## Abstract

We consider the problem of computing some basic quantities such

as defaultable bond prices and survival probabilities in a credit risk

model according to the intensity based approach. We let the default

intensities depend on an external factor process that we assume is

not observable. We use stochastic filtering to successively update

its distribution on the basis of the observed default history. On

one hand this allows us to capture aspects of default contagion

(information-induced contagion). On the other hand it allows us

to evaluate the above quantities also in our incomplete information

context. We consider in particular affine credit risk models and

show that in such models the nonlinear filter can be computed via

a recursive procedure. This then leads to an explicit expression

for the filter that depends on a finite number of sufficient statistics

of the observed interarrival times for the defaults provided one

chooses an initial distribution for the factor process that is of the

Gamma type.

as defaultable bond prices and survival probabilities in a credit risk

model according to the intensity based approach. We let the default

intensities depend on an external factor process that we assume is

not observable. We use stochastic filtering to successively update

its distribution on the basis of the observed default history. On

one hand this allows us to capture aspects of default contagion

(information-induced contagion). On the other hand it allows us

to evaluate the above quantities also in our incomplete information

context. We consider in particular affine credit risk models and

show that in such models the nonlinear filter can be computed via

a recursive procedure. This then leads to an explicit expression

for the filter that depends on a finite number of sufficient statistics

of the observed interarrival times for the defaults provided one

chooses an initial distribution for the factor process that is of the

Gamma type.

Original language | English |
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Title of host publication | Stochastic Processes and applications to mathematical finance |

Editors | Jiro Akahori, Shigeyoshi Ogawa & Shinzo Watanabe |

Place of Publication | Japan |

Publisher | World Scientific |

Pages | 97 - 113 |

Publication status | Published - 1 May 2007 |