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Pricing of Defaultable Securities under Stochastic Interest


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  • Nina Kordzakhia

    (Macquarie University)

  • Alex Novikov

    (University of Technology, Sydney)

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    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.

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    Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 193.

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    Length: 10
    Date of creation: 01 Feb 2007
    Date of revision:
    Handle: RePEc:uts:rpaper:193

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    1. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-70, May.
    2. G. O. Roberts & C. F. Shortland, 1997. "Pricing Barrier Options with Time-Dependent Coefficients," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 83-93.
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