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4.5 Methods for European options: Monte-Carlo sampling (MCS)

Monte-Carlo sampling is perhaps the easiest method to understand and
implement; it offers considerable flexibility when dealing with path
dependent exotic options and is generally adopted for problems
involving more than three independent random driving factors.
The main drawback of the method is the slow convergence, scaling with
the inverse square root of the number of samples and starting from
what is often a large initial error. It is therefore not uncommon to
use simulations with a million samples to guarantee a precision better
than one percent.
Clearly, this is prohibitively computer intensive for the valuations
of the simple options that can be calculated in a different manner.

**Subsections**