Pricing of defaultable securities under stochastic interest

Nino Kordzakhia, Alexander Novikov

    Research output: Chapter in Book/Report/Conference proceedingChapter

    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 languageEnglish
    Title of host publicationMathematical Control Theory and Finance
    EditorsAndrey Sarychev, Albert Shiryaev, Manuel Guerra, Maria do Rosário Grossinho
    Place of PublicationBerlin; London
    PublisherSpringer, Springer Nature
    Pages251-263
    Number of pages13
    ISBN (Electronic)9783540695325
    ISBN (Print)9783540695318
    DOIs
    Publication statusPublished - 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