Pricing of Defaultable Securities Under Stochastic Interest

Nina Kordzakhia and Alex Novikov
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Nina Kordzakhia: Macquarie University
Alex Novikov: University of Technology Sydney

No 193, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: We reduce the problem of pricing continuously monitored defaultable securities (namely, barrier type options, corporate debts) under a stochastic interest rate framework to calculations of boundary crossing probabilities (BCP) for Brownian Motion (BM) with stochastic boundaries. For the case when the interest rate is governed by 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 provide an estimation for a rate of convergence of the suggested approximation as a function of number of nodes and illustrate the results by numerical examples.

Pages: 10 pages
Date: 2007-02-01
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Published as: Kordzakhia, N. and Novikov, A., 2008, "Pricing of Defaultable Securities Under Stochastic Interest", In: A. Sarychev et al (eds) Mathematical Control Theory and Finance, 251-263.

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