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Pricing of Defaultable Securities under Stochastic Interest

In: Mathematical Control Theory and Finance

Author

Listed:
  • Nino Kordzakhia

    (Macquarie University)

  • Alexander Novikov

    (University of Technology)

Abstract

Summary 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.

Suggested Citation

  • Nino Kordzakhia & Alexander Novikov, 2008. "Pricing of Defaultable Securities under Stochastic Interest," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 251-263, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_14
    DOI: 10.1007/978-3-540-69532-5_14
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