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A Stochastic Delay Model for Pricing Debt and Equity: Numerical Techniques and Applications

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      Abstract

      In the accompanied paper [14], a delayed nonlinear model for pricing corporate liabilities was developed. Using self-financed strategy and duplication we were able to derive two Random Partial Differential Equations (RPDEs) describing the evolution of debt and equity values of the corporate in the last delay period interval. In this paper, we provide numerical techniques to solve our delayed nonlinear model along with the corresponding RPDEs modeling the debt and equity values of the corporate. Using financial data from some firms, we compare numerical solutions from both our nonlinear model and classical Merton model [7] to the real corporate data. From this comparison, it comes up that in corporate finance the past dependence of the firm value process may be an important feature and therefore should not be ignored.

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      Most cited references 13

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      The Pricing of Options and Corporate Liabilities

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        Theory of Rational Option Pricing

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          On the Pricing of Corporate Debt: The Risk Structure of Interest Rates

           ROBERT MERTON (1974)
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            Author and article information

            Journal
            1304.2074

            Numerical & Computational mathematics, Probability

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