ABSTRACT
The Monte Carlo method is a very popular computational tool in financial economics. A typical application of the Monte Carlo method is the computation of areas and volumes of objects of complex shape and geometry. This type of Monte Carlo computation is based on two ideas: geometric probability and the frequentist definition of probability. The Monte Carlo method is based on two fundamental laws, namely, the Law of Large Numbers and the Central Limit Theorem. One of the main advantages of the Monte Carlo method is the ease of its parallelization. The bridge sampling algorithm is useful in pricing path-dependent financial instruments. Being applied with (randomized) low-discrepancy numbers, i.e., when the (randomized) quasi-Monte Carlo method is used, it allows us to reduce the variance of a path-dependent estimator. The Euler scheme is the simplest and most popular simulation method.
