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Financial Mathematics by Roman N. Makarov, Giuseppe Campolieti

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Chapter 18

Numerical Applications to Derivative Pricing

18.1 Overview of Deterministic Numerical Methods

18.1.1 Quadrature Formulae

One of the fundamental problems in numerical analysis is the evaluation of integrals. Consider a one-dimensional definite integral of a function f : [a, b] → ℝ,

I(f)I(f;[a,b]):=abf(x)dxwith<a<b<.

The function f is said to be integrable (and the integral of f is defined) if the integral I(|f|) exists and is finite. Assuming that a closed-form expression for I(f) is unavailable or intractable, we rely on a numerical evaluation. Any explicit formula that is suitable for providing an approximation of I(f) is called a quadrature formula, or a quadrature rule, or a numerical integration formula. A typical quadrature ...

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