## Monte Carlo method for financial option pricing

In the field of financial
mathematics, the problem of finding the
arbitrage-free value of a particular **derivative**,
requires the computation of a particular **integral**. In many cases these integrals can be valued analytically,
and in still more cases they can be valued using **numerical integration**. However when the number of dimensions (or
degrees of freedom) in the problem is large, numerical integration methods
become intractable. In these cases it is common to resort to the more widely
applicable **Monte Carlo methods** to solve the problem. For large dimension
integrals as can very often occur in financial problems, Monte Carlo methods
converge to the solution more quickly than numerical integration methods.

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