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. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Kordzakhia, N., & Novikov, A. (2008). Pricing of defaultable securities under stochastic interest. In Mathematical Control Theory and Finance (pp. 251–263). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-540-69532-5_14
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