–1032 (2010) MathSciNetCrossRefMATH

Fermanian, J.D., Vigneron, O.: 2010, On break-even correlation: the way to price structured credit derivatives by replication. Preprint

Filipović, D., Overbeck, L., Schmidt, T.: Dynamic CDO term structure modeling. Math. Finance (2009). Forthcoming

Filipovic, D., Hughston, L., Macrina, A.: Conditional density models for asset pricing. Preprint (2010)

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Jacod, J.: Grossissement initial, hypothèse (H’) et théorème de Girsanov. Lecture Notes in Math., vol. 1118, pp. 15–35. Springer, Berlin (1985)

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Kallianpur, G., Striebel, C.: Estimation of stochastic systems: arbitrary system process with additive white noise observation errors. Ann. Math. Stat. 39(3), 785–801 (1968) MathSciNetCrossRefMATH

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Jeanblanc, M., Song, S.: Explicit model of default time with given survival probability. Preprint (2010)

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Jeanblanc, M., Song, S.: Default times with given survival probability and their F-martingale decomposition formula. Preprint (2010)

13.

Keller-Ressel M., Papapantoleon, A., Teichman, J.: The Affine Libor Models. Preprint (2010)

14.

Liptser, R.S., Shiryaev, A.N.: Statistics of Random Processes, II Applications, 2nd edn. Springer, Berlin (2001) CrossRef

15.

Matsumoto, H., Yor, M.: A relationship between Brownian motions with opposite drifts via certain enlargements of the Brownian filtration. Osaka J. Math. 38, 383–398 (2001) MathSciNetMATH

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Meyer, P.-A.: Sur un problème de filtration. In: Séminaire de Probabilités VII. Lecture Notes in Math., vol. 321, pp. 223–247. Springer, Berlin (1973)

17.

Yor, M.: Grossissement de filtrations et absolue continuité de noyaux. Lecture Notes in Math., vol. 1118, pp. 6–14. Springer, Berlin (1985) CrossRef

Title: Conditional Default Probability and Density
Authors: N. El Karoui
M. Jeanblanc
Y. Jiao
B. Zargari
Publisher: Springer International Publishing
Book: Inspired by Finance
Print ISBN: 978-3-319-02068-6

Electronic ISBN: 978-3-319-02069-3

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-02069-3_9