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.

• 4.5.1 Forecast possible realizations of the underlying asset
• 4.5.2 Expected value of an option from sampled data