
PREFACE
XV
2. Part II, Input Analysis: Modeling and Estimation, is specifically aimed at
students and newcomers, as it includes two introductory chapters dealing
with stochastic model building (Chapter 3) and model fitting (Chapter 4).
Essentially, in this part of the book we are concerned with the modeling
of inputs of a Monte Carlo simulation. Many advanced books on Monte
Carlo methods for finance skip and take for granted these concepts. I have
preferred to offer a limited treatment for the sake of unfamiliar readers,
such as students in engineering or practitioners without an econometrics
background. Needless to say, space does not allow for a deep treatment,
but I believe that it is important to build at least a framework for further
study. In order to make this part useful to intermediate readers, too, I have
taken each topic as an excuse for a further illustration of R functionalities.
Furthermore, some more advanced sections may be useful to students
in economics and finance as well, such as those on stochastic calculus,
copulas, and Bayesian statistics.
3. Part III, Sampling and Path Generation, is more technical and consists
of two chapters. In Chapter 5 we deal with pseudorandom number and
variate generation. While it is certainly true that in common practice one
takes advantage of reliable generators provided by software tools like R,
and there is no need for an overly deep treatment, some basic knowledge
is needed in order to select generators and to manage simulation runs
properly. We also outline scenario generation using copulas. In Chapter 6
we deal with sample path generation for continuous-time models based on
stochastic differential equations. This is an essential tool for any financial
engineer and is at the heart of many derivative pricing methods. It is
important to point out that this is also relevant for risk managers, insurers,
and some economists as well.
4. Part IV, Output Analysis and Efficiency Improvement, looks at the fi-
nal step of the simulation process. Monte Carlo methods are extremely
powerful and flexible; yet, their output may not be quite reliable, and
an unreasonable computational effort may be called for, unless suitable
countermeasures are taken. Chapter 7 covers very simple, and possibly
overlooked, concepts related to confidence intervals. Counterexamples
are used to point out the danger of forgetting some underlying assump-
tions. Chapter 8 deals with variance reduction strategies that are essential
in many financial engineering and risk management applications; indeed,
the techniques illustrated here are applied in later chapters, too. Chapter 9
deals with low-discrepancy sequences, which are sometimes gathered un-
der the quasi-Monte Carlo nickname. Actually, there is nothing stochas-
tic in low-discrepancy sequences, which should be regarded as determin-
istic numerical integration strategies. For a certain range of problem di-
mensionality, they are a good alternative to pseudorandom sampling.
5. Part IV, Miscellaneous Applications, includes five more or less interre-
lated chapters dealing with: