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Advanced Quantitative Finance with C++ by Alonso Peña Ph.D

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The Finite Difference method

The Finite Difference (FD) method is a numerical technique that focuses directly on the approximate solution of a differential equation. As shown by (Black and Scholes 1973) for equity financial derivatives (contingent claims), the problem is expressed in terms of a Partial Differential Equation (PDE).

The basic idea of FDM is to discretize a differential equation. The method transforms the derivatives in the differential equation into quantities or ratios that approximate the derivatives. These quantities are not any more infinitesimal but finite, that is, they have a finite length. This is the origin of the name of finite differences. For more details, the reader can refer to The Mathematics of Financial Derivatives: ...

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