Principles of Financial Modelling

CHAPTER 15Introduction to Simulation and Optimisation

INTRODUCTION

This chapter introduces the topics of simulation (with a more complete discussion being the subject of Chapter 16). It also extends the earlier discussion of optimisation. These are both natural extensions of sensitivity and scenario analysis. The first section discusses the link between these methods, and uses a practical example to illustrate the discussion. The latter sections of the chapter highlight some additional points that relate to general applications of optimisation modelling.

THE LINKS BETWEEN SENSITIVITY AND SCENARIO ANALYSIS, SIMULATION AND OPTIMISATION

Simulation and optimisation techniques are in effect special cases of sensitivity or scenario analysis, and can in principle be applied to any model which is built appropriately. The specific characteristics are that:

• Several inputs are varied simultaneously. As a result, combinatorial effects are important, i.e. there are many possible input combinations and corresponding output values.
• There is an explicit distinction between controllability and non-controllability of the process by which inputs vary.

These points are described in more detail below.

The Combinatorial Effects of Multiple Possible Input Values

When models contain several inputs that may each take several possible values, the number of possible input combinations generally becomes quite large (and hence so does the number of possible values for the model's output). For example, ...