### Abstract

We reduce a problem of pricing continuously monitored defaultable securities (barrier options, corporate debts) in a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. In the case when the interest rate is governed by a linear stochastic equation (Vasicek model) we suggest a numerical algorithm for calculation of BCP based on a piece-wise linear approximation for the stochastic boundaries. We also find an estimation of the rate of convergence of the suggested approximation and illustrate results by numerical examples.

Original language | English |
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Title of host publication | Mathematical Control Theory and Finance |

Editors | Andrey Sarychev, Albert Shiryaev, Manuel Guerra, Maria do Rosário Grossinho |

Place of Publication | Berlin; London |

Publisher | Springer, Springer Nature |

Pages | 251-263 |

Number of pages | 13 |

ISBN (Electronic) | 9783540695325 |

ISBN (Print) | 9783540695318 |

DOIs | |

Publication status | Published - 2008 |

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## Cite this

Kordzakhia, N., & Novikov, A. (2008). Pricing of defaultable securities under stochastic interest. In A. Sarychev, A. Shiryaev, M. Guerra, & M. D. R. Grossinho (Eds.),

*Mathematical Control Theory and Finance*(pp. 251-263). Berlin; London: Springer, Springer Nature. https://doi.org/10.1007/978-3-540-69532-5_14