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

Author:Alonso Peña Ph.D. [Peña Ph.D., Alonso]
Language: eng
Format: epub, pdf
Publisher: Packt Publishing
Published: 2014-06-24T21:00:00+00:00

The preceding function is also known as the slope, which is the ratio between the growth (or decrease) in the function with respect to the step size dx. Using the preceding finite difference allows us to calculate the slope of the f(x) function in terms of algebraic quantities.

In quantitative finance, we encounter various types of PDEs. The most important is the Black-Scholes PDE, which is expressed as follows:

We now consider solving this equation in a rectangular domain in the S and t axes. In the S axis, the domain is [a,b]. In the t axis the domain is [0,T]. This can be written mathematically as the domain . In the case of a European Call, it has a final condition as follows:

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