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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

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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  • Elisabeth Kemajou & Salah-Eldin Mohammed & Antoine Tambue, 2012. "A Stochastic Delay Model For Pricing Debt And Loan Guarantees: Theoretical Results," Papers 1210.0570, arXiv.org, revised Oct 2012.
    • Handle: RePEc:arx:papers:1210.0570
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    References listed on IDEAS

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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 449-470, May.
    2. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    3. 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(4), pages 419-438, December.
    4. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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