Pricing of Defaultable Securities under Stochastic Interest

Nino Kordzakhia () and Alexander Novikov ()
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Nino Kordzakhia: Macquarie University
Alexander Novikov: University of Technology

A chapter in Mathematical Control Theory and Finance, 2008, pp 251-263 from Springer

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.

Keywords: Standard Brownian Motion; Fair Price; Barrier Option; Short Interest; Corporate Debt (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-69532-5_14

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DOI: 10.1007/978-3-540-69532-5_14

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