CHAPTER 5Monte-Carlo
In this chapter, we introduce the Monte-Carlo (MC) algorithm as a practical solution for pricing financial products in dynamic models and lay the groundwork for the serial implementation of Chapter 6 and the parallel implementation of Chapter 7. We establish the theoretical foundations of our implementation, but we don't cover all the details and facets of Monte-Carlo simulations. Monte-Carlo is more extensively covered in dedicated publications, the established references in finance being Glasserman's [62] and Jaeckel's [63]. Glasserman covers the many facets of financial simulations in deep detail while Jaeckel offers a practitioner's perspective, focused on implementation and including the most complete available presentation of Sobol's sequence.
5.1 THE MONTE-CARLO ALGORITHM
Introduction
The Monte-Carlo algorithm consists in the computer simulation of a number of independent outcomes of a random experiment with known probability distribution. It is applied in many scientific fields. In finance, the Monte-Carlo algorithm estimates the value of a financial product in contexts where faster methods (analytic, numerical integration, FDM) cannot be applied. With the notations of the previous chapter, the value of a product is its expected (numeraire deflated) payoff 
under an appropriate probability measure :
where is the set of event dates, or timeline, and ...
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