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A Stochastic Delay Model For Pricing Debt And Loan Guarantees: Theoretical Results

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  • Elisabeth Kemajou
  • Salah-Eldin Mohammed
  • Antoine Tambue
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    Abstract

    We consider that the price of a firm follows a non linear stochastic delay differential equation. We also assume that any claim value whose value depends on firm value and time follows a non linear stochastic delay differential equation. Using self-financed strategy and replication we are able to derive a Random Partial Differential Equation (RPDE) satisfied by any corporate claim whose value is a function of firm value and time. Under specific final and boundary conditions, we solve the RPDE for the debt value and loan guarantees within a single period and homogeneous class of debt.

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    File URL: http://arxiv.org/pdf/1210.0570
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1210.0570.

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    Date of creation: Oct 2012
    Date of revision: Oct 2012
    Handle: RePEc:arx:papers:1210.0570

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    Web page: http://arxiv.org/

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    1. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    2. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    3. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Scott, Louis O., 1987. "Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(04), pages 419-438, December.
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