Handbook in Monte Carlo Simulation: Applications in Financial Engineering, Risk Management, and Economics

3.8 Dimensionality reduction

Monte Carlo methods are often the only feasible approach to cope with high-dimensional problems. Nevertheless, they may require an excessive computational effort to produce a reliable answer. Hence, strategies to reduce the dimensionality of a problem are welcome anyway. Moreover, they can also be put to good use when applying alternative approaches, such as low-discrepancy sequences. Apart from computational convenience, there is another driving force behind dimensionality reduction. While in this chapter we are mainly concerned with model building, in the next one we will deal with model estimation. A rich model may be quite appealing in principle, but it turns into a nightmare if it calls for a huge amount of data for its estimation, and a badly estimated data will make the output of the most sophisticated Monte Carlo simulation utterly useless, if not worse.

Data and dimensionality reduction methods are an important and wide topic in multivariate statistics, and we cannot provide anything but some hints on the most relevant tools for applications in finance and economics, to provide the reader with a feeling for them. In this section we outline two methods:

Principal component analysis, PCA for short

Factor models

The second approach should not ...