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

Elisabeth Kemajou, Salah-Eldin Mohammed and 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.

Date: 2012-10, Revised 2012-10
New Economics Papers: this item is included in nep-ban
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