Financial engineering and numerical computation are genuinely different disciplines.
But in finance many computational methods are used and have become
indispensable. This book explains how computational methods work in
financial engineering. The main focus is on computational methods; financial
engineering is the application. In this context, the numerical methods are
tools, the tools for computational finance.
Faced with the vast and rapidly growing field of financial engineering,
we need to choose a subarea to avoid overloading the textbook. We choose
the attractive field of option pricing, a core task of financial engineering
and risk analysis. The broad field of option pricing is both ambitious and
diverse enough to call for a wide range of computational tools. Confining
ourselves to option pricing enables a more coherent textbook and avoids
being distracted away from computational issues. We trust that the focus
on option-related methods is representative of, or least helpful for, the entire
field of computational finance.


The book starts with an introductory Chapter 1, which collects financial
and stochastic background. The remaining parts of the book are devoted to
computational methods. Organizing computational methods, roughly speaking,
leads to distinguish stochastic and deterministic approaches. By “stochastic
methods” we mean computations based on random numbers, such as
Monte Carlo simulation. Chapters 2 and 3 are devoted to such methods. In
contrast, “deterministic methods” are frequently based on solving partial differential
equations. This is discussed in Chapters 4, 5 and 6. In the computer,
finally, everything is deterministic. The distinction between “stochastic” and
“deterministic” is mainly to motivate and derive different approaches