OUTLINE

• random number generation

• sample mean and variance

• kernel density estimation

• quantile–quantile plots

Motivation

The models that we develop for option valuation will involve randomness. One of the main thrusts of this book is the use of computer simulation to experiment with and visualize our ideas, and also to estimate quantities that cannot be determined analytically. This chapter introduces the tools that we will apply.

Pseudo-random numbers

Computers are deterministic – they do exactly what they are told and hence are completely predictable. This is generally a good thing, but it is at odds with the idea of generating random numbers. In practice, however, it is usually sufficient to work with pseudo-random numbers. These are collections of numbers that are produced by a deterministic algorithm and yet seem to be random in the sense that, en masse, they have appropriate statistical properties. Our approach here is to assume that we have access to black-box programs that generate large sequences of pseudo-random numbers. Hence, we completely ignore the fascinating issue of designing algorithms for generating pseudo-random numbers. Our justification for this omission is that random number generation is a highly advanced, active, research topic and it is unreasonable to expect non-experts to understand and implement programs that compete with the state-of-the-art. Off-the-shelf is better than roll-your-own in this context, and by making use of existing technology we can more quickly progress to the topics that are central to this book.